Oil price and exchange rate in India: Fresh evidence from continuous wavelet approach and asymmetric, multi-horizon Granger-causality tests

Applied Energy 179 (2016) 272–283

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Oil price and exchange rate in India: Fresh evidence from continuous wavelet approach and asymmetric, multi-horizon Granger-causality tests Aviral Kumar Tiwari a, Claudiu Tiberiu Albulescu b,⇑ a b

Faculty of Management, IBS Hyderabad, IFHE University, Dontanpalli, Hyderabad 501203, India Management Department, Politehnica University of Timisoara, 2, P-ta. Victoriei, 300006 Timisoara, Romania

h i g h l i g h t s
We assess the relationship between the oil price and India-US real exchange rate.
We use a wavelet approach and asymmetric, multi-horizon Granger-causality tests.
Co-movements are noticed in the post-reform period, especially for 2–4-years bands.
The Granger-causal relationship between variables is non-linear and asymmetric.
The short run oil price movements are important for the exchange rate stabilization.

a r t i c l e

i n f o

Article history: Received 5 January 2016 Received in revised form 21 June 2016 Accepted 29 June 2016

JEL classification: C40 E32

a b s t r a c t We use a continuous wavelet approach and deploy asymmetric, multi-horizon Granger-causality tests between the return series of the oil price and the India-US exchange rate, over the time-span 1980M1–2016M2. The results highlight important co-movements in the post-reform period, especially for the 2–4-years band. The wavelet Granger-causality tests show that the exchange rate Granger-causes the oil price in the long run, while the opposite applies in the short run. Moreover, we find that the Granger-causal relationship between variables is non-linear, asymmetric and indirect, which will help policymakers and traders to make better strategic and investment decisions. Ó 2016 Elsevier Ltd. All rights reserved.

Keywords: Cyclical and anti-cyclical effects Wavelet coherence Oil price-exchange rate Granger causality India

1. Introduction The effectiveness of energy policies are of vital importance for the macroeconomic environment due to supply-side shocks which might generate. After the 1973 oil crisis many researchers have empirically examined the relationship between oil prices and various macroeconomic issues, underlining the link between oil shocks and recessions [1]. The empirical literature has blossomed ⇑ Corresponding author at: Politehnica University of Timisoara, 2, P-ta. Victoriei, 300006 Timisoara, Romania. E-mail addresses: [email protected] (A.K. Tiwari), [email protected] (C.T. Albulescu). http://dx.doi.org/10.1016/j.apenergy.2016.06.139 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

again after the remarkable fluctuations recorded by international oil prices in 2008–2009, but especially after the 2014 free-fall in oil prices, highlighting the impact of energy policies in general and of oil prices in particular, on business cycles and inflation [2–4], on stock prices [5–7], on non-energy commodity markets [8], or on other monetary issues like the exchange rate [9,10]. However, because the oil represents one of the most traded commodities, assessing the impact of oil price shocks on the exchange rate deserve a special attention. There is a well-established theoretical link between the international oil price and the US Dollar exchange rate. On the one hand, Golub [11] and Krugman [12] document how the oil price explains exchange rate movements. In brief, according to these authors an

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283

oil-exporting (oil-importing) country may experience a currency appreciation (depreciation) when oil prices rise and depreciation (appreciation) when oil prices fall. On the other hand, Bloomberg and Harris [13] provide an explanation on the potential impact of exchange rates on oil price movements. In short, relying on the law of one price for tradable goods, they show that, since oil is a homogeneous and internationally traded commodity priced in US Dollars, a depreciation of this currency reduces the oil price to foreigners relative to the price of their commodities denominated in US Dollars. Thereby, as their purchasing power and oil demand increases, the crude oil price in US Dollars is pushed up. Further, as the US Dollar is the major billing and settlement currency in international oil markets, the domestic currency exchange rate with the US Dollar is the key channel through which an oil price shock is transmitted to the real economy, with different effects for oil-exporting and oil-importing countries [14]. Consequently, the response on monetary policies to oil price fluctuations can amplify the shocks in the oil price [2]. The empirical investigation of the oil price – exchange rate nexus shows mixed evidence. The dominant view in the literature, represented by Amano and van Norden [15], Chaudhuri and Daniel [16], Bénassy-Quéré et al. [17], Chen and Chen [18], Coudert et al. [19], Lizardo and Mollick [20] and more recently by Basher et al. [21], reports a unidirectional Granger causality from the oil price to the exchange rate. Another view argues that movements in the US Dollar exchange rate Granger-cause crude oil prices, showing thus the opposite phenomenon (see for example [22]). Most of these studies use cointegration techniques and one-shot measures of Granger-causality. However, recent studies show that the relationship between the oil price and the exchange rate is time-frequency dependent and bidirectional at the same time [10,23,24]. In line with these studies, our paper aims to analyze the lead-lag relationship between the return series of the oil price and the Indian Rupee exchange rate against the US Dollar, applying continuous wavelets. This method allows to see if the direction and the strength of the Granger causality and the lead-lag relationship between variables vary in time and over different frequencies. In addition, by applying Continuous Wavelet Transform (CWT) we are able to identify cyclical and anti-cyclical relations, as well as periods of volatility/jumps and structural breaks. Different from the works mentioned above, the present paper brings forward several contributions to the existing literature. First, the CWT methodology used in previous studies is largely based on Torrence and Compo [25], who use a parametric bootstrap approach to assess the significance of areas. However, the pointwise testing approach, especially for the phase difference, is questionable (for a discussion, see [26]). Therefore, in order to avoid this bias, we employ the bootstrapping method advanced by Cazelles et al. [27], who compare the consistency of different resampling techniques, and take into account the key components of a time series (i.e. mean, variance and distributions of values, in both time and frequency domains). Second, different from previous studies, the present paper explores the oil price – exchange rate relationship, applying a wavelet Granger-causality test, recently proposed by Olayeni [28]. This method circumvents the need for minimum-phase transfer functions and is able to identify causality in both time and frequency. We also contribute to the literature by employing a battery of newly proposed time-series based tests to disclose the Grangercausal relationship between the variables in question, and we compare them with frequency-domain and regime-switching based Granger-causal tests, in order to check the robustness of the wavelet Granger-causality test. All these tests allow to estimate the non-linear Granger-causal relationships between the oil price and the India-US exchange rate. In this line, we first use

273

time-series tests, as multi-horizon Granger-causality tests [29], non-linear Granger-causality tests [30,31], and asymmetric Granger-causality tests [32]. Second, we employ the frequencydomain Granger-causality test proposed by Lemmens et al. [33], and the Markov regime-switching VAR (MRS-VAR) to account for regime-switching in the Granger-causal relationship. Finally, we combine the Hatemi-J [32] and Dufour et al. [29] methodologies, in order to see if the asymmetric Granger-causal relationship is instantaneous or gradual. Another contribution of the present paper resides in the analysis of the particular case of India, which had in place a managed float exchange rate regime starting with 1975 (the pre-reform period), and introduced the Liberalized Exchange Rate Management System (LERMS) in March 1992 (the post-reform period). According to the Energy Information Agency (EIA) statistics, India recently became the fourth largest consumer of oil and petroleum products, and also the fourth largest importer. Between a wide range of oil suppliers, Nigeria stands as the main supplier at the moment, followed by the Saudi Arabia. India’s crude oil imports cover a basket of three varieties – Brent, Dubai and West Texas Intermediate (WTI). Given this composition, even if one of the three varieties experiences sharp increases in prices, the overall price of the basket does not get affected to the same extent. Consequently, when studying the oil price – exchange rate nexus, it is useful to refer to all the benchmarks, as we do in this paper, using the International Monetary Fund (IMF) statistics. We also focus on India because its dependence on oil imports has been growing rapidly in the recent years, creating a huge trade deficit. At the same time, the trade deficit can also widen due to the Rupee’s appreciation vis-à-vis other major currencies (i.e., the US Dollar). In this context conducting adequate energy policies is highly important for the Indian government. Finally, the results we obtain represent by their own a distinct contribution of this paper to the existing literature, as they allow the comparison of the oil prices – exchange rate nexus over two exchange rate regimes. Different from other studies with a focus on India, we discover a significant Granger-causality relationship between oil prices and the Rupee-US Dollar exchange rate, which is non-linear and bidirectional. In addition, this relationship manifests differently in the short and long run, and exists only in the post-reform period. The remainder of the paper is organized as follows. Section 2 presents a brief review of the literature on the oil prices – exchange rate nexus. Information about the wavelet methodology and Granger-causality test in the CWT is given in Section 3. Section 4 describes the data. Section 5 presents and discusses the results while Section 6 concludes and draws policy implications for policymakers and traders.

