Business cycle synchronization in Asia-Pacific: New evidence from wavelet analysis

Accepted Manuscript Title: Business cycle synchronization in Asia-Pacific: New evidence from wavelet analysis Author: Chun-Ping Chang PII: DOI: Reference:

S1049-0078(15)00005-6 http://dx.doi.org/doi:10.1016/j.asieco.2015.01.004 ASIECO 976

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Received date: Revised date: Accepted date:

2-12-2013 20-1-2015 24-1-2015

Please cite this article as: Chang, C.-P.,Business cycle synchronization in AsiaPacific: New evidence from wavelet analysis, Journal of Asian Economics (2015), http://dx.doi.org/10.1016/j.asieco.2015.01.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Aziz Berdiev, Chun-Ping Chang1 Department of Marketing Management, Shih Chien University, Kaohsiung, Taiwan Senior Visiting Fellow, School of Economics and Finance, Xi'an Jiaotong University, Shaanxi, China

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Corresponding author: Tel.: +886 7 6678888 5713; Fax: +886 7 6679999; E-mail address: [email protected].

Aziz Berdiev1 Page 1 of 34

Business cycle synchronization in Asia-Pacific: New evidence from wavelet analysis

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Abstract

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We investigate the synchronization of growth cycles between China, Japan, the United States and other Asia-Pacific countries using wavelet analysis. While we find that the growth cycles of China, Japan, and the United States are synchronized with the other Asia-Pacific economies, the strength of business cycle synchronization fluctuates across frequencies and over time. Overall, China and other Asia-Pacific countries display a high degree of comovement at long-run developments, especially during and following the recent global financial crisis. Likewise, the strength of business cycle synchronization between Japan and most other Asia-Pacific economies increases at long-run fluctuations, however, for the entire sample period of 1993:2-2012:4. Also, the United States and other Asia-Pacific countries mostly experience a high degree of comovement at frequencies linked with fluctuations that range from between two and four years. Our results thus emphasize the importance of examining the strength of business cycle synchronization using a time-frequency framework.

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Keywords: Business cycle synchronization; Wavelet analysis; Asia-Pacific

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JEL Classifications: E30; E32; F44

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1.

Introduction Many countries in Asia have enjoyed a considerable amount of economic growth in the past

few decades. Certainly, the periods of the Asian financial crisis in 1997 and the recent global

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financial crisis are exceptions. Nevertheless, these countries have attempted to promote economic integration through various agreements in the region, primarily following the Asian financial crisis (Allegret and Essaadi, 2011; Xie et al., 2013). These activities have enabled

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greater regional economic collaboration and also have facilitated growth in these economies

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(Shin and Wang, 2003; Xie et al., 2013). This is especially the case for China, which has experienced substantial economic development after 1978, when it commenced major economic reforms (Gerlach-Kristen, 2009). Indeed, China has surfaced as the foremost force in this process

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of global integration in Asia.2

Specifically, China has increasingly influenced the economic structure of the world in recent

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decades. Fidrmuc and Korhonen (2010), for example, indicate that China has altered the allocation of national income in the global economy. As of 2013, its share of global national income came to about 8 percent (World Bank, 2014). Its percentage of world exports and

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imports has also significantly increased in recent years (see Allegret and Essaadi, 2011; Kim et

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al., 2011; Dufrénot and Keddad, 2014). Su et al. (2014:228) argue that “the choices and effectiveness of monetary and fiscal policies in East Asian economies will be highly influenced

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by external factors originating in China.” Therefore, China plays a vital role in the global economy and even more importantly in the Asia-Pacific region. Research also indicates that many Asian economies have enjoyed high intraregional trade in recent decades, with the exclusion of the period of the Asian financial crisis and the latest global financial crisis.3 The literature attributes some of this increase in trade integration to the amazing growth and influence of China in the region.4 Moneta and Rüffer (2009:1), for example, note that China has become “a major assembly and processing centre, thereby increasing intra-regional trade and financial flows, while simultaneously strengthening the links between countries within 2

See, for a discussion, Moneta and Rüffer (2009), Fidrmuc and Korhonen (2010), Park and Song (2011), Kim et al. (2011), Burdekin and Siklos (2012), De Grauwe and Zhang (2012), Quah (2012), and Su et al. (2014). 3 See, among others, Choe (2001), Shin and Wang (2003), Shin and Sonn (2006), Moneta and Rüffer (2009), Allegret and Essaadi (2011), Park and Song (2011), Kim et al. (2011), Sharma and Mishra (2012), De Grauwe and Zhang (2012), and Dufrénot and Keddad (2014). 4 See, for example, Shin and Sonn (2006), Moneta and Rüffer (2009), Allegret and Essaadi (2011), Park and Song (2011), Kim et al. (2011), Su et al. (2014), and Dufrénot and Keddad (2014).

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the region.” Similarly, Dufrénot and Keddad (2014:188) indicate that China is at the focal point of a “regional supply network that is crucial in promoting intra- and inter-regional trade.” Likewise, Athukorala (2011:80) argues that “China’s rise in world trade has brought about a notable shift in the division of labor within regional production networks.” Indeed, previous

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studies emphasize the significance of regional production networks in promoting economic integration in Asia-Pacific (Kimura, 2006; Yeung, 2009; De, 2011; Athukorala, 2011; Dufrénot

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and Keddad, 2014).

