Asymmetric impacts of fundamentals on the natural gas futures volatility: An augmented GARCH approach

    Asymmetric Impacts of Fundamentals on the Natural Gas Futures Volatility: An Augmented GARCH Approach Ibrahim Ergen, Islam Rizvanoghlu PII: DOI: Reference:

S0140-9883(16)30038-X doi: 10.1016/j.eneco.2016.02.022 ENEECO 3285

To appear in:

Energy Economics

Received date: Revised date: Accepted date:

20 January 2015 14 February 2016 25 February 2016

Please cite this article as: Ergen, Ibrahim, Rizvanoghlu, Islam, Asymmetric Impacts of Fundamentals on the Natural Gas Futures Volatility: An Augmented GARCH Approach, Energy Economics (2016), doi: 10.1016/j.eneco.2016.02.022

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ACCEPTED MANUSCRIPT Asymmetric Impacts of Fundamentals on the Natural Gas Futures Volatility: An Augmented GARCH ApproachI

Quantitative Supervision and Research Unit, Federal Reserve Bank of Richmond, Baltimore, MD, USA b Department of Economics, University of Houston, Houston, TX

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Ibrahim Ergena , Islam Rizvanoghlub,∗

Abstract

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We investigated the determinants of daily volatility for natural gas nearby-month futures traded on the NYMEX within a GARCH framework augmented with market fundamentals. Consistent with the previous literature, we found that volatility is much higher on the natural gas and crude oil storage report announcement days, on Mondays and during winters. We also confirmed that high volatility is associated with divergence of storage levels and temperatures from seasonal norms. The asymmetric impact of storage levels on volatility across different seasons is empirically investigated and documented. The mainstream finding in the literature that lower storage levels result in higher volatility is valid only during winter. At other times, it is actually higher storage levels causing higher volatility. Also, time to maturity effect is present only in winters. Additionally, weather shocks have asymmetric impact on volatility depending on the sign of the shock. Finally, we found that augmentation with market fundamentals improves the out-of-sample forecast accuracy of standard GARCH models.

Volatility

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Keywords: Natural Gas Futures, GARCH, Price Volatility, Storage, Weather, Asymmetric

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JEL: G13, Q40, Q47

We would like to thank Laurel Mazur and Ross Podbielski for excellent research assistance. We also thank Professors Mahmoud El-Gamal, Kenneth Medlock, Peter Hartley, Barbara Ostdiek, Jun Park, Yosoon Chang, Heejoon Han, Xiaoyi Mu and two anonymous referees for valuable discussions and feedback on our original manuscript. All remaining errors are ours. ∗ Corresponding author: University of Houston, Department of Economics, 77204, Houston, TX, USA. Tel: 713-743-4709 Email addresses: [email protected] (Ibrahim Ergen), [email protected] (Islam Rizvanoghlu) I

Preprint submitted to Energy Economics

February 14, 2016

ACCEPTED MANUSCRIPT 1. Introduction Financial markets have witnessed highly volatile energy prices in the last two decades.

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Considering that energy commodities have an irreplaceable role in any economy, researchers

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have been trying to analyze and understand the determinants of swings in energy prices. The most active traders in energy products and derivatives are producers, distributors, wholesale

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consumers and, as a result of significant deregulation, large and complex financial institutions. For all these market players, it is important to examine the dynamics of energy prices

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and volatility in order to make correct risk management, hedging and investment decisions. In this paper, we will investigate the determinants of short-term volatility for natural

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gas futures contracts traded on the New York Mercantile Exchange (NYMEX). As a crucial energy source, natural gas has gained substantial importance in the US. Evolved from a

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highly regulated market to a highly unregulated market, the natural gas futures market has proven to be one of the most volatile markets. Trading volumes in natural gas futures have

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skyrocketed in recent years with open interest in NYMEX growing at a compound annual

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rate of 13.5% between January 1998 and January 2012 (Chiou-Wei et al. (2014)). Daily volume ranges from 60,000 to 100,000 contracts for the nearby-month futures and 20,000 to

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60,000 contracts for the second nearby-month futures1 . In order to investigate the volatility dynamics of these contracts, we need a good understanding of the fundamental drivers of the U.S. natural gas market. The response of prices to shifts in supply and demand depends on the price elasticity. Demand and supply for natural gas are highly inelastic in the short-run; therefore price is very responsive to shortterm changes in both, resulting in high volatility. Two fundamental pieces of information affecting natural gas markets are the amount of working gas in storage facilities and changes 1

Nearby-month futures contract is the earliest maturing contract. It corresponds to the next month delivery for natural gas futures. Second nearby-month futures contract is the second earliest maturing contract. It corresponds to the contract for delivery on the month after the next.

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ACCEPTED MANUSCRIPT in weather conditions. The weekly storage report is currently released by the Energy Information Administration

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(EIA) of the Department of Energy (DOE). Anecdotal evidence on the impact of the natural

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gas storage report is abundant in the financial press. For example, the following appeared on Bloomberg on December 24, 20142 :

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Natural gas futures slid in New York to the lowest level since September 2012 after a government report showed U.S. inventories fell last week by less than forecast. The Energy

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Information Administration said stockpiles dropped 49 billion cubic feet in the week ended Dec. 19 to 3.246 trillion. Analysts estimated a decline of 63 billion while a survey of

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Bloomberg users predicted a withdrawal of 59 billion.

The theory of storage suggests that a lower storage amount is perceived as a tight supply

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situation and therefore increases price volatility due to concerns about the availability of the commodity for future consumption3 Linn and Zhu (2004) demonstrate that weekly gas

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storage report announcements during 1999-2002 were responsible for considerable intra-day volatility at the time of their release. Mu (2007) confirms the storage announcement effect

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in natural gas futures and further elaborates how it can be driven by weather shocks. While

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all these studies focus on storage level surprises or divergences from historical averages, Karali and Ramirez (2014) examine the effect of percentage changes in inventory levels on natural gas nearby-month futures price volatility and conclude that there is no significant relationship between those two variables. As it can be seen, the impact of storage surprises or deviations from historical averages on volatility has been documented in many studies. However, we believe that this impact 2

http://www.bloomberg.com/news/2014-12-24/natural-gas-drops-as-mild-december-weather-slowssupply-declines.html 3 See, for instance, Brennan (1958), Telser (1978), Williams and Wright (2005), and Thurman (1988).. This impact is studied widely in the context of energy and natural gas markets. For example, using a sample from 2002-2011 period, Chiou-Wei et al. (2014) identifies an inverse empirical relationship between futures price changes and surprises in the change of the natural gas storage amount.