2. The oil price – exchange rate relationship: literature review There is a voluminous body of literature analyzing the causal relationship between the oil price and the exchange rate. A first strand finds evidence of unidirectional causal relationships, usually running from the oil price to the exchange rate [17,18,34]. Different from these studies, Zhang et al. [22] find that causality is running from the US Dollar exchange rate to the oil price and documents that the US Dollar depreciation is a key factor in driving up the international crude oil price. A second strand of research finds evidence of bidirectional Granger-causality between the oil price and exchange rates [35,36]. However, most of the previous studies analyze the oil price – exchange rate nexus in the case of developed countries, leaving small open economies and emerging countries outside the main research arena, with few exceptions (i.e., [37–40]). In line

274

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283

with the research conducted on developed economies, most of these studies employ cointegration analyses and Granger-causality tests and find that the oil price influences the exchange rate for Russia [41], for China [37], for Fiji Islands [38] or for the African countries [39,40]. Nevertheless, in this case also we notice mixed results. On the one hand, Basher et al. [21] examine the dynamic relationship between oil prices, exchange rates and emerging market stock prices, and find that a positive shock to oil prices tends to depress emerging market exchange rates in the short run. On the other hand, Turhan et al. [42] find that a rise in the oil price leads to a significant appreciation of emerging economies’ currencies against the US Dollar. These findings support the idea that the causality between the oil price and exchanges rates might not be linear. So, recent studies use non-linear causality tests to investigate the causal relationships between oil prices and exchange rates (i.e., [23,43]). In the case of India, the oil price – exchange rate nexus is empirically prospected by Ghosh [9], who uses daily data for the period 2007–2008 and an exponential-GARCH (EGARCH) model, and shows that an increase in oil price returns leads to the depreciation of the Indian currency vis-à-vis the US Dollar. The Indian case is also analyzed in the larger context of emerging markets. In this line, Beckmann and Czudaj [44] study the link between oil prices and the US Dollar exchange rates using monthly data for various oil-exporting and oil-importing countries and employ a Markov-switching vector error correction model. For India, they find a direct relationship between the nominal exchange rate and the oil price, where an increase in the oil price coincides with a depreciation of the Indian currency. According to our records, the only study addressing the oil price – exchange rate relation in the case of India, using a wavelet framework, belongs to Tiwari et al. [10]. Applying a Discrete Wavelet Transform (DWT) and non-linear causality tests, the authors document both linear and non-linear causal relationships between the oil price and the India’s real effective exchange rate at higher time scales (lower frequency), but also at the lower time-scales (higher frequency). Bal and Rath [43] investigate in their turn the oil price – exchange rate nexus in the context of India and China applying the non-linear causality test advanced by Hiemstra and Jones [45]. They report significant bidirectional nonlinear Granger causality between oil prices and exchange rates in both countries. However, different from the aforementioned studies, in the present paper we use the wavelet cohesion following Rua [46] and we use the bootstrapping method advanced by Cazelles et al. [27]. Further, different from the above-mentioned papers, we employ the recent Granger-causality test in the CWT, following Olayeni [28]. Moreover, we compare the Granger-causality results for robustness purpose, using different newly proposed time-series, frequency-domain and regime-switching based Granger-causal tests.

3. Methodology The wavelet approach was proposed to circumvent the limitations of the Fourier transform (see [47–49]) and it is based on two filters which operate with low- and high-frequency trend components, namely the father and the mother wavelet. While the wavelet approach was first applied in geophysics and signal processing [50–53], starting with Rua and Nunes [54] it became largely used in economics and finance [46,55–62]. Noteworthy studies investigate the impact of energy prices on the macroeconomy, with a focus on oil prices [10,23,63]. A distinctive category of wavelet transforms is the CWT, which allows the interpretation of the variables’ variances on a single

diagram and it is recommended to assess the common movements of the series and the phase differences. 3.1. Continuous wavelet transform1 Wavelet transforms are used to decompose the signal or time series over dilated and translated functions called mother wavelets. These wavelets (function of two parameters, one for the time position and the other for the time scale) could be defined as:



1 a

ua;t ðtÞ ¼ pffiffiffi u

ts a

 ð1Þ

where a and s denote the dilation (scale factor) and translation (time shift), respectively. A time series xðtÞ with respect to a chosen mother wavelet can be decomposed as:

1 W x ða; sÞ ¼ pffiffiffi a

Z

þ1

xðtÞu

1

  Z þ1 ts xðtÞua;s ðtÞdt dt ¼ a 1

ð2Þ

where ⁄ denotes the complex conjugate form and the wavelet coefficients, W x ða; sÞ, represents the contribution of the scales a at different time positions s. The factor p1ffiffia normalizes the wavelets so that they have unit variance and hence are comparable for all scales a. In line with previous studies, we have chosen the Morlet wavelet in our analysis:

uðtÞ ¼ p1=4 expði2f 0 tÞ expðt2 =2Þ

ð3Þ

A complex number W x ða; sÞ can be written in terms of its phase /x ða; sÞ and modulus kW x ða; sÞk. The phase of the Morlet transform varies cyclically between p and p over the duration of the component wave forms and is defined as:

/x ða; sÞ ¼ tan1 The

IðW x ða; sÞÞ RðW x ða; sÞÞ

‘‘local

wavelet

ð4Þ power

spectrum”

is

given

by:

Sx ðf ; sÞ ¼ kW x ðf ; sÞk2 . The ‘‘global wavelet power spectrum”, defined as the averaged variance contained in all wavelet coefficients of the same scale a, can be written as:

Sx ðaÞ ¼

r2x T

Z

T

0

kW x ða; sÞk2 ds

ð5Þ

with r2x being the variance of the time series x and T its duration. The mean variance at each time location is obtained by averaging the frequency components and is given as:

Sx ðsÞ ¼

r2x p1=4 s1=2 Cg

Z

1

0

a1=2 kW x ða; sÞk2 da

ð6Þ

In economics, it is often desirable to quantify statistical relationships between two non-stationary time series. To quantify the relationships between two non-stationary signals, the ‘‘wavelet cross spectrum” and the ‘‘wavelet coherence” are often of interest. The wavelet cross-spectrum is given by W x;y ða; sÞ ¼ W x ða; sÞ W y ða; sÞ where ⁄ denotes the complex conjugate. The wavelet coherency is defined as the cross-spectrum normalized by the spectrum of each signal:

Rx;y ða; sÞ ¼

khW x;y ða; sÞik

khW x;x ða; sÞik1=2 khW y;y ða; sÞik1=2

ð7Þ

where ‘hi’ denotes a smoothing operator in both time and scale. Using this definition, Rx;y ða; sÞ is bounded by 0 6 Rx;y ða; sÞ 6 1. 1

The elaboration of this section is based on Cazelles et al. [27].