Similarly, Japan plays a critically important role in advancing economic integration in the

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region (Park, 2007; Quah, 2012; Kim et al., 2013; Dufrénot and Keddad, 2014). In particular, Japan promotes regional economic integration via trade and foreign investment (see Kang et al.,

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2002; Hughes Hallett and Richter, 2009; Capannelli et al., 2010; Quah, 2012; Kim et al., 2013). Hughes Hallett and Richter (2009:208), for example, emphasize that Japan is a “provider of sophisticated manufactures, partner in network trade and a source of investment” in the Asia-

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Pacific region. According to Kim et al. (2013:309), the yen is the “third-most traded currency” in the world. Nevertheless, the majority of trade in the region is invoiced in US dollars (McKinnon,

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2000; McKinnon and Schnabl, 2004a; 2004b; Quah and Crowley, 2010; 2012). McKinnon and Schnabl (2004a:181), for example, note that the US dollar is employed “as the invoice currency

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for most of East Asian trade even though Japanese trade in the region is as large as that of the

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USA.” Frankel and Wei (1994) and Chow et al. (2007) also provide evidence that the US dollar represents a major force in long-run exchange rate policy in East Asia. Thus, even with the growth of China in the Asia-Pacific, Japan and the US continue to play a key role in the region. As such, these movements have caused the Asia-Pacific economies to become extensively integrated in the region.5 This process of greater trade integration in Asia may have influenced the comovement of growth cycles between the countries.6 Recently, the region also has been experiencing even greater financial integration (Rana, 2007; Xie et al., 2013). Hence, higher

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According to Petras and Veltmeyer (2001:11), global integration represents the “widening and deepening of the international flows of trade, capital, technology and information within a single integrated market.” The literature also examines the impact of globalization, among other areas, on economic growth and the type of exchange rate regime a country implements (see Dreher, 2006; Chang et al., 2013; Berdiev et al., 2012). 6 Theoretically, the association between trade integration and business cycle synchronization is uncertain (see, for a discussion, Crosby, 2003). However, Frankel and Rose (1998) find that economies with greater trade relations experience higher business cycle synchronization.

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financial integration may also impact business cycle synchronization in the Asia-Pacific region.7 As such, a considerable amount of empirical literature has been devoted to understanding business cycle synchronization in Asia.8 Most of these studies have investigated the causes of synchronization of growth cycles in Asia.9 However, the literature overall has not measured the

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strength of business cycle synchronization in the region across frequencies and over time.

In particular, previous research has studied the synchronization of growth cycles in the Asia-

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Pacific region using the time-domain; this framework nevertheless provides no information about the frequency domain (see Aguiar-Conraria et al., 2012a). Moreover, a linear approach

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undervalues the strength of comovement of growth cycles between countries as it places trivial “weight on sharp movements during recessions (Herrerias and Ordóñez, 2014:161).” Kim et al.

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(2003), for example, distinguish between “secular and cyclical components” to study the dynamics of business cycles in Asia. Allegret and Essaadi (2011) also emphasize the importance of separating growth cycles at different frequencies in East Asia. The strength of the

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comovement of growth cycles in Asia may vary across different frequencies as “different economic policies may cause divergence between business cycles” as argued by Fidrmuc and

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Korhonen (2010:301). It is possible for example that the synchronization of growth cycles may be high at long-run developments, whereas there may be a low degree of comovement between

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the growth cycles at short-run fluctuations for a particular sample period.

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In this paper, we contribute to this important literature by examining the degree of business cycle synchronization between China, Japan, the United States and other Asia-Pacific economies in the time-frequency domain. Specifically, we assess the strength of comovement of growth cycles for different country pairs while distinguishing between short-run and long-run fluctuations and across time. We employ a “wavelet-based measure of comovement”, recently proposed by Rua (2010), to investigate the comovement of growth cycles in the Asia-Pacific region. The advantage of the wavelet-based measure of comovement is that it provides a more

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Likewise, the relationship between financial integration and business cycle comovement is uncertain (see Shin and Sohn, 2006; Park and Shin, 2009; Gong and Kim, 2013; Xie et al., 2013). 8 See Loayza et al. (2001), Choe (2001), Crosby (2003), Shin and Wang (2003; 2004), Kumakura (2006), Sato and Zhang (2006), Shin and Sohn (2006), Rana (2007), Plummer and Wignaraja (2007), Zhang and Sato (2008), Moneta and Rüffer (2009), Gerlach-Kristen (2009), Park and Shin (2009), Hughes Hallett and Richter (2009), Fidrmuc and Korhonen (2010), Lee and Azali (2010), Allegret and Essaadi (2011), Kim et al. (2011), Quah (2012a; 2012b), Quah and Crowley (2010; 2012), Xie et al. (2013), Gong and Kim (2013), and Dufrénot and Keddad (2014). 9 Most of these studies provide evidence that trade significantly influences the synchronization of growth cycles in Asia. Allegret and Essaadi (2011) provide a detailed literature review on business cycle synchronization in Asia.