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ACCEPTED MANUSCRIPT should not be uniform across seasons. Efimova and Serletis (2014) showed that inventory levels have an asymmetric impact on natural gas prices across seasons. However, to the best

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our knowledge there has not been any study that empirically demonstrates the seasonally

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asymmetric impact of storage levels on futures volatility. In this paper, we intend to close this gap following similar intuition with Efimova and Serletis (2014). To this end, we add

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a term to the volatility equation of a GARCH model that interacts our storage variable with a seasonal dummy. By taking this interaction into account, we were able to document

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seasonally asymmetric impact of storage deviations from historical averages. Basically, the mainstream finding in the literature that lower storage levels result in higher volatility is

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valid only during winter. At other times, it is actually higher storage levels that lead to higher volatility. The economic intuition behind this novel finding is discussed in detail.

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Simply put, during winter, the demand for natural gas rapidly increases, but the supply is unable to react in the short-run since the production of natural gas does not exhibit

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seasonality. When this happens, low storage levels as compared to historical averages are regarded as tight supply situations putting pressure on natural gas prices, thereby resulting in

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high volatility. Conversely, during other seasons, storage amounts higher than the historical

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averages may increase concerns regarding the capacity of storage facilities resulting in highly volatile natural gas price. Another important piece of information for the level of short-term volatility in the natural gas market is the change in weather conditions. As documented by Mu (2007), Ates and Wang (2007), Efimova and Serletis (2014) and Hu et al. (2014), upon the occurrence of unexpected cold weather during the winter months, the extra demand for heating pushes the price up resulting in higher volatility since the supply cannot adjust to these changes in the short run. Also, there has been a shift in the technology used in power generation plants that increased natural gas usage for the purpose of electricity generation from 12 percent to 27 percent between 1990 and 2013 (EIA (2015)). As a result, higher than expected 4

ACCEPTED MANUSCRIPT temperatures during the summer months precipitate an increase in demand for cooling which in turn may increase volatility. In this paper, we also present empirical evidence to confirm

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the previous findings in the literature that weather anomalies, measured as the number of

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degree days in excess of seasonal norms, result in increased short-term volatility of natural gas prices. We also found this impact to be asymmetric: positive and negative weather

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shocks of same magnitude have differing impacts on volatility. Only colder shocks in winter and hotter shocks in summer increase the volatility. Also, we found that only the weather

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shocks during winter has a statistically significant impact on volatility. It is important to note that change in the storage level reflects both production and

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consumption of natural gas, signaling the difference between injections and withdrawals from the storage facilities. Therefore, it is a proxy for the net effect of supply and demand forces.

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However, realized weather conditions only impact the consumption and therefore can be considered a proxy for demand only. As a result, the information contained in weather data

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is already reflected in the storage data. In fact, our estimations demonstrate that storage level is a more significant determinant of natural gas volatility. Out-of-sample forecasting

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exercise also confirms this intuition. We do not interpret this as weather being insignificant.

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On the contrary, weather conditions are very important, but the storage levels reflect the information about the past weather conditions in addition to supply side information. In order to develop a good model purely based on weather data, we believe that forecasted weather data is required instead of realized weather data. However, such data set not available to us. We also consider the impact of time to maturity, thereby testing Samuelson’s hypothesis which claims futures price volatility increases as the contract maturity gets closer. Using a very large futures dataset containing 6,805 contracts, Daal et al. (2006) found that the maturity effect was much stronger for agricultural and energy commodity futures than it was for financial futures. This is not a surprising result given that financial futures do 5

ACCEPTED MANUSCRIPT not have an underlying commodity. Using the extreme value method to measure the daily volatility of natural gas futures from daily low and high prices, Gregoire and Boucher (2008)

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found that the maturity effect was significant even after controlling for storage surprises. Mu

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(2007) documented the maturity effect by fitting separate GARCH models to the nearbymonth and the second nearby-month futures contract returns. In this paper, we present

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empirical evidence of the maturity effect by directly including time to maturity in days as a variable to the conditional variance equation of the GARCH model. We should note that

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regression based models with time to maturity as a regressor appeared in several studies for other commodity futures4 . We implement this idea for natural gas futures but within a

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GARCH model setting. We also interacted this variable with seasonality, which produced an interesting result, namely that the maturity impact is also seasonally asymmetric and

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present only during the winter.

In addition to storage and weather surprises, the previous literature found significantly

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higher volatility of natural gas futures prices on Mondays (Mu (2007), Murry and Zhu (2004)) and storage report announcement days for natural gas and crude oil (Pindyck (2004a))

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regardless of the information content of the reports. Using day of the week dummy variables,

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we obtained results consistent with these studies. In this study, we used GARCH models augmented with market fundamentals as an econometric tool in order to account for the dynamic nature of short-term volatility. Therefore, in terms of empirical methodology, our paper closely follows Mu (2007). However, in our paper, we make significant changes to the fundamental variable creation to demonstrate the asymmetric impact of storage levels, time to maturity and weather shocks on volatility. Another study closely related to ours is Suenaga et al. (2008). They use POTs (partially overlapping time series) model to analyze the volatility dynamics of natural gas futures with 4

See, for example, Milonas (1986), Chatrath et al. (2002), Duong and Kalev (2008), Kalev and Duong (2008), Karali et al. (2010a), Karali et al. (2010b) and Karali and Thurman (2010).

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ACCEPTED MANUSCRIPT varying maturities. Although this paper mentions the effect of the interplay between the storage and the seasonality on natural gas futures price volatility, it arrives at these three

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broad findings: (i) the volatility of the close-to-maturity contracts to be significantly higher

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for winter contracts than for late spring and summer contracts, (ii) volatility increases from early May to late September for the contracts that expire before the end of the peak season,

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and (iii) during the early winter, volatility rises for all 12 contracts. In short, Suenega et al. (2008) mainly focus on seasonal variations in volatility rather than direct effect of the

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storage levels on volatility. Our study, on the other hand, quantifies the direct effect of storage deviations on the short-term volatility and documents the asymmetric effect across

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seasons. In addition, our study documents asymmetric maturity impact. Another important contribution of our study relates to the forecasting accuracy of the

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augmented GARCH models which was overlooked in the previous literature5 . In this paper, we fill this gap by testing the out-of-sample forecasting accuracy of augmented GARCH

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models. We found that augmentation with market fundamentals improves forecast accuracy evidenced by the reduced mean absolute error and mean squared error compared to standard

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GARCH models with no market fundamentals. This is an important contribution to the

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literature, as it indicates that GARCH models with covariates in the volatility equation are not only an elegant econometric tool with theoretical rigor, but that they are also useful in empirical work to obtain more precise volatility forecasts. Finally, it is noteworthy that among the augmented GARCH models, the storage-based model performs better than the weather-based model in out-of-sample forecasting, since storage captures both supply and demand. The remaining sections of this paper are organized as follows: In Section 2, a descriptive analysis of the nearby-month futures returns is presented. Also, natural gas volatility 5

Please see Ates and Wang (2007), Mu (2007), Pindyck (2004b), Murry and Zhu (2004).