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283

275

However, the CWT is useful for bivariate cases only. As several macroeconomic variables are asymmetrically or non-linearly related to each other, the CWT fails to take them into account as endogenous variables and obtain the true relationship. Therefore, in order to assess the statistical significance of the patterns exhibited by the wavelet approach we adopt bootstrapping methods. Thus, following Cazelles et al. [27], we use a resampling procedure of the observed data, and a Markov process scheme that preserves only the short temporal correlations.

Sterling until 1966, and to the US Dollar afterward. The fact that the Rupee experienced a managed floating regime only after 1975 also sustains the choice of the analyzed time-span. Before proceeding to the estimations, both series are transformed to the first difference of their natural logarithms and then were standardized.

3.2. Causality in continuous wavelet transform

5.1. Wavelets results

As an alternative to the discrete wavelet transform (DWT) usually employed for Granger-causality tests, we employ the CWT for the Granger-causality proposed by Olayeni [28], which in turn is built on the CWT-based correlation measure by Rua [64]. It is given by:

The wavelet approach enables the description of the evolution of oscillating characteristics of a given time-series. Therefore, we present summarized results of the wavelet analysis in Fig. 1a–e. Fig. 1a presents the time-series plot of the standardized variables i.e., the oil price (DLNOP) and the exchange rate (DLNEXINUS). Both series have high peaks around 1987, 1992, and 2008. The results of the wavelet analysis are summarized in Fig. 1b–e. Fig. 1b and d presents the plots of local wavelet power spectra (LWPS) of the oil price returns and exchange rate. The LWPS is helpful in detecting common islands or regions where (i.e., at which time-frequency) variance of both series is very high, and where the wavelet coherency and phase differences give meaningful results. Fig. 1c and e presents the global wavelet power spectrum (GWPS), or the average WPS for the two series. By the visual assessment of color contour plots in Fig. 1b and d, we notice that the WPS is not constant over time, as well as across frequencies. While the power spectrum shows that high power (variance) is concentrated in medium and higher frequencies (i.e., lower and medium time-scales) for the oil price, in the case of the exchange rate it is concentrated in lower and medium frequencies (i.e., high and medium time-scales). Nevertheless, it is not clear from the GWPS at which time actually the highest power is concentrated. Thus, we focus on the LWPS to analyze the local variance of the series. For the oil price, the WPS shows a continuous oscillating mode at both 1–2-years and 2–4-years bands, but with varying time periods (Fig. 1b). However, these modes of oscillation vary in strength. The dominant modes for the oil price are 1986–1988, 1990–1991 and 2006–2010 at the 1–2-years band, and 1998–2001 at the 2–4-years band. Similarly, for the India-US exchange rate, the WPS shows a continuous oscillating mode at the 1–2 years, at the 2–4 years and at the 2–8-yearsband, but with a varying time period (Fig. 1d). Consequently, although the wavelet analysis reveals similar oscillating components for the time-series, these components are not always present at the same moment in time. Figs. 1b and 2d show that there are several common islands for the two series. In particular, the common features in the wavelet power of the two time-series are evident during 1990–1992 and 2007–2010. During these periods, both series have the power above the 5% significance level, as marked by the thick black dotted contour. In other words, the wavelet coherence that quantifies the co-movements between the time-series should be significant only for 1991–1992 and 2008–2009, around the 1–2-years band and 2–4-years band modes. The similarity between the portrayed patterns of both series in these periods can be assessed through the CWT, if it is merely a coincidence. But, as the wavelet cross-spectrum describes the common power of two processes without normalization to the single WPS, it may produce misleading results because the CWT is multiplied. For instance, if one of the spectra is local, and the other exhibits strong peaks, these may have nothing to do with any relation of the two series. Therefore, in our analysis, we rely on the wavelet cohesion (a measure of co-movements developed by [46] and on the wavelet coherency, along with the phase relationship.

GY!X ðs; sÞ ¼

ffs1 jRðW m XY ðs; sÞÞIY!X ðs; sÞjg qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 m 1 jW X ðs; sÞj2 g  ffs1 jW m ffs Y ðs; sÞj g

ð8Þ

m m where W m Y ðs; sÞ, W X ðs; sÞ and W XY ðs; sÞ are the wavelet transforms and IY!X ðs; sÞ is the indicator function defined as [28]:

IY!X ðs; sÞ ¼



1; if /XY ðs; sÞ 2 ð0; p=2Þ [ ðp; p=2Þ 0; otherwise

ð9Þ

In order to check for the robustness of the results provided by the Granger-causality in the CWT analysis, we apply several time-series, frequency-domain, and regime-switching based Granger-causal tests, which emphasis the asymmetry and non-linearity which might appear between variables. The Hatemi-J’s [32] test is asymmetric in the sense that it performs Granger-causality between positive and negative components of the data, where the positive component represents the positive shock, and the negative component represents the negative shock. The Dufour et al. [29] propose a multi-horizon Granger-causality test which helps us to find out if the Granger-causal relationship is instantaneous (significant Granger-causality at horizon 1) or gradual, i.e., indirect (significant Granger-causality at horizons higher than 1). We also analyze non-linear Granger-causalities using the Péguin-Feissolle et al. [30] test (in mean), and the Nishiyama et al. [31] test (in mean and variance). However, all the above stated time-domain approaches ignore the importance of the frequency component. Therefore, we use the frequency-domain Granger-causality test proposed by Lemmens et al. [33]. Furthermore, in order to estimate the influence of business cycles, we use the Markov regime-switching VAR (MRSVAR), to account for the regime switching in the Granger-causal relationship. 4. Data description We use monthly data covering the period 1980M1–2016M2. The exchange rate is measured by the India-US real exchange rate, provided by the Federal Reserve Bank of St. Louis (FRED St. Louis). The oil price is measured by the average of Brent, Dubai, and WTI benchmarks and the data are extracted from the IMF (External data), being thus available starting with 1980. Even if the WTI monthly statistics can be found on a historical basis, Dubai represents the main benchmark in the case of India, and this benchmark gained in importance only in the 1980s. Further, given India’s reduced oil consumption before 1980 (less than 1% out of the world consumption, compared to almost 5% at present), the investigation of the oil price – exchange rate nexus for the selected period is reasonable. In addition, before 1975, India had in place a fixed exchange rate regime, as the Rupee was pegged to the Pound

5. Empirical findings and discussions

276

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283

Fig. 1. Wavelet power spectrum for the return series of the oil prices and Rupee-US Dollar exchange rate. Notes: (a) Time series plots of variables, where black continuous line is for the oil price and the red broken line is for the India-US exchange rate. (b and d), respectively, are the plots of the wavelet power spectrum (WPS) of the oil price and India-US exchange rate. The color code for power values ranges from dark blue (low values) to dark red (high values). Dotted white lines materialize the maxima of the undulations of the WPS and the black line indicates the cone of influence that delimitates the region not influenced by edge effects. (c and e) Represent the average WPS of the oil price and India-US exchange rate. On the graphs (b–e), the dashed lines show the a = 5% significance level computed based on 1000 Markov bootstrapped series. On the graphs (b and d), the p-values within the area delineated by the dashed line are less than 5%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