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comprehensive analysis by simultaneously characterizing the strength of business cycle synchronization across frequencies and over time (Rua, 2010). Moreover, Aguiar-Conraria and Soares (2011b:646) suggest that wavelet analysis conducts “natural local analysis of a timeseries in the sense that the length of wavelets varies endogenously: it stretches into a long

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wavelet function to measure the low-frequency movements; and it compresses into a short wavelet function to measure the high-frequency movements.” Using wavelet analysis, we are

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able to observe how the comovement of growth cycles between China, Japan, the United States and other Asia-Pacific economies have transformed across frequencies and over time in an

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integrated framework.

To anticipate our results, we provide evidence that the strength of business cycle

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synchronization between China, Japan, the United States and other Asia-Pacific countries fluctuates significantly across frequencies and over time. Specifically, our results illustrate that the degree of comovement between the growth cycles varies across different country pairs in our

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time-frequency analysis. In general, there is a high degree of comovement between China and other Asia-Pacific economies at long-run fluctuations, particularly during and following the

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recent global financial crisis. In the case of Japan and other Asia-Pacific countries, the strength of business cycle synchronization also increases at long-run developments, however, for the

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entire sample period. The United States and other Asia-Pacific countries mostly display a high

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degree of comovement at frequencies linked with fluctuations that range between two and four years. We therefore emphasize the importance of investigating the strength of business cycle synchronization for different country pairs using a time-frequency approach. The remainder of the paper is structured as follows. In Section 2, we provide a preliminary data analysis. Section 3 presents the wavelet analysis, specifically, the wavelet-based measure of comovement. In Section 4, we discuss the strength of business cycle synchronization between China, Japan, the United States and other Asia-Pacific countries in the time-frequency space. The final section summarizes the major findings.

2.

Preliminary Data Analysis We examine the comovement between the growth cycles of China, Japan, the United States

and other Asia-Pacific countries, namely, Australia, Hong Kong, Indonesia, Korea, Malaysia, New Zealand, Philippines, Singapore, Thailand and Taiwan. The literature generally utilizes real 6 Page 6 of 34

gross domestic product (GDP) and/or the industrial production index to evaluate real output (see, for example, Rua, 2010; Aguiar-Conraria and Soares, 2011a). We employ real GDP. Our argument follows Chang et al. (2013: 215), who indicate that the industrial production index national income that are dominated by the service sector.”10

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“captures only the manufacturing sector which accounts for increasingly smaller portions of

As such, we collect quarterly data for GDP, in local currency units, from the Global Financial

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Database (2013). We utilize the consumer price index, also in local currency units, to transform the time series into real GDP. Subsequently, we calculate quarterly real GDP growth rates for

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each country. The analysis is, with one exception, based upon quarterly data over the period 1993:2-2012:4. The exception is Australia, for which data is available only to the third quarter of

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2012.

In Table 1, we provide summary statistics for quarterly real GDP growth rates for all the countries in our sample over the period 1993:2-2012:4. As can be seen, China (2.679 percent)

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and Indonesia (1.773 percent) enjoy the highest average quarterly growth rates, whereas Thailand (– 0.071 percent) and Japan (0.212 percent) experience the lowest average quarterly

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growth rates. Moreover, the volatility of output growth is comparatively higher in Thailand and China than those of other Asia-Pacific countries. Alternatively, Australia and Philippines have

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sample.

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the lowest standard deviation of quarterly real GDP growth rates among all the economies in our

Next, we plot the quarterly real GDP growth rates for all the countries in our sample over the period 1993:2-2012:4 in Figure 1. We notice that China (8.906 percent) in 1993:4 and Singapore (6.677 percent) in 2010:2 exhibit the highest quarterly output growth, while Indonesia (– 10.95 percent) in 1998:2 and Thailand (– 25.13 percent) in 2010:1 display the lowest quarterly output growth. The figures also confirm that the volatility of real GDP growth is relatively higher in China as compared to other Asia-Pacific economies. Like most countries in our sample, Japan and the United States experienced the lowest quarterly output growth during the recent global financial crisis. As expected, we also observe that most of the countries realized the lowest output growth around the periods of the Asian financial crisis.

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Moreover, Chang et al. (2013: 215) argue that “business cycles of the whole economy and their correlations across countries are more pressing issues than those of a sector within an economy.”

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In addition, we provide the correlation coefficients of real GDP growth rates among all the countries in Table 2. As can be seen, the correlation coefficients of China with the other countries are all positive, with the exception of Australia and New Zealand. Interestingly, the correlation coefficients of China with the other countries are statistically insignificant at

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conventional levels, with the exception of the United States. Also, both China (0.342) and Japan (0.767) have the highest output growth correlation with the United States. Japan experiences a

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correlation coefficient larger than 0.600 with six countries. The United States has the largest output growth correlation with Singapore (0.878). Other notable country correlations are

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between Singapore and Taiwan (0.809), and Korea and Malaysia (0.805). Nevertheless, country correlation coefficients “average the degree of contemporaneous convergence across all