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ACCEPTED MANUSCRIPT with respect to several market fundamentals is analyzed without imposing any econometric structure. In Section 3, the econometric model is introduced and empirical results are

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presented. In Section 4, we test the accuracy of out-of-sample volatility forecasts from aug-

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mented GARCH models. Finally, in Section 5, we discuss the conclusions.

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2. Data and Statistical Analysis

Natural gas futures contracts began trading on the NYMEX in April 1990. A contract

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is written for 10,000 MMBTU of natural gas to be delivered to Henry Hub6 . Contracts for delivery in each month, and up to six years into the future are traded at any point in time.

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Most of the trading volume for natural gas futures is concentrated on the nearby month contract and therefore, working with nearby month futures data became quite common in

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the literature. We also follow this approach in this study. First, contract-by-contract price data for NYMEX natural gas futures from the January 2001 contract to the November 2013

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contract were downloaded from a Bloomberg terminal. This gives us time series price data on a total of 155 contracts. The return series for each contract are constructed as percentage

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log-differences as shown below:

rt,i = ln(Ft,i /Ft−1,i ) ∗ 100

(1)

where Ft,i is the price of the futures contract i at time t. Then we roll-over the contracts to obtain the nearby-month futures return series. This procedure makes sure we do not calculate returns from prices of different contracts eliminating any upward bias for returns in some of the earlier studies.7 At the end of this procedure, the nearby-month futures return 6

MMBTU= 1 Million British Thermal Units (BTU). A BTU is a unit used to describe the heat value and energy content of fuels and Henry Hub is a point on the natural gas pipeline system in Erath, Louisiana. Spot and future prices set at Henry Hub are denominated in $/MMBTU and are generally regarded as the primary price set for the North American natural gas market 7 The rolling over from one contract to the next contract is done one day before the maturity, so the return

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ACCEPTED MANUSCRIPT data span the time period from January 4, 2001 to November 26, 2013 yielding a total of T = 3,234 daily observations.

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Summary statistics for nearby-month futures returns are presented in Table 1. The

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numbers in parentheses represent the probability values for the associated hypothesis tests. The returns have a negative mean and median for this sample period. They are skewed to

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the right (0.37) and exhibit slight excess kurtosis (4.27). Consequently, the Jarque-Bera test rejects the null hypothesis of normal distribution for natural gas futures returns. LBQ(5) 17.77 (0.003) LBQ(10) 20.69 (0.0234) LBQ2 (5) 164.74 (2.2e-16) LBQ2 (10) 211.352 (2.2e-16) ADF -14.74 (0.01) ARCH-LM(5) 134.57 (0.00) ARCH-LM(10) 148.70 (0.00)

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-0.1386% -0.1332% 10.9906 3.3152 0.3693 4.2689 2534.35 (0.00)

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Mean Median Variance Standard deviation Skewness Kurtosis Jarque-Bera

Table 1: Summary Statistics for nearby-month Futures Returns

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The Ljung-Box tests at lags 5 and 10 reject the null hypothesis of no autocorrelation for

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raw returns. More importantly, the null hypothesis of no autocorrelation is rejected very strongly for squared returns, which suggests that there is a strong volatility persistence and

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volatility clustering in the data. Therefore, the LM-ARCH test (Engle (1982)) is performed to confirm the presence of ARCH effects and the null hypothesis of no ARCH effects is strongly rejected. This justifies our modeling choice to use a GARCH framework with covariates from natural gas market fundamentals. Finally, we perform an augmented Dickey-Fuller test with a constant and 12 lags in the unit root regression with no time trend. This test rejects the null hypothesis of non-stationarity and therefore non-stationarity is not a concern in our subsequent modeling and analysis. of the nearby-month contract at the last trading day is replaced by the return of the next deferred contract. This is because, in the last day of trading, traders are forced to close their open positions resulting in huge price changes that distort the data.

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ACCEPTED MANUSCRIPT Next, we will analyze the gas storage data. The gas storage reports used to be released by the American Gas Association (AGA) on Wednesdays at 2:00 pm eastern time until May

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2002. Since then, the report is released on Thursdays at 10:30 am by the EIA. The report

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provides information on storage levels as of the Friday prior to the announcement. The report provides information on the net weekly changes in storage levels, the storage levels a

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year earlier, the five-year historical average for the requisite time period, and the difference between the current level and the five-year average. There is plenty of anecdotal evidence

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in financial press also supported by formal research such as Mu (2007) which suggests that the market reacts to the deviation of storage level from its 5-year average in the EIA report.

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The reports are publicly available from the EIA website but only the storage level data are available for download.8 In other words, obtaining a time series for the difference between

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the storage level and five-year historical average requires one to either compile data manually or replicate the EIA methodology. We preferred to replicate the two-step procedure used

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by the EIA.9 First, the weekly data are populated to obtain daily storage level data using a

SDd,t

i=5 1 X = Sd,t − Sd,t−i 5 i=1

(2)

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linear interpolation. Then, the storage deviation variable SDd,t is calculated as below:

where Sd,t is the storage level on calendar day d of year t. This information is absorbed into prices as soon as the report is announced and therefore, we zero-out its value on all other days when entering this variable into our econometric model in the next section. As such, the linear interpolation method has an influence on the value of this variable only on report announcement days and only through the five-year historical average term. Therefore, we do not expect the interpolation method to have an impact on our results. 8

The data are downloadable from http://www.eia.doe.gov/dnav/ng/ng stor wkly s1 w.htm A complete documentation of the EIA methodology can be found at http://www.eia.doe.gov/oil gas/natural gas/ngs/methodology.html. 9

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the

link:

ACCEPTED MANUSCRIPT We loosely interpret this storage deviation variable as an indicator of market surprise which implicitly interprets the 5-year historical average as a reasonable proxy for the expected

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storage level. Arguably, a more precise method of deriving a surprise variable would be

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calculating the difference between ex-ante analyst forecasts and ex-post realization of storage level. For example, Gay et al. (2009), Bu (2014), and Halova et al. (2014) used such forecast

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data to construct storage surprise variables. We do not have access to well-populated storage forecast data for our sample period but it will be interesting to check the sensitivity of our

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results to this alternative in a future research.

A time series plot of the working gas in underground storage is presented in Figure 1

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Panel A. In the natural gas market, demand is highly seasonal, but supply is more or less uniform across seasons. Therefore, storage levels exhibit very strong seasonality as it provides

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a buffer to the market by balancing the difference between supply and demand. In Figure 1 Panel B, we present the time series plot of storage deviation from the five-year historical

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average. As can be seen, there are some winters where storage deviation was positive and there are other winters where it was negative. The seasonality observed for the level of

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storage in Panel A vanishes since subtracting the five year average deseasonalizes the data.