The wavelet cohesion is used to disclose the correlation between the oil price and the India-US exchange rate (Fig. 2). This measure ranges from +1 to 1, similar to the correlation. We notice from Fig. 2 that there is a high degree of positive correlation between the oil price and the India-US exchange rate during 1991–1993 and 1998–2002, in the 0.5–1.0-years of scale. However, we also find evidence of high negative correlation in the 1–2-years of scale up to 1990, and in the 2–4-years of scale since 1994. These findings reconfirm the need to evaluate the degree of correlation over scale and time. Hence, in the final step of the wavelet analysis, we estimate the wavelet coherence, along with the phase-difference for three scale bands (2–4-years, 4–6years and 8–10-years). We also analyze the normality of phase difference plots for these scale bands and their oscillating nature. All these results are presented in Fig. 3. The wavelet coherence is used to identify both, frequency bands and time intervals within which pairs the two series are co-varying (Fig. 3a). We focus the 2–4-years band because the WPS indicates a significant amount of common power for this band only. So, in the case of the 2–4-years band, there is a significant degree of coherence around 1986–1987, 1990–2000, and 2005–2010. Fig. 3f shows that the phase difference around 1986–1987 lies in ½0; p=2 indicating that both series move in-phase, and the oil price is leading. The period 1990–2000, which is the period of first-generation economic reforms, experiences huge inconsistency in the phase and lead-lag relationship between variables questioned across time-scales. For example, the phase difference during the period 1990–1992 lies in ½0; p=2, indicating that both series move in-phase, and the exchange rate leads the oil price. Further, the phase difference during the 1993–1997 interval, lies in ½p=2; p, indicating that both series have an anti-phase relation. All in all, the wavelets results are pointing toward the fact that economic agents might have specific reactions to oil price changes, depending on their long or short run perspectives on the relationship between the oil price and the exchange rate. Moreover, the influence of the exchange rate upon the oil price is time-frequency dependent. Therefore, we need further clarification and we resort to a battery of Granger-causality tests. 5.2. Results of Granger-causality tests between the oil price and the exchange rate

Rua(2010): Oil Price-EXINUS 1

0.25

0.8 0.6

0.5

Period

0.4 0.2

1

0

2

-0.2 -0.4

4

-0.6

8

-0.8

1985

1990

1995

2000

2005

2010

2015

-1

Fig. 2. Cohesion between return series of the oil price and the Rupee-US Dollar exchange rate. Notes: The red islands represent a positive correlation, while the blue islands a negative one. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

This is because these methods are able to detect a significant interrelation and the phase difference can provide evidence on the lead-lag relationship between the two time-series.

We start this analysis with the wavelet Granger-causality advanced by Olayeni [28]. We notice from Fig. 4a that the wavelet causality from the exchange rate to the oil price is significant around the year 2000, for the 0.5–1-years band (i.e., 6–12months band). A second moment which characterizes the Granger-causality from the exchange rate to the oil price can be noticed between 1992 and 1995, for the 2–4-years band. This result is in agreement with the findings generated by Fig. 3f, where both series move in-phase and the exchange rate is leading. Fig. 4b shows that the oil price Granger-causes the exchange rate in two different periods. The first period arises around 1995, for the 4–6-months band (that is 0.5-years band), while the second period can be noticed after the outburst of the recent financial crisis, for the 2–4-years band, when the oil price significantly Granger-causes the India-US exchange rate. This result corresponds to the findings presented in Fig. 3a for the 2–4-years band, and remains unchanged if we modify the time-span to the 1973M1–2012M4 period (see Appendix A). We also check for the robustness of these findings using several recently developed time-series Granger-causality tests. For all these tests, we first present the results for the full sample, and later break it into pre- and post-reform periods. Further, we use two types of data in the estimation process i.e., the first difference of

277

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283

(a)

(b) 2~4 year frequency band) 2

Signals

1

1 0 -1 -2 1985

1990

1995

2000

2005

2010

2015

2010

2015

2010

2015

2 (c) 4~6 year frequency band) Signals

Period

2

4

1 0 -1 -2 1985

1990

8

1995

2000

2005

(d) 8~10 year frequency band) Signals

2

16

1 0 -1 -2

1985

1990

1995

2000

2005

2010

2015

1985

1990

1995

2000

2005

Year

Fig. 3. Coherence between return series of the oil price and the Rupee-Dollar exchange rate. Note: The thick dotted white contours designate the 5% and 10% significance levels and those are computed based on 1000 Markov bootstrapped series. The cone of influence, which indicates the region affected by edge effects, is also shown with a light black line. The color code for the coherence ranges from blue (low coherence-close to zero) to red (high coherence-close to one). The phase difference is represented by a thick dotted black line in subplots (e, g and i). The light black line and light black dotted line represent the phase of the oil price, and the phase of the India-US exchange rate, respectively, in subplots (e, g and i). The subplots (f, h and j) are the normality plots of the phase difference plots. The subplots (e, g and i) represent phases and phase differences of 2–4-years, 4–6-years, and 8–10-years bands, respectively. Subplots (b, c and d) represent oscillating components with the wavelet transform in the series at 2– 4-years, 4–6-years, and 8–10-years periodic bands, respectively. The normalized entropy of the phase difference distribution for (e) is Q = 0.2523 and it is not significant with p-value 0.48, for (g) is Q = 0.3244 and it is not significant with a p-value = 0.32, and for (i) is Q = 0.3661 with p-value 0.48 and it is not significant, computed with 1000 Markov bootstrapped series less than 0.1%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the series and the standardized first difference. As in the wavelet analysis, the standardized first difference data are used. Thus, in purely time-series analysis, our conclusions would be based on the latter type of data set.2 We begin with the asymmetric Granger-causality test proposed by Hatemi-J [32]. When standardized data are used (Table 1), we find that in the case of the full sample there is no significant Granger-causality, either in the negative components, or in the positive components. So, the asymmetric Granger-causality test shows no impact of the oil price shocks on the Indian Rupee’s exchange rate. 2 The results for all time-series Granger-causality tests for raw data can be provided upon request.

These results do not support the general findings of the wavelet analysis. However, we must notice that here we could not capture whether the Granger-causal relationship is instantaneous or gradual. Therefore, in the next step we use the multi-horizon causality test proposed by Dufour et al. [29]. The multi-horizon causality test is also applied to the positive and negative components obtained from the procedure described by Hatemi-J [32]. Table 2 presents the results for the standardized series. We find a significant evidence of bidirectional Granger-causality at different horizons. Most of the causal relationships appear for the full sample, where the exchange rate Granger-causes the oil price at horizons 4–8, while the oil price Granger-causes the exchange rate at horizons 3. In the case of the full data sample, for the negative components of both variables

278

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283

Fig. 4. Wavelet Granger-causality between the oil price and the exchange rate. Notes: The white (red) contour indicates a 5% (10%) significance level. The significance levels are based on 3000 draws from Monte Carlo simulations estimated on an ARMA(1,1) null of no statistical significance. The green line is the cone-of-influence (COI) earmarking 1=2 the areas affected by the edge effects or phase. The scale has been converted to period using the relation: Ft ¼ k  s, where k ¼ 4p=½xo þ ð2 þ x2o Þ  for the Morlet wavelet function. Using xo ¼ 6 for optimal balance [25], we have Ft ¼ 1:033  s. Monthly bands are represented. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 1 Results of asymmetric Granger-causality analysis for standardized series [32]. H0: OP –> ER