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frequencies (Hughes Hallett and Richter, 2009:208).” Thus, they are unable to provide a detailed picture on the strength of business cycle correlations across frequencies and over time. Next, we investigate the time-variation in the correlation of output growth between countries,

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following Longin and Solnik (1995) and Ragunathan and Mitchell (1997). In particular, we employ a Generalized Autoregressive Conditional Heteroskedastic model presented in Bollerslev

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et al. (1988) and Bollerslev (1990). We compute the likelihood ratio test to investigate the null hypothesis of constant correlations (Bollerslev, 1990) against the alternative of time-varying

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correlations (Bollerslev et al., 1988). The likelihood ratio tests for different country pairs are

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displayed in Table 3. As can be seen, all test statistics significantly reject the null of constant correlation in all tables, at the 1% level. These findings therefore suggest that the correlations of real GDP growth between different countries are time-varying. Hence, these results provide evidence that the correlations of output growth between different country pairs fluctuates significantly through time. The advantage of wavelet analysis is that it enables us “for a thorough appraisal of the time-variation” in the comovement of growth cycles (Aguiar-Conraria et al., 2012a:1950). In general, the wavelet analysis presents the “estimation of the spectral characteristics of a time-series as a function of time, revealing how the different periodic components of a particular time-series evolve over time (Aguiar-Conraria and Soares, 2011a:478).” Moreover, as we emphasized earlier, the wavelet analysis provides a detailed picture on the strength of the business cycle correlations across frequencies and over

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time.11 Gencay et al. (2005: 56) note that a wavelet analysis allows us to “decompose a time series, measured at the highest possible frequency, into different time scales.” We therefore use wavelet analysis to examine the comovement of growth cycles between China, Japan, the United

3.

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States and other Asia-Pacific countries in the time-frequency domain.

Wavelet Analysis

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We assess the strength of business cycle synchronization between China, Japan, the United

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States and other Asia-Pacific economies across time and frequencies utilizing a wavelet-based measure of comovement. According to Rua (2010:687), the advantage of the wavelet-based measure of comovement is “to quantify the comovement in the time-frequency space and assess

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over which periods of time and frequencies is the comovement higher.” In what follows, we describe the wavelet-based measure of comovement in greater detail, following Rua (2010). To

1 s



(t   ) s

(1)

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  , s (t ) 

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start, the literature defines wavelets as follows:

This wavelet function is being normalized by 1/ s to make certain that the wavelet transforms

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are effectively analogous across scales and time series; the parameter  reveals the time location of the wavelet; and the parameter s denotes the scale, which is inversely linked to the frequency (Blatter, 1998; Percival and Walden, 2000; Gencay et al., 2002). Hence, a higher value for the parameter s (higher scale) illustrates that the wavelet is less compacted (Vacha and Barunik, 2012). Also, a higher scale describes the gradually varying elements of the wavelet, i.e., low frequencies of the time series (Rua, 2012a; 2012b). The expression  (t   ) suggests that the range of the wavelet is being moved by  factors to the right, whereas the term  (t / s ) indicates that the range of the wavelet is being extended by multiplicative units (Gencay et al., 2002). The literature generally employs the Morlet wavelet as the mother wavelet (see, among others, Torrence and Compo, 1998; Grinsted et al., 2004; Aguiar-Conraria et al., 2008; 2012a; 11

The literature documents the significance of investigating the comovement between two time series in the timefrequency framework (see, among others, Rua, 2010; 2012a; 2012b; Rua and Nunes, 2009; 2012; Aguiar-Conraria and Soares, 2011a; 2011b; Aguiar-Conraria et al., 2012a; 2012b; Kiviaho et al., 2012; Vacha and Barunik, 2012).

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2012b; Aguiar-Conraria and Soares, 2011a; 2011b; Rua, 2010; 2012a; 2012b; Rua and Nunes, 2009; 2012; Kiviaho et al., 2012; Vacha and Barunik, 2012). In particular, the Morlet wavelet is defined as follows:

1 t2  4 i 0 t 2

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

 (t )   e e

(2)

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The term t denotes dimensionless time, while the term 0 refers to dimensionless frequency

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(see, for a discussion, Torrence and Compo, 1998; Grinsted et al., 2004). In particular, the term

0 manages the time-frequency localization; for example, rising 0 generates enhanced

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frequency localization, however, attains inferior time localization (Rua, 2012a; 2012b; Rua and Nunes, 2012). Previous studies have normally placed 0 equal to 6 (see, among others, Torrence

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and Compo, 1998; Grinsted et al., 2004; Aguiar-Conraria et al., 2008; 2012a; Aguiar-Conraria and Soares, 2011a; 2011b; Rua, 2010; 2012a; 2012b; Rua and Nunes, 2009; 2012; Kiviaho et al., 2012; Vacha and Barunik, 2012).

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We also place 0 = 6 for two important reasons: (1) it generates “a good balance between

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time and frequency localization (Grinsted et al., 2004: 563)” and (2) it ensures that the scale parameter s is nearly equal to the Fourier period to facilitate the explanation of the wavelet

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analysis (Rua, 2010; Rua, 2012a; 2012b; Rua and Nunes, 2012). Thus, our mother wavelet encompasses the “optimal joint time-frequency concentration”, which suggests that it produces the most favorable balance in the time and frequency framework (Aguiar-Conraria et al., 2012b:505).