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We also confirmed this by running a regression of our storage deviation variable on seasonal dummies. This regression does not produce any significant coefficients indicating the storage deviation variable does not exhibit seasonality. Next, we discuss the weather data and modeling. We obtained the daily realized temperature data from January 1970 to November 2013 from Bloomberg. The dataset includes daily minimum and maximum temperatures for seven locations: New York City Center, New York JFK Airport, New York LaGuardia Airport, Chicago O’Hare Airport, Chicago Midway Airport, Atlanta Hartsfield Airport and Dallas Fort Worth Airport. We use the well-known degree-day variables in our statistical and econometric analysis. These variables are quantitative indices that capture the demand for energy. The concept 11

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(a) Storage Levels

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(b) Storage Deviations Figure 1: Working Gas In Underground Storage and Its Deviation From Five Year Historical Mean

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ACCEPTED MANUSCRIPT of degree days was introduced by Strachey (1878) and used in numerous studies including Mu (2007) which we closely follow in this paper in terms of empirical methodology. It is

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a well-established assumption that there is minimal need for heating and/or cooling if the

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outside temperature is 65o F . Consequently, the variables Heating Degree Days (HDD) and

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Cooling Degree Days (CDD) are defined as:

(3)

CDDt = M ax(0, Tave,t − 65)

(4)

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HDDt = M ax(0, 65 − Tave,t )

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where Tave,t is the average of the maximum and minimum observed temperatures on day t. There are two common ways of modeling weather shocks, either with ex-post forecast errors

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if retrospective weather forecast data are available or with temperature anomalies defined as the deviation of the degree day variables from their seasonal norms, which requires realized

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weather data. Here, we follow the latter approach since the forecast data are unavailable. After calculating HDD and CDD variables for each day, we construct the weather shocks as

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their deviation from the 30-year averages over a forecasting horizon of seven days.

(5)

i=t+7 1 X CDD.Shockt = (CDDi − CDD.N ormi ), 7 i=t+1

(6)

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i=t+7 1 X (HDDi − HDD.N ormi ), HDD.Shockt = 7 i=t+1

where HDD.N ormt and CDD.N ormt are the 30-year historical average of HDD and CDD on day t defined by the National Weather Service (NWS). Since we do not have the actual forecast data, the realized HDD and CDD are used while creating these weather shock variables. This assumes that realized temperatures were forecasted perfectly before they occurred whereas in reality, the forecasts also have an error. Therefore, if the forecast data was available, our weather based models could have performed better. 13

ACCEPTED MANUSCRIPT All weather variables are constructed for Chicago, New York, Atlanta and Dallas. If multiple locations are available for a city, we take the simple averages of those locations. For

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example, we use the average temperatures for Central Park, JFK and Laguardia airports as

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the New York City temperature. Then, natural gas consumption weighted average of these locations is calculated.10 The national averages for weather shock variables are plotted in

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Figure 2. Heating degree day shocks are close to zero in summer months, whereas cooling degree day shocks are close to zero in winter months.

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2.1. Descriptive Analysis of Natural Gas Futures Volatility

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In this section, we analyze the nearby-month futures volatility with respect to market fundamentals without employing any econometric structure. In Table 2, we present the standard deviations of nearby-month futures returns for several subsamples. In Table 3,

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we formally test for variance equality among these subsamples using the robust Brown and

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Forsythe (1974) type Levene (1960) test. Winter impact: We define winter as December, January, and February in order to

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capture the impact of really cold weather. As shown in Panel A of Table 2, the return volatility for winter days, 3.78%, is higher than for non-winter days, 3.16%. Also, in the first

days.

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row of Table 3, we reject the null hypothesis of equal variances for winter and non-winter

Day of the week impact: According to Panel A of Table 2 the return volatility in all seasons is highest for Mondays at 4.13% followed by natural gas storage report announcement days (STRAD) at 3.73%, followed by oil storage report announcement days (OSTRAD) at 3.15% and it is lowest for all other days at 2.83%. More information accumulates over the non-trading weekends in commodity markets, which explains the high volatility on Mondays. 10

We used the same weights used in Mu (2007): 0.42 for Chicago, 0.28 for New York, 0.17 for Atlanta, and 0.13 for Dallas.

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(a) HDD Shocks

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(b) CDD Shocks Figure 2: National Weather Shock Variables

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Panel-A: By Mondays STRADs, OSTRADs and Winter Winter Non-Winter All Seasons Monday 5.31 3.75 4.13 STRAD 3.90 3.68 3.73 OSTRADs 3.36 3.08 3.15 Other Days 3.27 2.68 2.83 All Days 3.78 3.16 3.57

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Panel B: By Winter and Bidweek Bidweek Non-Bidweek Winter 4.34 3.58 Non-Winter 3.25 3.13 All Seasons 3.55 3.24

All Days 3.78 3.16 3.57

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Panel C: By SD and Winter SD > 0 SD < 0 Winter 3.54 5.37 Non-Winter 3.80 3.19 All Seasons 3.74 3.71

All Days 3.78 3.16 3.57

(1) (2) (3) (4) (5) (6)

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Table 2: Standard Deviation of Daily Returns Broken into Groups

Groups

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BFL Test Statistic

p-value

Winter; Non-Winter

2 4 2 2 2 2

17.109 24.648 1.9788 7.0373 7.4949 13.683

0.00 0.00 0.1596 0.008022 0.00057 0.0002

Monday; STRAD; OSTRAD; Other Days Bidweek; Non-Bidweek Winter&Bidweek; Winter&Non-Bidweek Non-Winter&SD > 0; Non-Winter&SD < 0 Winter&SD > 0; Winter&SD < 0

Note: STRAD and OSTRAD denotes storage report announcement days for natural gas and crude oil respectively.

Table 3: Brown-Forsythe Type Levene Tests for Equality of Variances

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ACCEPTED MANUSCRIPT The impact of natural gas and oil storage report announcements is trivial and intuitive. Consequently, we also reject the equal variance hypothesis for the day of the week groups in

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the second row of Table 3.

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Maturity impact: The largest volume of natural gas futures trading takes place in the last five business days of each month, known as ‘bidweek’ which we use as a natural cutoff

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point. According to Panel B of Table 2 the volatility of bidweek daily returns in winter is 4.34%, whereas it is 3.58% for non-bidweek daily returns. However, outside of winter the

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volatility is 3.25% for bidweek daily returns and 3.13% for non-bidweek daily returns. Also, in row 3 of Table 3 we cannot reject the equality of variances for bidweek and non-bidweek

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days in general. However, in row 4 we reject the equality of variances for bidweek and non-bidweek days during winter. Collectively, our results indicate the existence of maturity

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impact only during winter.