Test value

OP+ –> ER+ OP –> ER OP+ –> ER OP –> ER+

Full sample 0.644 1.420 1.061 0.054

14.54 9.878 9.239 8.776

6.774 6.439 5.964 4.719

OP+ –> ER+ OP –> ER OP+ –> ER OP –> ER+

Pre-reform 0.362 0.554 0.069 0.115

12.79 10.54 11.40 9.745

OP+ –> ER+ OP –> ER OP+ –> ER OP –> ER+

Post-reform 1.776 1.323 0.633 0.468

9.540 10.66 6.373 9. 591

BCV at 1%

H0: ER –> OP

Test value

BCV at 1%

BCV at 5%

BCV at 10%

5.020 4.901 4.576 4.719

ER+ –> OP+ ER –> OP ER+ –> OP ER –> OP+

Full sample 2.270 1.704 0.313 2.781

9.944 9.672 10.66 10.29

6.084 5.867 6.038 5.656

4.340 4.307 4.669 4.257

3.704 4.247 3.677 3.967

2.159 2.553 2.183 2.441

ER+ –> OP+ ER –> OP ER+ –> OP ER –> OP+

Pre-reform 0.029 0.069 0.155 0.483

11.35 11.12 9.664 12.74

3.893 4.191 3.960 4.026

2.228 2.529 2.554 2.239

6.312 6.143 3.885 6.415

4.827 4.743 2. 659 4.947

ER+ –> OP+ ER –> OP ER+ –> OP ER –> OP+

Post-reform 3.023 1.148 3.146 1.150

10.24 9.890 9.582 6.353

6.236 6.054 6.392 3.915

4.763 4.699 4.792 2.624

BCV at 5%

BCV at 10%

Notes: (a) The max lag order considered is 12; (b) the symbol OP –> ER means that the oil price does not cause the exchange rate; (c) BCV means critical value; (d) ⁄ shows causality significant at 10% level of significance.

we find unidirectional Granger-causality running from the India-US exchange rate to the oil price at horizons 4–7. In the pre-reform period, we find only one instance of significant Granger-causality, running from the exchange rate to the oil price, at horizon 5. For the post-reform period, the results show that the exchange rate Granger-causes the oil price at horizons 4–8, whereas the oil price does not Granger-causes the exchange rate. As in the case of the full sample, for the negative components we find a unidirectional causality from the exchange rate to the oil price. These results support our previous findings, stating that the Granger-causal relationship between the India-US exchange rate and the oil price is not only indirect but also asymmetric. We further apply a more powerful non-linear Granger-causality test proposed by Nishiyama et al. [31]. Table 3 shows significant evidence of unidirectional Granger-causality running from the oil price to the exchange rate, only in the post-reform period.3 We continue the analysis with the Markov regime-switching VAR (MRS-VAR) model to account for the regime switching in the Granger-causal relationship in time-series. This is due to the fact that, sufficiently long time-series data often exhibit dramatic

3 We also use the non-linear Granger-causality test proposed by Péguin-Feissolle et al. [30], but the results obtained for the standardized data seem to be contrary to the results obtained through the application of Nishiyama et al. [31], which represent a more powerful test (see the authors for argumentation).

shifts in their behavior, due to changes in the government policies, technological shocks, and financial crises. Hamilton [65] proposes a probabilistic model, called the Markov regime-switching model, where such institutional changes are approximated by a random variable instead of a deterministic dummy variable.4 Thus we estimated a two-state MRS-VAR model following Perlin [68] and Ding [69]. The Perlin [68] packages assume that the transition probabilities are constant, whereas Ding [69] packages assume that the transition probabilities are time-varying. We define the two states for an oil price shock as increasing and decreasing regime of the oil price. Table 4 exhibits the MRS-VAR estimation results for both states. As shown in Table 4, in the regime represented by the state 1, an oil price shock, with a two months lag, has a significant and negative impact on the India-US exchange rate. At the same time, a positive shock in the exchange rate has a positive impact on the oil price, indicating that the Rupee’s appreciation increases the oil demand, with a positive influence on international oil prices. The transition probability matrix in Table 5 shows that regime 1 is highly persistent. The probability that the state 1 will be followed by 5 months of state 2 is 0.87. Furthermore, Table 5 shows that regime 1 will persist for 8 months while regime 2 will stay for 5 months in average. The conditional probability of 4 For other developments of the Markov regime-switching models, please refer to Hansen and Seo [66] and Lam [67].

279

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283 Table 2 Multi horizon Granger-causality tests for standardized data [29]. Null hypothesis

H=1

H=2

H=3

H=4

H=5

H=6

H=7

H=8

Full sample OP –> ER ER –> OP OP+ –> ER+ ER+ –> OP+ OP –> ER ER –> OP OP+ –> ER ER –> OP+ OP –> ER+ ER+ –> OP

0.4505 0.1591 0.3505 0.1541 0.1802 0.0594 0.3783 0.0914 0.6062 0.6094

0.3198 0.2995 0.1281 0.1473 0.1569 0.1764 0.6039 0.2576 0.5681 0.6319

0.1675 0.3604 0.0805 0.5673 0.1874 0.1374 0.5219 0.3436 0.4166 0.5523

0.1853 0.0878 0.1659 0.3131 0.2325 0.0849 0.5029 0.5968 0.3731 0.3059

0.2491 0.0489 0.2710 0.1936 0.272 0.0357 0.4179 0.1739 0.4108 0.2827

0.3682 0.0439 0.3845 0.1534 0.4002 0.022 0.3137 0.1618 0.3807 0.3325

0.3386 0.0491 0.4517 0.1281 0.3793 0.0282 0.4718 0.0997 0.4706 0.3676

0.4384 0.0637 0.5054 0.0794 0.5509 0.1057 0.4264 0.3352 0.5094 0.3919

Pre-reform OP –> ER ER –> OP OP+ –> ER+ ER+ –> OP+ OP –> ER ER –> OP OP+ –> ER ER –> OP+ OP –> ER+ ER+ –> OP

0.623 0.230 0.377 0.282 0.323 0.221 0.326 0.521 0.273 0.456

0.508 0.391 0.402 0.273 0.342 0.440 0.383 0.555 0.309 0.479

0.285 0.229 0.385 0.322 0.384 0.400 0.381 0.416 0.217 0.346

0.379 0.238 0.280 0.336 0.274 0.336 0.408 0.358 0.284 0.512

0.323 0.025 0.368 0.254 0.263 0.292 0.266 0.330 0.317 0.320

0.414 0.342 0.326 0.249 0.406 0.364 0.449 0.340 0.250 0.391

0.502 0.336 0.420 0.349 0.357 0.402 0.446 0.329 0.308 0.390

0.345 0.201 0.473 0.313 0.378 0.355 0.458 0.375 0.473 0.397

Post-reform OP –> ER ER –> OP OP+ –> ER+ ER+ –> OP+ OP –> ER ER –> OP OP+ –> ER ER –> OP+ OP –> ER+ ER+ –> OP

0.3770 0.1128 0.3757 0.1764 0.2676 0.3453 0.3260 0.3015 0.3915 0.5626

0.3376 0.2775 0.2302 0.2133 0.2213 0.4037 0.3771 0.3011 0.3727 0.4466

0.2516 0.1490 0.0988 0.6235 0.2708 0.2480 0.4562 0.2940 0.3685 0.3451

0.2974 0.0542 0.1430 0.3664 0.5499 0.1329 0.4029 0.4267 0.4354 0.3270

0.3700 0.0300 0.1389 0.0815 0.5485 0.0597 0.2738 0.2461 0.5043 0.3942

0.5118 0.0173 0.1335 0.2914 0.5146 0.0266 0.2403 0.1079 0.4612 0.2798

0.4877 0.0142 0.1475 0.1324 0.5487 0.0295 0.2916 0.2420 0.2829 0.3805

0.6051 0.0260 0.1435 0.1032 0.2900 0.0751 0.2276 0.5158 0.2178 0.3058

Notes: (a) The max lag order considered is 12. The optimal lag order is selected based on AIC for each combination; (b) the symbol OP –> ER means that the oil price does not cause the exchange rate; (c) only p-values are presented; (d) OP+ are the positive components of the oil price series, while OP are the negative components (the same applies for the ER); (e) significant causal relationships are marked in bold.