In addition, this particular Morlet wavelet has a zero mean   (t )dt  0 ; its square integrates 



to unity   2 (t )dt  1 ; and, more importantly, it meets the admissibility condition described as 

follows:

V 





0

( f ) df f 2

(3)

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where the expression V ranges between 0 to  , and the term  ( f ) represents the Fourier transform of a wavelet  (t ) (see, for a discussion, Percival and Walden, 2000; Gencay et al., 2002; Aguiar-Conraria et al., 2008; Aguiar-Conraria and Soares, 2011b; Vacha and Barunik,

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2012). The admissibility condition enables the formation of a function x(t ) from its continuous wavelet transform (Percival and Walden, 2000). Therefore, consider the following continuous wavelet transform of a time series x(t ) with respect to the wavelet function  (t ) expressed as

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follows:

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

Wx ( , s)   x(t ) , s (t )dt

(4)

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

where * represents the complex conjugate (see, among others, Torrence and Compo, 1998; Jevrejeva et al., 2003; Grinsted et al., 2004; Aguiar-Conraria et al., 2008; 2012a; 2012b; Aguiar-

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Conraria and Soares, 2011a; 2011b; Rua, 2012a; 2012b; Rua and Nunes, 2009; 2012; Vacha and







x(t ) 

(t   ) dt s

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1 s

(5)

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Wx ( , s) 

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Barunik, 2012). Furthermore, it is possible to state equation (4) as the following:

As such, we are able to generate a resolution that illustrates “the amplitude of any features versus the scale and how this amplitude varies with time” by varying the parameters  and s (Torrence and Compo, 1998:64). This continuous wavelet transform of a time series x(t ) can be dilated by the parameter s and translated by the parameter  to build a picture in the time and frequency space (Jevrejeva et al., 2003). Given that our mother wavelet – the Morlet wavelet – meets the admissibility condition, we conduct an inverse procedure to generate an expression from its wavelet transform (Percival and Walden, 2000; Gencay et al., 2002). Thus, we produce the following inverse wavelet transform (Rua, 2010):

x(t ) 

1 



 



  ,s (t )Wx ( , s)

 

dds s2

(6)

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As noted above, this function enables us to rebuild the time series x(t ) from its wavelet transform by integrating across the parameters  and s (see, for a discussion, Percival and Walden, 2000; Gencay et al., 2002; Aguiar-Conraria et al., 2008; Rua, 2010; Rua and Nunes, 2009; 2012; Vacha and Barunik, 2012). Similarly, we reconstruct the total variance of the time

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series x(t ) by integrating the wavelet power spectrum Wx ( , s ) 2 over the parameters  and s (Rua, 2010; 2012a; Rua and Nunes, 2012). The total variance of the time series x(t ) explains the

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significance of the parameter s across the parameter  – more simply, it allows us to understand

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the significance of frequencies across time (Aguiar-Conraria et al., 2012b).

Next, we construct a cross wavelet transform to describe the covariance between the two time series – x(t ) and y (t ) – in a time-frequency space (see, for example, Rua, 2010; 2012a;

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2012b; Rua and Nunes, 2012; Aguiar-Conraria et al., 2012a; 2012b; Aguiar-Conraria and Soares, 2011a; 2011b). More specifically, for a time series x(t ) with its wavelet transform of Wx ( , s)

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two time series is expressed as follows:

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and for a time series y (t ) with its wavelet transform of W y ( , s ) , the covariance between these

(7)

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Wxy ( , s)  Wx ( , s)W y ( , s)

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The term Wxy ( , s) denotes the cross wavelet spectrum of a time series x(t ) and y (t ) (see, among others, Torrence and Compo, 1998; Jevrejeva et al., 2003; Grinsted et al., 2004; AguiarConraria et al., 2008; 2012a; 2012b; Aguiar-Conraria and Soares, 2011a; 2011b; Rua, 2010; 2012a; 2012b; Rua and Nunes, 2009; 2012; Kiviaho et al., 2012; Vacha and Barunik, 2012). Next, we produce the wavelet-based measure of comovement by dividing the cross wavelet spectrum of a time series x(t ) and y (t ) with the wavelet power spectrum of the time series x(t ) and y (t ) as follows:

 1   xy ( , s ) 

(Wxy ( , s )) Wx ( , s ) Wy ( , s ) 2

2

1

(8)

The expression  represents “the real part of the cross-wavelet spectrum which measures 12 Page 12 of 34

contemporaneous covariance”, while the expression  xy ( , s) denotes the wavelet-based measure of comovement that “plays a role as a contemporaneous correlation coefficient around each moment in time and for each frequency (Rua, 2010: 687).” In particular, this wavelet-based

x(t ) and y (t ) across frequencies and over time (Rua, 2010).

Empirical Results

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measure of comovement  xy ( , s) determines the strength of the comovement of a time series

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We present the wavelet-based measure of comovement between the growth cycles of China and other Asia-Pacific countries in Figure 2; Japan and other Asia-Pacific countries in Figure 3;

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and the United States and Asia-Pacific countries in Figure 4.