Storage impact: Efimova and Serletis (2014) found a seasonally asymmetric impact

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of storage levels on returns. Following similar intuition, we explore potentially asymmetric impact of storage deviation on volatility. As shown in Panel C of Table 2, during winter,

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daily volatility is higher at 5.37% when the storage level is below the historical average

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(SD < 0) compared to 3.54% when it is above (SD > 0). However, during the non-winter period volatility is higher at 3.80% when the storage level is above the historical average (SD > 0) compared to the 3.19% when it is below. We believe that this might be a result of differing market concerns during different seasons. In winter, the market is concerned about having enough supply to meet the demand. However, outside of winter the market is potentially more concerned about having enough storage capacity for the excess supply. This places pressure on the price of storage space, which naturally spills over to natural gas prices, causing excessive volatility11 . Consequently, in row 5 of Table 3, we reject the 11

Van Atta (2008) cites excess volatility as one of the most important factors leading to extensive storage construction over the past few decades. This view is consistent with our findings.

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ACCEPTED MANUSCRIPT equality of variances for days with positive and negative storage deviation outside of winter months. In row 6, we reject the equality of variances for these groups during winter as well.

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3. Empirical Model and Estimation Results

The Ljung-Box test statistics for squared returns in Table 1 suggests that there is strong

SC

volatility persistence in natural gas nearby-month futures returns. Consequently, the LMARCH tests confirmed the existence of ARCH effects. In order to incorporate time varying

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and the persistent nature of volatility, we use a GARCH model. Results presented in table 1 also suggests that returns have a long term average of -0.1386% and they exhibit reasonable

MA

autocorrelation. Therefore, we include a first order autoregressive term in the mean equation

ED

in addition to a constant. Consequently, the specification of the empirical model is as follows:

rt = c + k rt−1 + σt zt

PT

2 2 + βσt−1 + γXt σt2 = ω + αrt−1

(7)

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where rt is the nearby-month futures return on day t given by (1), σt is the conditional volatility, zt represents the standard normal distributed shocks to the data generation pro-

AC

cess12 . Finally, Xt is a vector of exogenous variables capturing the volatility dynamics of the natural gas market. Inspired by the statistical analysis presented in Section 2, we use dummy variables for Mondays, storage report announcement days of natural gas and crude oil and winter days. We also use variables capturing the impact of time to maturity, storage deviations and weather surprises. As argued earlier, the weather information already has an impact on the storage levels which makes them correlated. Inclusion of both storage 12

We checked the sensitivity of model results to a generalized error distribution and found that the results of our storage based model are robust, whereas the degree day shock variables in our weather based model become insignificant. We believe that this is driven by the fact that the variables were constructed from realized temperatures rather than the real-time temperature forecasts.

18

ACCEPTED MANUSCRIPT and weather variables in the model, therefore, would lead to unintuitive and biased results. Consequently, we develop two main models in this study: one using storage information and

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the other using weather information. These models and their empirical estimation results

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are presented in sections 3.1 and 3.2 respectively. 3.1. The Storage Model

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We use three dummy variables to capture day of the week effects: A dummy for Monday

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(M ON ) and dummies for storage report announcement days for natural gas (ST RAD) and crude oil (OST RAD). We also use a dummy variable to capture the impact of winter

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W IN . In order to capture the maturity impact we construct two variables. The T T M is simply the number of business days to the maturity of nearby-month futures contract. The second variable is interaction of the T T M with the winter dummy and is calculated

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as T T M W IN = T T M ∗ W IN . It helps to capture the asymmetric maturity impact as

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suggested by the statistical analysis presented in Section 2. In order to incorporate the seasonally asymmetric effect of storage levels, we construct

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two additional variables. The first one, SD, was already discussed in Section 2 and is defined as the deviation of the storage level from its five-year historical average. This variable is

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calculated only for storage announcement days and it takes a value of zero on other days. This treatment is consistent with the previous literature such as Mu (2007) and it indicates that the information content of the storage report is fully incorporated into the price on the day of the announcement as suggested by Linn and Zhu (2004).The second variable is an interaction of the storage deviation variable with the winter dummy and is constructed as SDW IN = SD ∗ W IN . This variable enables us to capture the asymmetric effect of storage levels across different seasons. The results for several sets of estimations are presented in Table 4. The first estimation, Model (1), is for a simple GARCH(1,1) model. The coefficient estimates are statistically

19

ACCEPTED MANUSCRIPT 2

3

4

5

6

7

-0.1278

-0.0927

-0.0722

-0.1187

-0.0680

-0.0702

-0.0797

***

*

-0.0266

(-2.621)

(-1.857)

(-1.427)

(-2.342)

(-1.342)

**

(-1.383)

k

-0.0254

-0.0231

-0.0280

-0.0277

-0.0306

-0.0278

ω

0.1201

0.2014

0.3299

0.1172

0.2862

0.3200

***

***

**

***

**

(3.598)

(4.936)

(2.386)

0.0657

0.0599

0.0575

***

***

***

(8.98)

0.9162

0.9112

***

***

(107.73)

(94.83)

0.9320

0.9186

(133.91)

(105.14)

***

***

**

*

0.0642

0.0698

***

***

(8.59)

(9.13)

0.9115

0.9086

***

***

(90.65)

(93.15)

4.9405

5.1217

5.1075

***

***

***

***

(7.702)

2.0108

2.4694

***

***

(7.897)

(5.008)

1.0789

1.5585

**

***

(1.950)

(2.828)

0.7595 (3.935) ***

TTM

-0.0082

2.3908

***

***

(5.005)

1.6642

1.1836

**

***

**

(2.194)

(2.909)

0.5451

0.8405

**

***

(2.130)

-0.0416

-0.0725

***

*

***

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(-1.668)

(2.497) ***

(-1.013)

(-2.939)

0.0012 (4.230) ***

-0.0023

-0.0026

***

***

(-5.923)

(-4.619)

-0.0034

0.0412

-0.0131

-0.0208

0.0218

0.0399

-0,0579

-0.0584

16,514

16,520

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(-0.195)

(-0.805)

(0.851)

CDD−

(-1.431)

16,514

16,509

16,549

(2.164)

(3.165)

-0.0689

0.0006

(4.605)

1.2206

-0.0122

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SD

2.9169

(-0.657)

(-3.789)

(7.658)

***

-0.0075

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TTMWIN

(7.781)

2.1500 (4.183)

(-0.713)

16,558

(1.928)