Table 3 Results of non-linear Granger-causality tests for standardized data [31]. H0: OP –> ER

Full sample Pre-reform Post-reform

Table 5 Transition probability matrix and expected duration of each date.

H0: ER –> OP

ð1Þ b ST

ð2Þ b ST

ð1Þ b ST

ð2Þ b ST

6.502 5.692 4.188

9.477 7.969 16.78⁄

4.539 6.211 3.365

10.60 9.552 5.458

S T are the test statistics for first moment (i.e., mean) and second Notes: (a) b S T and b moment (i.e., variance), respectively. That is, the first and second test checks the null hypothesis of non-linear Granger-non-causality in mean and variance, respectively. The procedure runs as follows: we start testing the null for the first movement and if it is not rejected, then we test for the second moment and continue the procedure till the null is rejected. (b) [———] denotes that results are not calculated. Critical value at 5% level of significance is 14.38. (c) ⁄ means that the null hypothesis of Granger-causality is rejected from the oil prices to the exchange rate for example (denoted as OP –> ER). ð1Þ

1

2

1 2

0.87 0.13

0.19 0.81

Duration of stay

7.76 time periods  8 months

5.19 time periods  5 months

ð2Þ

Table 4 MSVAR results for a constant probability model. Equation: OP State 1 OP(1) OP(2) ER(1) ER(2)

States

0.08 (0.27) 0.10⁄ (0.09) 0.19 (0.15) 0.16 (0.19)

regimes 1 and 2 is shown in Appendix B, which verifies that the probability of regime 1 is more prevalent than regime 2 in the entire sample period. Last but not least, we use the frequency-domain Granger-causality test developed by Lemmens et al. [33]. For the standardized data (Fig. 5), we notice that there is a bidirectional Granger-causality between the oil price and the India-US exchange rate, around the frequency 0.5-years. However, for lower frequencies (i.e., over a year), significant evidence of unidirectional Granger-causality running from the exchange rate to the oil price is found.

Equation: ER State 2 ⁄⁄⁄

0.68 0.10 0.02 0.05

(0.00) (0.40) (0.75) (0.38)

State 1

State 2

0.00 (0.97) 0.05⁄ (0.07) 0.44⁄⁄⁄ (0.00) 0.14⁄⁄ (0.01)

0.05 (0.68) 0.12 (0.46) 0.22⁄⁄ (0.01) 0.01 (0.92)

Notes: (a) p-values in brackets; (b) ⁄, ⁄⁄, and ⁄⁄⁄ denotes respectively, significance at level 10%, 5% and 1% of significance level; (c) OP – the oil price, ER – the exchange rate; (d) the lag order is chosen based on AIC information criteria.

5.3. Discussions Our results show the importance of energy policies on monetary issues and complement previous findings on the oil price – exchange rate nexus, underlining the non-linear, asymmetric and indirect effects which characterize this relationship in the context of India. The first set of results is based on the CWT analysis and its developments, namely the wavelet power spectrum and the

280

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283

Granger Causality over the Spectrum from DlnEXstd to DlnOPstd 1.0 0.8 0.6 0.4 0.0

0.2

Granger Coherence

0.8 0.6 0.4 0.2 0.0

Granger Coherence

1.0

Granger Causality over the Spectrum from DlnOPstd to DlnEXstd

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

0.5

frequency

1.0

1.5

2.0

2.5

3.0

frequency Fig. 5. Frequency-domain Granger-causality [33].

wavelet cohesion. One must note that our major discussion about these results and phase difference is for the 2–4-years band, where a high degree of coherence is observed around 1986–1987, 1990–2000, and 2005–2010. First, between 1986 and 1987 both series move in-phase, and the oil price is leading. This period corresponds to the situation when India is experiencing a lot of political uncertainty and implements a managed floating regime (the Rupee is pegged to a basket of currencies of India’s trading partners and the exchange rate is officially determined by the Reserve Bank of India within a nominal band of ±5%), starting with 1975, till 1992. The period starting with 1985 is marked by continuous downward adjustments in the external value of the Rupee which is mainly brought by the sharp increase in the oil price in 1986–1987, as a result of the oil demand shock. Thus, these results confirm the arguments put forward by Golub [11] and Krugman [12]. Second, 1990–2000 is the period of the first-generation economic reforms, characterized by huge inconsistency in the phase and lead-lag relationship between variables questioned across time-scales. For example, during the period 1990–1992 both series move in-phase, and the exchange rate leads the oil price. In the same period, the Reserve Bank of India devalues the Rupee two times, on July 1, and 3, 1991 (with 18% and 19% respectively). In March 1992, the partial convertibility of the Rupee is introduced, also known as a dual exchange rate system. For this period, the supply side argument put forward by Bloomberg and Harris [13] holds very well. That is, during this period the economy experiences mounting inflation, which reduces the consumption capacity and consequently decreases the demand of non-tradable goods, contributing to a fall in their prices. Thus, the real exchange rate depreciates, which in turn leads to increases in the oil price. On contrary, during the interval 1993–1997 the variables are out-ofphase. This is the period when the oil price falls in general and the Rupee consistently depreciates because of demand shocks, phenomenon explained by Turhan et al. [42]. The phase difference in 2000–2002 shows that both series move in-phase and the oil price is leading. This is again the result of an oil demand shock. These results highlight the fact that the oil price – exchange rate relationship is largely influenced by the presence of oil demand shocks and monetary reforms. Therefore, on the one hand the findings based on the CWT analysis are similar with those reported by Tiwari et al. [10] who discover the leading relationship of the oil price upon the Rupee exchange rate for the 16–32-months band (approximately a part of Indian business cycle). On the other hand, different from Tiwari et al. [10] the present paper underlines that we may have periods where the exchange rate is leading (i.e. 1990–1992). The bootstrapping method that we use allows to see the complexity of the oil price – exchange rate nexus in the case of India.

The second set of results is generated by the use of wavelet Granger-causality test advanced by Olayeni [28] and of various multi-horizon, non-linear and asymmetric Granger-causality tests. The wavelet Granger-causality test documents a bidirectional causality in the very short run for some periods, while for the 2– 4-years band, which corresponds to fundamental traders and institutional investors, a unidirectional causality is shown between 1992 and 1995, running from the exchange rate to the oil price. In general, the oil price Granger-causes the exchange rate in the short run, while the opposite applies in the long run. The remaining time domain tests show in general a bidirectional causality (dominated however by the exchange rate influence on the oil price), which manifests in particular in the post-reform period. These findings are somehow different from those reported by Tiwari et al. [10] who do not find any causal relationship at lower time scales and only unidirectional causality from the exchange rate to the oil price at higher scales. However, our findings are in line with those reported by Bal and Rath [43] regarding the time domain Granger-causality tests. As in Bal and Rath [43] we find a significant bidirectional non-linear Granger causality between the oil price and the Indian Rupee exchange rate. All in all we show on the one hand that the India-US exchange rate Granger-causes the oil price in the long run, while the opposite applies in the short run. This main results can be explained by the fact that oil prices are more volatile and shocks in oil prices are rapidly transmitted to the India-US exchange rate (with a two months lag according to the MRS-VAR test). On contrary, the exchange rate Granger-causes the oil price only in the long run because, on the one hand, oil prices are established on the international market where different factors determine the oil supply and demand and, on the one hand, the increasing role of India which became the fourth larger oil consumer and importer cannot be neglected. Thus, a real appreciation of the Indian Rupee will be followed by a higher demand for oil products, which finally will generate an increase in international oil prices. These findings are supported by the newly proposed non-linear and regime-switching Granger-causality tests. Therefore, the findings of previous studies should be considered with caution because, on the one hand, the lead-lag relationship is documented only for certain frequencies (i.e. 2–4-years band) and time intervals, and, on the other hand, the bidirectional relationship is not only non-linear, but also asymmetric.