As can be seen, these figures contain three dimensions. In particular, the wavelet-based measures of comovement between growth cycles of the above country pairs are displayed using a

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contour plot in Figures 2-4. The vertical axis denotes the frequency, which is measured in time units, i.e., years. The horizontal axis represents the time period of the analysis: 1993:2-2012:4.

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The final dimension – the grayscale – evaluates the strength of the wavelet-based measure of

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comovement between the two time series. Thus, a rise in the darkness in the grayscale refers to a higher value of the wavelet-based measure of comovement between the growth cycles for a

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particular country pair. The figures also contain black solid lines, which indicate that a waveletbased measure of comovement between growth cycles of country pairs for a particular time and frequency area are statistically significant at the 5% level. To start, we observe a relatively low degree of comovement between the growth cycles of China and Australia especially at long-run fluctuations during the entire sample period. Likewise, Japan and Australia exhibit a low degree of comovement at lower frequencies, however, only at the start of the sample period. Actually, the strength of this comovement increases at intermediate and higher frequencies. There is also a high degree of business cycle synchronization between United States and Australia at frequencies linked with fluctuations that continue more than two years almost the entire sample period. Next, the degree of comovement between the growth cycles of China and Hong Kong has been low during the entire sample period. The only exception is at lower frequencies at the conclusion of the sample period, where the strength of comovement increases. In addition, there 13 Page 13 of 34

is a high degree of synchronization of growth cycles between Japan and Hong Kong at long-run fluctuations during the entire sample period. The strength of this comovement increases to all frequencies after 2005. We notice similar characteristics in the comovement between United States and Hong Kong, particularly at lower frequencies.

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Moreover, China and Indonesia illustrate a high degree of comovement at short-run fluctuations in the 1990s and early 2000s. The strength of this comovement begins to decrease at

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frequencies linked with fluctuations that continue more than four years during the entire sample period. We identify comparable attributes in the comovement between the growth cycles of

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United States and Indonesia. Alternatively, we find evidence of business cycle synchronization between Japan and Indonesia at lower frequencies during the entire sample period. Nevertheless,

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the strength of this comovement decreases at intermediate frequencies after 2005. The strength of comovement between the growth cycles of China and Korea increases at higher frequencies in the mid 1990s and at lower frequencies after 2005. Conversely, Japan and

M

Korea display high degree of comovement at frequencies linked with fluctuations that continue more than two years; this is especially the case at the start and conclusion of the sample period.

d

There is however a low degree of comovement at short-run fluctuations in the early 1990s and between 2000 and 2005. In addition, the synchronization of growth cycles between the United

te

States and Korea is the highest at intermediate frequencies, especially after 2005.

Ac ce p

As can be seen, the comovement of growth cycles between China and Malaysia display similar patterns as in the case of China and Korea. In contrast, Japan and Malaysia demonstrate a high degree of business cycle synchronization; this is particularly evident between 2005 and 2010, where the strength of comovement increases to all frequencies. Similarly, the United States and Malaysia also experience a high degree of comovement, however, only at frequencies that range between two and four years during the entire sample period. The strength of this comovement decreases particularly at short-run fluctuations. We also notice a relatively low degree of comovement of growth cycles between China and New Zealand almost at all frequencies. The exception is after 2005, where the strength of this comovement increases at lower frequencies. Japan and New Zealand also exhibit a comparatively low degree of comovement; there is however evidence of business cycle synchronization at higher frequencies toward the conclusion of the sample period. In the case of

14 Page 14 of 34

the United States and New Zealand, the strength of comovement increases at long-run fluctuations during the entire sample period. Next, business cycle synchronization between Japan and Philippines has been high during the entire sample period; this is especially the case at long-run fluctuations. For the United States

ip t

and Philippines, the strength of comovement increases at higher frequencies in the early 1990s and at frequencies linked with fluctuations between two and four years during the entire sample

cr

period. In the case of China and Philippines, there is a comparatively high degree of comovement between the growth cycles at short-run fluctuations during the 2000s. Yet, the

us

strength of this comovement declines at the conclusion of the sample period.

We also observe that business cycle synchronization between China and Singapore has been

an

high predominantly at lower frequencies after 2005. While there is a relatively high degree of comovement between the growth cycles of the United States and Singapore at frequencies linked with fluctuations that continue more than two years, the strength of this comovement weakens at

M

higher frequencies around 2000 and toward the conclusion of the sample period. In general, Japan and Singapore display a high degree of comovement at all frequencies through time, with

d

the exception at short-run fluctuations between 2000 and 2005. Alternatively, Japan and Thailand experience a comparatively low degree of comovement;

te

this is apparent especially at lower frequencies after 2000. Overall, we find parallel facets in the

Ac ce p

comovement of growth cycles between the United States and Thailand. The exception is in the 1990s, where the strength of this comovement is high at frequencies linked with fluctuations between two and four years. In the case of China and Thailand, we notice a high degree of business cycle synchronization during the entire sample period. The degree of comovement is lower however at short-run fluctuations at the start and conclusion of the sample period. The synchronization of growth cycles between China and Taiwan increases at long-run fluctuations, especially after 2000. Furthermore, the United States and Taiwan demonstrate a high degree of comovement; this is particularly present at frequencies linked with fluctuations that continue more than four years during the entire sample period. We observe comparable characteristics in the comovement of growth cycles between Japan and Taiwan, particularly at lower frequencies. Nevertheless, the strength of this comovement declines at higher frequencies in the early 1990s and between 2000 and 2005.