5.0296

WIN

AIC

0.1252

***

(4.401)

OSTRAD

(8.69)

(2.110)

(-1.330)

4.9246 (7.382)

MON

(9.46)

(-1.409)

SC

(10.05)

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STRAD

CDD+

(2.111)

***

***

HDD−

(3.757)

0.0671

0.9257

HDD+

(-1.556)

***

(118.49)

SDWIN

(-1.402)

0.0663 (10.13)

β

(-1.419)

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α

(-1.196)

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(-1.329)

(-1.571)

T

c

1

16,497

(3.497) ***

(-1.351)

(1.556)

(-1.517)

Significance Codes: * 10%, ** 5%, *** 1%

rt σt2

= =

c + krt−1 + σt zt 2 2 ω + αrt−1 + βσt−1 + γ1 ST RADt + γ2 M ONt + γ3 OST RADt + γ4 W INt + γ5 T T Mt +γ6 T T M W INt + γ7 SDt + γ8 SDW INt + γ9 HDD+ + γ10 HDD− + γ11 CDD+ + γ12 CDD− Table 4: Empirical Estimation Results

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ACCEPTED MANUSCRIPT significant and they are typical for GARCH models estimated on financial return series. Starting with the next estimation, additional variables are included in the model. The

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estimated coefficients of Model (2) are consistent with the literature and the findings in

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Table 2. Basically, volatility is significantly higher on Mondays, natural gas storage report announcement days, and oil storage report announcement days.

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The coefficients of Model (3) confirm our hypothesis that the maturity impact is significant only during winter. First, we hypothesize that there is no maturity impact outside of

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winter (Ho : γ5 = 0 against alternative γ5 6= 0). The t statistic for γ5 is -0.71 and therefore we cannot reject the null hypothesis. We conclude that there is no significant maturity im-

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pact outside of winter. Next, we hypothesize that there is no significant maturity impact during winter (Ho : γ5 + γ6 = 0 against alternative γ5 + γ6 < 0). We decided to perform a

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one-tailed test as it has a smaller size than a two-tailed test. In addition, we chose the sign of the alternative hypothesis based on economic intuition as well as the signs of estimated

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coefficients from the model on Table 4. The t statistic for γ5 + γ6 is calculated as -5.28 using the variance-covariance matrix of parameter estimates. Therefore, we reject the null in favor

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of the alternative hypothesis and conclude that there is a significant maturity effect during

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winter. This confirms the seasonally asymmetric maturity impact. In Model (4), we present the estimation results of a GARCH (1,1) model with only two storage variables, namely SD and SDW IN . Both variables are statistically significant and have expected sign consistent with the descriptive statistics presented in section 2. Next, we perform statistical tests to confirm our hypothesis that the impact of storage deviation is seasonally asymmetric. To this end, we first test the hypothesis of no impact during the nonwinter period (Ho : γ7 = 0 against the alternative γ7 > 0). The t statistic for γ7 is 2.49 and we reject the null hypothesis. We conclude that higher storage levels in non-winter months increase volatility. Then, we perform the same test for winter months (Ho : γ7 + γ8 = 0 against the alternative γ7 + γ8 < 0). The t statistic for γ7 + γ8 is calculated as -5.78 using the 21

ACCEPTED MANUSCRIPT variance-covariance matrix of parameters estimates. So, we reject the null hypothesis and conclude that lower storage levels increase volatility in winter. This confirms the seasonally

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asymmetric effect of the storage level on volatility.

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In Model (5), we include all variables to disentangle various impacts in a single model. All variables are still significant with expected signs, but the significance levels are lower for

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some of them. Also, the asymmetric impact of storage deviation and time to maturity across

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seasons is still valid13 .

0.5

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0.3 0.2 0.1

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0.0 -0.1 -0.2 -0.3 -0.4 -0.5

21

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23

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Effect of winter days on volatility

0.4

19

17

15

13

11

9

8

7

6

5

4

3

2

1

Number of days till maturity, TTM

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Figure 3: The effect of winter days on short-term volatility at different maturities.

The coefficients of W IN and T T M W IN provide more insights into the interaction of maturity and seasonal effects. For example, on a day where the storage level is equal to its five-year historical average, the partial impact of winter on volatility will be γ4 + γ6 ∗ T T M . Since γ4 > 0 and γ6 < 0, volatility is highest just before the contract expiration during winter. When time to maturity is 23 days, variance is 0.411 less for a winter day compared 13

The t statistic for γ5 + γ6 is calculated as -2.18 and the t statistic for γ7 + γ8 is calculated as -2.86 based on Model (5) results.

22

ACCEPTED MANUSCRIPT to a non-winter day. On the other hand, one day before the maturity, the variance is 0.504 higher for a winter day compared to a non-winter day. A plot of the TTM versus the partial

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impact of winter on the conditional variance is provided in Figure 3. So, winter alone doesn’t

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increase volatility. Winter leads to higher volatility just before contract expiration and lower volatility right after contract expiration. The median of TTM variable is 11. So, in the

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middle of the month when time to maturity is 11 days, the partial effect of winter is 0.088 and therefore winter leads to higher volatility on average. We also test this formally using

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null hypothesis γ4 + γ6 ∗ 11 = 0 against the alternative γ4 + γ6 ∗ 11 > 0. Using the variance covariance matrix, we calculate the t statistic as 2.01. We reject the null and confirm that

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winter leads to significantly higher volatility on average. Model (5) includes all variables and they all have economically intuitive sign. It also

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provides the lowest value of Akaiki Information Criteria (AIC). Therefore, we select model 5 as the final storage model. It will be used in the out-of-sample forecasting study in the next

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3.2. The Weather Model

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section.

The weather modeling is accomplished by utilizing the degree day variables that were

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introduced in Section 2. In order to incorporate the asymmetric impact of weather shocks on volatility, we define below variables14 : HDD+ = max(HDD.Shock, 0) HDD− = min(HDD.Shock, 0) CDD+ = max(CDD.Shock, 0) CDD− = min(CDD.Shock, 0) 14

We thank the anonymous referee for pointing out the asymmetric effects of weather shocks.