6. Conclusions and policy implications Energy policies and macroeconomic issues are closely related. The particular subject of oil price – exchange rate nexus is intensively investigated by the empirical literature, due to numerous

281

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283

interdependences which can arise between shocks in the oil price and the monetary policy. Because India became one of the major oil importers, it represents an interesting case study for analyzing this relationship. For this purpose, the present paper uses novel techniques, as the CWT, wavelet Granger-causality tests, together with several recently proposed time-series, frequency-domain and regime-switching Granger-causality models. The wavelet cohesion shows a high degree of positive correlation between the oil price and the India-US exchange rate in the postreform period, in particular in the short run. Our time-frequency analysis reveals some more interesting findings. For example, we document a significant amount of common power in the WPS for both series for the 2–4-years band. In the post-reform period, we find the existence of both phase- and anti-phase relationships, at different frequencies. In the post-reform period, we also observe, for particular year-scales at different frequencies, that the direction of the lead-lag relationship varies. The wavelet Granger-causality test shows that in general the exchange rate Granger-causes the oil price in the long run, while the opposite applies in the short run. In order to prove the robustness of these findings, a battery of newly proposed Granger-causality tests are performed. From the findings of the time-series causality tests, we conclude that: (1) the significant Granger-causal relationship between the variables in question is non-linear and bidirectional and exists only in the post-reform period; (2) the significant lead-lag relationship is indirect and asymmetric; (3) there is a significant regime effect. The frequency-domain analysis shows a significant bidirectional causal relationship at 0.5-years frequency, and a unidirectional Granger-causality running from the India-US exchange rate to the oil price for higher frequencies. The above findings have some important policy implications for the policy makers and market traders. In the first case, the

At the same time, the monetary authorities shall consider the short run oil price movements when establishing their exchange rate strategies. An oil price shock will generate a shock in the exchange rate. This means that the general equilibrium models and the systemic stress-tests used by the Reserve Bank of India should incorporate the short run (gradual) asymmetries existing between the analyzed variables. Further, there are implications in terms of the choice of adequate monetary policies to control inflationary pressures originating from oil prices or exchange rate fluctuations. In the second case, the market traders who invest in oil and exchange rate products can better adapt their investment strategies, depending on their risk profile. For example, the short run oriented speculative traders might diversify their portfolios toward oil and exchange rate market products, as there is no evidence of causality from any direction. However, for the institutional investors, it is noteworthy to know that oil price – exchange rate co-movements are time-frequency dependent and manifest especially for the 2–4-years band. So, considering this time-frequency interval, it is not recommended to invest in both categories of products as their higher correlation negatively affects the potential gains and the risk mitigation. In addition, our findings have real applications for the investors acting on energy derivative markets. For the forward contracts, in order to anticipate the oil price movements, it is highly recommended to correctly estimate the oil demand coming from emerging markets as India. In this context, forecasting the exchange rate of emerging markets currencies is compulsory for a correct assessment of international oil price trends.

authorities shall be aware that in a floating exchange rate regime, which corresponds to the post-reform period, the currency appreciation makes imports cheaper. However, in the long run the Rupee appreciation will lead to an increase of international oil prices. Consequently, in the short run the appreciation of the Rupee, favored by higher economic growth, will contribute to the correction of the current account deficit generated by the increased oil consumption. In the long run the opposite applies.

Notes: The white (red) contour indicates a 5% (10%) significance level. The significance levels are based on 3000 draws from Monte Carlo simulations estimated on an ARMA(1,1) null of no statistical significance. The green line is the cone-of-influence (COI) earmarking the areas affected by the edge effects or phase. The scale has been converted to period using the relation: Ft ¼ k  s, where

Appendix A. Wavelet Granger-causality between the oil price and the exchange rate (robustness check on the time-span 1973M1–2012M4)

k ¼ 4p=½xo þ ð2 þ x2o Þ  for the Morlet wavelet function. Using xo ¼ 6 for optimal balance [25], we have Ft ¼ 1:033  s. Monthly 1=2

282

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283

bands are represented. The oil price is represented by the WTI Cushing and the data are extracted from Macro Trends database. (For interpretation of the references to colour in this figure note, the reader is referred to the web version of this article.) Appendix B. The conditional probability of regimes 1 and 2 for the MSVAR model Smoothed states probability of the system being in regime 1 and regime 2.

[9] Ghosh S. Examining crude oil price – exchange rate nexus for India during the period of extreme oil price volatility. Appl Energy 2011;88:1886–9. [10] Tiwari AK, Dar AB, Bhanja N. Oil price and exchange rates: a wavelet based analysis for India. Econ Model 2013;31:414–22. [11] Golub SS. Oil prices and exchange rates. Econ J 1983;93:576–93. [12] Krugman P. Oil and the dollar. In: Bhandari JB, Putnam BH, editors. Economic interdependence and flexible exchange rates. Cambridge, MA: MIT Press; 1983. [13] Bloomberg SB, Harris ES. The commodity consumer price connection: fact or fable? Econ Policy Rev 1995;1:21–38. [14] Reboredo JC. Modelling oil price and exchange rate co-movements. J Policy Model 2012;34:419–40. [15] Amano RA, van Norden S. Oil prices and the rise and fall of the US real exchange rate. J Int Money Financ 1998;17:299–316.

15

Explained Variable #1 Explained Variable #2

10 5 0 -5 0

50

100

150

200

250

300

350

400

450

1.5

Conditional Std of Equation #1 Conditional Std of Equation #2

1

0.5

0

Smoothed States Probabilities

0

50

100

150

200

250

300

350

400

450

1

State 1 State 2 0.5

0 0

50

100

150

200

250

300

350

400

450

Time

References [1] Hamilton JD. This is what happened to the oil price-macroeconomy relationship. J Monet Econ 1996;38:215–20. [2] Cavalcanti T, Jalles JT. Macroeconomic effects of oil price shocks in Brazil and in the United States. Appl Energy 2013;104:475–86. [3] Ju K, Zhou D, Zhou P, Wu J. Macroeconomic effects of oil price shocks in China: an empirical study based on Hilbert-Huang transform and event study. Appl Energy 2014;136:1053–66. [4] Ju K, Su B, Zhou D, Zhang Y. An incentive-oriented early warning system for predicting the co-movements between oil price shocks and macroeconomy. Appl Energy 2016;163:452–63. [5] Narayan P, Narayan S. Modelling the impact of oil prices on Vietnam’s stock prices. Appl Energy 2010;87:356–61. [6] Huang S, An H, Gao X, Sun X. Do oil price asymmetric effects on the stock market persist in multiple time horizons? Appl Energy 2016;2015. http://dx. doi.org/10.1016/j.apenergy.2015.11.094. [7] Li Q, a Cheng K, Yang X. Response pattern of stock returns to international oil price shocks: from the perspective of China’s oil industrial chain. Appl Energy 2016. http://dx.doi.org/10.1016/j.apenergy.2015.12.060. [8] Ji Q, Fan Y. How does oil price volatility affect non-energy commodity markets? Appl Energy 2012;89:273–80.