15 Page 15 of 34

In addition, we assess the degree of comovement between the growth cycles of China, Japan and the United States. The strength of comovement between United States and China increases at short-run fluctuations, especially at the start and conclusion of the sample period. In the case of the United States and Japan, there is a high degree of business cycle synchronization at lower

ip t

frequencies. The strength of this comovement weakens at higher frequencies in the 1990s and early 2000s. Also, China and Japan display a high degree of comovement at long-run

cr

fluctuations; the strength of this comovement increases to all frequencies, particularly after 2005. We also notice several interesting patterns when we group the countries. For example,

us

Australia and New Zealand display a high degree of comovement with the United States at intermediate frequencies. Likewise, Indonesia, Malaysia, Philippines and Thailand experience a

an

high degree of comovement with the United States at frequencies that range between two and four years. Moreover, the strength of comovement between China and Hong Kong, Korea, Singapore and Taiwan has been high at long-run fluctuations, particularly after 2005. A similar

M

pattern is displayed between these countries and Japan and the United States but for the entire sample period.

d

Lastly, we overall note that there is a relatively low degree of comovement for different country pairs at short-run fluctuations. One possibility is that extremely short-run fluctuations are

te

idiosyncratic (see Rua, 2010). This finding is in line with Rua (2010), who shows that the

Ac ce p

strength of business cycle synchronization has been low at short-run developments for different country pairs in the Euro region.

In general, while we find that the growth cycles of China, Japan and the United States are synchronized with other Asia-Pacific countries, the strength of business cycle synchronization fluctuates significantly across frequencies and over time. These results are broadly consistent with Moneta and Rüffer (2009), Fidrmuc and Korhonen (2010) and Allegret and Essaadi (2011). For example, Moneta and Rüffer (2009) find that the strength of business cycle synchronization varies across time, whereas Fidrmuc and Korhonen (2010) and Allegret and Essaadi (2011) show that the comovement of growth cycles fluctuates across frequencies in Asia. Moreover, our results illustrate that the degree of comovement between the growth cycles varies across different countries pairs in our time frequencies analysis. Besides, previous research documents that the degree of synchronization of growth cycles varies across frequencies and over time (see, for example, Rua, 2010; Aguiar-Conraria and Soares, 2011a). Employing 16 Page 16 of 34

wavelet analysis, both Rua (2010) and Aguiar-Conraria and Soares (2011a) demonstrate that there is a considerable amount of variation in the comovement of growth cycles in the Euro region across frequencies and over time. Although the degree of comovement of growth cycles fluctuate significantly across

ip t

frequencies and over time for different country pairs in Figures 2-4, we nevertheless observe that overall Japan experiences a stronger comovement with the other Asia-Pacific countries as

cr

compared to China and the United States.

In summary, there is a relatively high degree of comovement between China and most other

us

Asia-Pacific economies at lower frequencies toward the conclusion of the sample period. In the case of Japan and other Asia-Pacific countries, the strength of business cycle synchronization

an

increases at long-run fluctuations for the entire sample period. Allegret and Essaadi (2011: 352) show that “China and Japan share common movements with the rest of Asian countries”, while Moneta and Rüffer (2009) find that China and Japan display a high degree of comovement in

M

exports with other Asian countries. The United States and other Asia-Pacific countries mostly

Conclusion

te

5.

d

display a high degree of comovement at frequencies that range between two and four years.

We examine the synchronization of growth cycles between China, Japan, the United States

Ac ce p

and other Asia-Pacific economies across time and frequencies using a wavelet-based measure of comovement. We find that the degree of comovement of growth cycles varies significantly across frequencies and over time.

Overall, China and other Asia-Pacific countries experience a high degree of comovement of growth cycles at lower frequencies, particularly toward the conclusion of the sample period (the exceptions are for Australia, Indonesia and Philippines). This finding suggests that the strength of business cycle synchronization between China and most other Asia-Pacific countries increases at long-run fluctuations, especially during and following the recent global financial crisis. Moreover, we find evidence of business cycle synchronization between Japan and other Asia-Pacific economies at long-run fluctuations for the entire sample period (the exceptions are for Australia, Thailand and New Zealand). In general, there is a relatively low degree of comovement between the growth cycles of Japan and other Asia-Pacific countries at short-run fluctuations between 1995 and 2005. 17 Page 17 of 34

In the case of the United States and other Asia-Pacific economies, there is a relatively high degree of comovement of growth cycles at frequencies linked with fluctuations that range between two and four years. Overall, there is a comparatively low degree of comovement between the growth cycles of the United States and other Asia-Pacific countries at higher

ip t

frequencies in the 1990s and early 2000s.