23

ACCEPTED MANUSCRIPT In Model (6), we replace the storage deviation variables with the above four variables and none of them turned out to be significant in this specification. Also, the coefficient

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signs doesn’t make economically intuitive sense. We believe that this is probably because

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the winter dummy and the weather variables are not orthogonal to each other. Therefore, we exclude the variables with winter dummy in Model (7). While doing this, we also exclude

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maturity variable since it is significant only during winter. In Model (7), HDD+ has a positive and significant sign indicating colder than average winter days have significantly

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higher volatility. The HDD− has an insignificant sign implying that warmer than average winter days do not have a significant impact on volatility. These results are consistent

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with energy demand dynamics. Weather shocks leading to more energy demand increases volatility significantly whereas shocks leading to less energy demand do not have significant

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impact on volatility. As for CDD, neither positive nor negative shocks have a significant impact on volatility indicating that weather shocks during summers do not have a significant

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impact on volatility. That said, the probability values for these two variables are 0.12 and 0.13 respectively indicating that they are close to being significant. Also, it is important

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to note that positive and negative CDD shocks have asymmetric impact on volatility as in

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the HDD shocks. This is probably because hotter than average summer can increase the demand for natural gas to produce electricity. Although the AIC suggests that Model (6) fits the data marginally better than Model (7), we select Model (7) as the final weather model since it has economically intuitive results. The final storage model (Model 5) performs better than the final weather model (Model 7) based on the AIC. This is probably because we use realized weather data due to the unavailability of forecasted data. The storage level already reflects the past weather information and proxies the supply-demand imbalance. On the other hand, weather data can proxy only the demand.

24

ACCEPTED MANUSCRIPT 4. Out-of-Sample Forecast Accuracy Studies that employ GARCH models to investigate the effects of natural gas market

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fundamentals on the volatility of natural gas futures have historically reported results for

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in-sample estimations. These estimation results yield valuable information for understanding the volatility dynamics of natural gas futures. However, the out-of-sample predictive power of

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these augmented GARCH models have yet to be tested. In this section, we make day-ahead volatility predictions for natural gas nearby-month futures using simple GARCH models, as

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well as the augmented GARCH models developed in the previous section. We will use two variants of the storage model (Model 5a and 5b) and the weather model (Model 7) from

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Table 4. The accuracy levels of these forecasts are compared with a standard GARCH (1,1) model, a random walk model and two moving average models. The empirical methodology

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followed in forecasting is known as a sliding window scheme. To make a prediction for day t where t ∈ {501, 502, ..., T }, only the returns {rt−1 , rt−2 , ...rt−500 } are used.

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One challenge with out-of-sample forecasting is that the variables HDD+ , HDD− ,

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CDD+ , CDD− and SD uses contemporaneous values to explain the volatility, i.e., the values of these variables on day t are used to explain the volatility on day t. However, we

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need to make the forecast for day t on day t − 1 when these variables are not yet available in the information set. To solve this problem, weather shock forecasts are obtained by fitting an ARIMA(2,1,2) model to the last 1000 calendar days of temperature data for all four cities. The ARIMA(2,1,2) model is selected based on the Akaike Information Criterion (AIC). The natural gas consumption weighted average of weather shock variables across the four cities are calculated as the final weather shock forecasts. Then, these weather shock forecasts are used in the weather model (Model 7) to forecast volatility. Regarding the SD variable in the storage model (Model 5), we adopted two alternative approaches. In Model (5a), we assume that the storage deviation for the upcoming Thursday is equal to the storage deviation on the most recent Thursday, whereas in Model (5b) we 25

ACCEPTED MANUSCRIPT assumed that the expected value of storage deviation is always zero. There is a theoretical intuition behind this reasoning. Since storage deviation for t + 1 is theoretically equal to

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St+1 − Et (St+1 ), its expected value at time t will be equal to Et [St+1 − E(St+1 )]. Taking this

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into consideration, we can easily check that Et [St+1 − Et (St+1 )] = Et (St+1 ) − Et (St+1 ) = 0. Note that Model (5b) doesn’t imply dropping the variable from the model. In the estimation

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step, the realized values of storage deviations are used and therefore it impacts the parameter estimates for other variables.

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4.1. Simple Benchmark Forecasts

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Random Walk Benchmark: Assuming that futures price volatility follows a random walk process, the volatility for the next day t + 1 can be forecasted with the observed volatility on day t.

(8)

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σ ˆt+1 = |rt − r¯|

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where r¯ is the long-term mean return, i.e. -0.1386% from Table 1. Moving Average Benchmark: Moving average models are widely used by natural gas mar-

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ket practitioners. In this paper, 20-day and 60-day moving averages are used that correspond

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to one-month and three-months of trading days.

σ ˆt+1

v u m−1 u1 X =t (rt−i − r¯)2 m i=0

(9)

where r¯ is the long-term mean return. 4.2. Forecast Accuracy Results After making a day-ahead forecast and observing the market realizations the next day, we can evaluate the accuracy of our forecasts. The volatility forecast error is defined as

ˆt+1 , F E = σt+1 − σ 26

(10)

ACCEPTED MANUSCRIPT where σ ˆt+1 is the volatility forecast for day t + 1 that was made at the end of day t , and σt+1 is the observed (realized) volatility for day t + 1. We calculate the realized volatility as

(11)

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T

σt+1 = |rt+1 − r¯|

realized volatility as15

c | 1−k

(12)

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σt+1 = |rt+1 −

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for the random walk and moving average models. For the GARCH models, we calculate the

Two statistical measures are used for determining forecast accuracy: mean absolute error

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(MAE) and mean squared error (MSE). Table 5 presents out-of-sample forecasting accuracy

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measures for the simple and augmented GARCH models as well as other simple benchmarks.

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Garch(1,1) Model (5a) Model (5b) Model (7) MA(20) MA(60) Ramdom Walk

MAE

Rank

MSE

Rank

1.7722 1.7532 1.7384 2.0525 1.6970 1.7585 2.0709

5 3 2 6 1 4 7

5.0022 4.9598 4.9116 6.6043 5.0059 5.1165 8.3543

3 2 1 6 4 5 7

(MAE)

(MSE)

Table 5: Accuracy Statistics for Out-of-Sample Forecasting

Surprisingly, the weather model cannot outperform the simple GARCH model. As discussed earlier, this is probably because the weather variables only partially reflect the demand side of the market. In order to develop a good model purely based on weather data, we believe that forecasted weather data is required instead of realized weather data. Model (5b) ranks first according to MSE and it ranks second based on MAE. It out15

The long-run mean of the AR(1) process in the mean equation is

27

c 1−k

ACCEPTED MANUSCRIPT performs the standard GARCH model with no market fundamentals under both criteria. Besides, the Diebold-Mariano test for significance of forecast accuracy for Model (5b) and

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the standard GARCH model produces p-value of 0.09 and thus reject the null hypothesis of

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the equal forecast accuracy for those methods. Therefore we can argue that the augmentation of GARCH models with market fundamentals improves forecast accuracy significantly.

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The 20-day moving average ranks first under the MAE measure but its performance declines significantly under the MSE measure. Since the MSE method penalizes models with

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the square of their errors, this implies that the MA(20) model produces relatively accurate

MA

forecasts in general, but when it does not perform well, it produces quite large errors.