[16] Chaudhuri K, Daniel BC. Long run equilibrium real exchange rates and oil price. Econ Lett 1998;58:231–8. [17] Bénassy-Quéré A, Mignon V, Penot A. China and the relationship between the oil price and the dollar. Energy Policy 2007;35:5795–805. [18] Chen S-S, Chen H-C. Oil price and real exchange rates. Energy Econ 2007;29:390–404. [19] Coudert V, Mignon V, Penot A. Oil price and the dollar. Energy Stud Rev 2007;18 [Article 3]. [20] Lizardo RA, Mollick AV. Oil price fluctuations and U.S. dollar exchange rates. Energy Econ 2010;32:399–408. [21] Basher SA, Haug AA, Sadorsky P. Oil prices, exchange rates and emerging stock markets. Energy Econ 2012;34:227–40. [22] Zhang Y-J, Fan Y, Tsai H-T, Wei Y-M. Spillover effect of US dollar exchange rate on oil prices. J Policy Model 2008;30:973–91. [23] Tiwari AK, Mutascu MI, Albulescu CT. The influence of the international oil prices on the real effective exchange rate in Romania in a wavelet transform framework. Energy Econ 2013;40:714–33. [24] Uddin GS, Tiwari AK, Arouri MEH, Teulon F. On the relationship between oil price and exchange rates: a wavelet analysis. Econ Model 2013;35:502–7. [25] Torrence C, Compo GP. A practical guide to wavelet analysis. Bull Am Meteorol Soc 1998;79:61–78.

A.K. Tiwari, C.T. Albulescu / Applied Energy 179 (2016) 272–283 [26] Aguiar-Conraria L, Soares MJ. The continuous wavelet transform: moving beyond uni- and bivariate analysis. J Econ Surv 2014;28:344–75. [27] Cazelles B, Chavez M, Berteaux D, Ménard F, Vik JO, Jenouvrier S, et al. Wavelet analysis of ecological time series. Oecologia 2008;156:287–304. [28] Olayeni OR. Causality in continuous wavelet transform without spectral matrix factorization: theory and application. Comput Econ 2016;47:321–40. [29] Dufour J-M, Pelletier D, Renault E. Short run and long run causality in time series: inference. J Econ 2006;132:337–62. [30] Péguin-Feissolle A, Strikholm B, Teräsvirta T. Testing the Granger non causality hypothesis in stationary non-linear models of unknown functional form. CREATES research paper 2008-19. School of Economics and Management, University of Aarhus; 2008. [31] Nishiyama Y, Hitomi K, Kawasaki Y, Jeong K. A consistent nonparametric test for nonlinear causality specification in time series regression. J Econ 2011;165:112–27. [32] Hatemi-J A. Asymmetric causality tests with an application. Empirical Econ 2012;43:447–56. [33] Lemmens A, Croux C, Dekimpe MG. Measuring and testing Granger-causality over the spectrum: an application to European production expectation surveys. Int J Forecast 2008;24:414–31. [34] Wang Y, Wu C. Energy prices and exchange rates of the U.S. dollar: further evidence from linear and nonlinear causality analyses. Econ Model 2012;29:2289–97. [35] Chen Y-C, Rogoff K, Rossi B. Can exchange rates forecast commodity prices? Quart J Econ 2010;125:1145–94. [36] Huang AY, Tseng Y-H. Is crude oil price affected by the US dollar exchange rate? Int Res J Financ Econ 2010;58:109–20. [37] Huang Y, Guo F. The role of oil price shocks on China’s real exchange rate. Chin Econ Rev 2007;18:403–16. [38] Narayan PK, Narayan S, Prasad A. Understanding the oil price – exchange rate nexus for the Fiji islands. Energy Econ 2008;30:2686–96. [39] Iwayemi A, Fowowe B. Impact of oil price shocks on selected macroeconomic variables in Nigeria. Energy Policy 2011;39:603–12. [40] Oriavwote VE, Eriemo NO. Oil prices and the real exchange rate in Nigeria. Int J Econ Financ 2012;4:198–205. [41] Rautava J. The role of oil prices and the real exchange rate in Russia’s economy – a cointegration approach. J Comparat Econ 2004;32:315–27. _ Hacihasanog˘lu E, Soytasß U. Oil prices and emerging market exchange [42] Turhan I, rates. Emerg Market Financ Trade 2013;49:21–36. [43] Bal DP, Rath BN. Nonlinear causality between crude oil price and exchange rate: a comparative study of China and India. Energy Econ 2015;51:149–56. [44] Beckmann J, Czudaj R. Is there a homogeneous causality pattern between oil prices and currencies of oil importers and exporters? Energy Econ 2013;40:665–78. [45] Hiemstra C, Jones JD. Testing for linear and nonlinear Granger causality in the stock price volume relation. J Financ 1994;49:1639–64. [46] Rua A. Measuring comovement in the time–frequency space. J Macroecon 2010;32:685–91. [47] Rudin W. Fourier analysis on groups. New York: Interscience; 1962. [48] Lee DTL, Yamamoto A. Wavelet analysis: theory and applications. Hewlett-Packard J 1994;45:44–54.

283

[49] Gençay R, Selçuk F, Whitcher B. An introduction to wavelets and other filtering methods in finance and economics. Academic Press, Elsevier; 2001. [50] Ricker N. Further developments in the wavelet theory of seismogram structure. Bull Seismol Soc Am 1943;33:197–228. [51] Ricker N. Wavelet contraction, wavelet expansion, and the control of seismic resolution. Geophysics 1953;18:769–92. [52] Grinsted A, Moore JC, Jevrejeva S. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Process Geophys 2004;11:561–6. [53] Cohen EAK, Walden AT. A statistical study of temporally smoothed wavelet coherence. IEEE Trans Signal Process 2010;58:2964–73. [54] Rua A, Nunes LC. International comovement of stock market returns: a wavelet analysis. J Empirical Financ 2009;16:632–9. [55] Aguiar-Conraria L, Soares MJ. Business cycle synchronization and the Euro: a wavelet analysis. J Macroecon 2011;33:477–89. [56] Aguiar-Conraria L, Magalhães PC, Soares MJ. Cycles in politics: wavelet analysis of political time series. Am J Polit Sci 2012;56:500–18. [57] Aguiar-Conraria L, Magalhães PC, Soares MJ. The nationalization of electoral cycles in the United States: a wavelet analysis. Public Choice 2013;156:387–408. [58] Caraiani P. Stylized facts of business cycles in a transition economy in time and frequency. Econ Model 2012;29:2163–73. [59] Ranta M. Contagion among major world markets: a wavelet approach. Int J Manage Financ 2013;9:133–50. [60] Tiwari AK, Oros C, Albulescu CT. Revisiting the inflation – output gap relationship for France using a wavelet transform approach. Econ Model 2014;37:464–75. [61] Tiwari AK, Mutascu MI, Albulescu CT, Kyophilavong P. Frequency domain causality analysis of stock market and economic activity in India. Int Rev Econ Financ 2015;39:224–38. [62] Tiwari AK, Mutascu MI, Albulescu CT. Continuous wavelet transform and rolling correlation of European stock markets. Int Rev Econ Financ 2016;42:237–56. [63] Aguiar-Conraria L, Soares MJ. Oil and the macroeconomy: using wavelets to analyze old issues. Empirical Econ 2011;40:645–55. [64] Rua A. Worldwide synchronization since the nineteenth century: a waveletbased view. Appl Econ Lett 2013;20:773–6. [65] Hamilton JD. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 1989;57:357–84. [66] Hansen BE, Seo B. Testing for two-regime threshold cointegration in vector error-correction models. J Econ 2002;110:293–318. [67] Lam P. A Markov-switching model of GNP growth with duration dependence. Int Econ Rev 2004;45:175–204. [68] Perlin M. MS regress – the MATLAB package for Markov regime switching modelsAvailable from: 2015 [accessed April 2015]. [69] Ding Z. m_Files_tvtp package – the MATLAB package for Markov regime switching modelsAvailable from: 2012 [accessed April 2015].