5. Conclusion

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In this paper, we augment the standard GARCH models with the natural gas market fundamentals in order to isolate the sources of high volatility in natural gas futures prices.

PT

We document asymmetric impact of storage amount, time to maturity and weather shocks on the short term volatility of natural gas futures. We also analyze the forecasting accuracy

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of these augmented GARCH models for the first time.

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First, storage levels have an asymmetric effect on short-term volatility across the seasons. During the winter months, storage levels lower than the five-year historical average were found to increase short-term volatility. In contrast, it is high storage levels that cause excess volatility in other seasons. This can be attributed to the changing concerns of market practitioners during different seasons. In the winter, low storage levels are perceived as signaling an environment of scarce supply which causes excess volatility. At other times, the market is mainly concerned with the supply of storage space. Therefore, high storage levels cause excess volatility. Second, the maturity effect for natural gas nearby-month futures is found to be a significant determinant of volatility only during winter period. Since demand is highly inelastic 28

ACCEPTED MANUSCRIPT in winter, traders might be overreacting to new information arriving closer to the maturity, thus causing excess volatility.

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Third, we documented the asymmetric impact of weather shocks on volatility. In par-

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ticular, volatility is significantly higher in colder than average winter days but warmer than average winter days do not have a significant impact. Although the impact of weather shocks

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during summer is not statistically significant, similar asymmetric impact is observed. More specifically, hotter than average summer temperatures increase volatility whereas cooler than

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average summer temperatures reduce it. These results are intuitive and driven by energy demand for heating or cooling.

MA

In addition, this study confirms that volatility is higher on Mondays and storage report announcement days for natural gas and crude oil. Volatility on winter days, defined as

ED

December, January, and February, is found to be higher than in other seasons. With regards to forecasting accuracy, the augmented GARCH models including carefully

PT

chosen fundamental variables have the potential to improve the forecast accuracy measured by MAE and MSE. This is an important finding, because more accurate volatility forecasts

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can be used in pricing, risk management, hedging and investment decisions.

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Fleming et al. (2001) suggests that one should focus on the economic significance of time varying predictable volatility instead of evaluating the statistical performance of volatility models. Future research can be conducted in such applications of augmented GARCH models for natural gas volatility. It will be interesting to backtest these models’ performances using a trading rule based on volatility forecasts. References Ates, A., Wang, G. H., 2007. Price dynamics in energy spot and futures markets: The role of inventory and weather. CFTC Working Paper. Brennan, M. J., 1958. The supply of storage. The American Economic Review, 50–72. 29

ACCEPTED MANUSCRIPT Brown, M. B., Forsythe, A. B., 1974. The small sample behavior of some statistics which test the equality of several means. Technometrics 16 (1), 129–132.

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Chiou-Wei, S.-Z., Linn, S. C., Zhu, Z., 2014. The response of us natural gas futures and spot prices to storage change surprises: Fundamental information and the effect of escalating

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physical gas production. Journal of International Money and Finance 42, 156–173. Daal, E., Farhat, J., Wei, P. P., 2006. Does futures exhibit maturity effect? new evidence

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from an extensive set of us and foreign futures contracts. Review of Financial Economics

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using intraday data. Journal of Banking & Finance 32 (4), 489–500.

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Efimova, O., Serletis, A., 2014. Energy markets volatility modelling using garch. Energy Economics 43, 264–273. EIA, 2015. Annual energy outlook. Engle, R. F., 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica: Journal of the Econometric Society, 987– 1007. Fleming, J., Kirby, C., Ostdiek, B., 2001. The economic value of volatility timing. The Journal of Finance 56 (1), 329–352.

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ACCEPTED MANUSCRIPT Gay, G. D., Simkins, B. J., Turac, M., 2009. Analyst forecasts and price discovery in futures markets: The case of natural gas storage. Journal of Futures Markets 29 (5), 451–477.

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Gregoire, P., Boucher, M., 2008. Maturity effect and storage announcements: the case of

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natural gas. International Journal of Business Forecasting and Marketing Intelligence 1 (1),

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21–29.

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Hu, J. W.-S., Hu, Y.-C., Lin, C.-Y., 2014. Effect of temperature shock and inventory surprises

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on natural gas and heating oil futures returns. The Scientific World Journal 2014. Kalev, P. S., Duong, H. N., 2008. A test of the samuelson hypothesis using realized range.

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Karali, B., Dorfman, J. H., Thurman, W. N., 2010a. Delivery horizon and grain market

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futures contracts? insights from a smoothed bayesian estimator. Journal of Futures Markets 30 (3), 257–277.

Karali, B., Ramirez, O. A., 2014. Macro determinants of volatility and volatility spillover in energy markets. Energy Economics 46, 413–421. Karali, B., Thurman, W. N., 2010. Components of grain futures price volatility. Journal of agricultural and resource economics, 167–182. Levene, H., 1960. Robust tests for equality of variances1. Contributions to probability and statistics: Essays in honor of Harold Hotelling 2, 278–292.

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ACCEPTED MANUSCRIPT Linn, S. C., Zhu, Z., 2004. Natural gas prices and the gas storage report: Public news and volatility in energy futures markets. Journal of futures markets 24 (3), 283–313.

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Milonas, N. T., 1986. Price variability and the maturity effect in futures markets. Journal of

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Mu, X., 2007. Weather, storage, and natural gas price dynamics: Fundamentals and volatility. Energy Economics 29 (1), 46–63.

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market. The Energy Journal, 57–74.

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24 (11), 1029–1047.

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Pindyck, R. S., 2004b. Volatility and commodity price dynamics. Journal of Futures Markets

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comparison with progress of vegetation. Quarterly Weather Report. Suenaga, H., Smith, A., Williams, J., 2008. Volatility dynamics of nymex natural gas futures prices. Journal of Futures Markets 28 (5), 438–463. Telser, L. G., 1978. Economic theory and the core. University of Chicago Press Chicago. Thurman, W. N., 1988. Speculative carryover: an empirical examination of the us refined copper market. The RAND Journal of Economics, 420–437. Williams, J. C., Wright, B. D., 2005. Storage and commodity markets. Cambridge university press. 32

ACCEPTED MANUSCRIPT Ms. Ref. No.: ENEECO-D-15-00042R1 Title: Asymmetric Impacts of Fundamentals on the Natural Gas Futures Volatility: An

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Augmented GARCH Approach

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Energy Economics

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ED PT CE

• •

We investigated the determinants of daily volatility for natural gas nearby-month futures. Both storage deviations from historical norms and weather shocks have seasonally asymmetric impact on volatility. The maturity impact is also seasonally asymmetric and present only during the winter. The augmented GARCH models produce more accurate out-of-sample volatility forecasts.

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• •

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Highlights

February 13, 2015