In summary, our evidence suggests that there is considerable amount of heterogeneity in the

cr

degree of business cycle synchronization between China, Japan, the United States, and other Asia-Pacific economies across frequencies and over time. We therefore emphasize the

us

importance of investigating the degree of comovement between the growth cycles of different

Ac ce p

te

d

M

an

country pairs in the time-frequency framework.

18 Page 18 of 34

Acknowledgements

Ac ce p

te

d

M

an

us

cr

ip t

We thank the editor and two anonymous referees for their helpful comments and suggestions. We are also grateful to Dr. António Rua for kindly providing us with the codes. An earlier version of this paper was circulated under the title “How synchronized is China with the other Asia-Pacific countries? Evidence from wavelet analysis.” Aziz N. Berdiev gratefully acknowledges the financial support from the Center for Global and Regional Economic Studies, Bryant University. Chun-Ping Chang is grateful to the National Science Council of Taiwan for financial support through grant NSC 102-2410-H-158-001. All remaining errors are our own.

19 Page 19 of 34

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23 Page 23 of 34

Max 8.906 2.606 2.729 5.497 1.461 2.901 2.972 2.956 2.202 6.677 4.343 3.011 1.871

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te

d

M

an

Source: Authors’ calculations.

Observations 79 79 79 79 79 79 79 78 79 79 79 79 79

ip t

Min -6.488 0.068 -2.149 -10.95 -2.400 -2.096 -3.046 -0.632 -0.857 -2.156 -25.13 -1.986 -2.135

cr

Std. Dev. 3.973 0.432 1.021 2.279 0.620 0.960 1.140 0.617 0.508 1.441 4.479 0.957 0.644

us

Table 1: Descriptive Statistics Country Mean China 2.679 Australia 0.909 Hong Kong 0.953 Indonesia 1.773 Japan 0.212 Korea 1.187 Malaysia 1.329 New Zealand 0.767 Philippines 1.084 Singapore 1.572 Thailand -0.071 Taiwan 1.114 United States 0.624

24 Page 24 of 34

ip t cr

Malaysia New Zealand Philippines Singapore Thailand

**

*

Taiwan

us

Korea

M an

Table 2: Country Correlations China Australia Hong Kong Indonesia Japan Australia -0.093 Hong Kong 0.034 0.005 Indonesia 0.124 -0.176 0.357** Japan 0.038 0.215 0.678** 0.072 ** 0.451** 0.431** Korea 0.052 -0.092 0.625 Malaysia 0.024 0.092 0.783** 0.382** 0.608** ** ** New Zealand -0.012 0.253 0.347 0.056 0.311** * ** ** Philippines 0.111 0.208 0.715 0.323 0.638** 0.141 0.637** Singapore 0.026 -0.033 0.703** * Thailand 0.021 0.064 -0.210 -0.007 -0.248** ** Taiwan 0.063 0.134 0.622 -0.031 0.649** United States 0.342** 0.033 0.455** -0.002 0.767**

0.805** 0.529** 0.431** 0.515** -0.051 0.477** 0.656**

0.460** 0.667** 0.620** -0.112 0.565** 0.124

0.123 0.274** 0.230** 0.389** 0.474**

0.480** -0.386** 0.394** 0.554**

-0.485** 0.809** 0.878**

-0.332** 0.004

-0.534**

Ac

ce pt

ed

Notes: and denotes statistical significance at the 5% and 10% level, respectively. Source: Authors’ calculations.

25 Page 25 of 34

ip t cr

9.443 (0.001)*** 12.003 (0.001)*** 5.009 (0.002)*** 4.909 (0.001)*** 21.837 (0.001)*** 5.938 (0.002)*** 12.039 (0.001)*** 10.929 (0.001)*** 4.009 (0.002)*** 11.009 (0.001)*** 7.028 (0.001)***

us

Japan Japan vs. Australia Japan vs. Hong Kong Japan vs. Indonesia Japan vs. Korea Japan vs. Malaysia Japan vs. New Zealand Japan vs. Philippines Japan vs. Singapore Japan vs. Thailand Japan vs. Taiwan Japan vs. USA

M an

Table 3: Likelihood ratio tests China China vs. Australia 6.573 (0.001)*** China vs. Hong Kong 7.346 (0.001)*** China vs. Indonesia 5.036 (0.002)*** China vs. Japan 11.833 (0.001)*** China vs. Korea 10.213 (0.001)*** China vs. Malaysia 8.209 (0.001)*** China vs. New Zealand 7.075 (0.002)*** China vs. Philippines 9.933 (0.001)*** China vs. Singapore 7.065 (0.001)*** China vs. Thailand 15.209 (0.002)*** China vs. Taiwan 14.756 (0.001)*** China vs. USA 4.299 (0.001)***

USA USA vs. Australia USA vs. Hong Kong USA vs. Indonesia USA vs. Korea USA vs. Malaysia USA vs. New Zealand USA vs. Philippines USA vs. Singapore USA vs. Thailand USA vs. Taiwan

16.093 (0.001)*** 12.445 (0.001)*** 5.309 (0.002)*** 6.993 (0.001)*** 12.393 (0.001)*** 5.393 (0.002)*** 6.923 (0.001)*** 15.445 (0.001)*** 12.098 (0.002)*** 8.345 (0.001)***

Ac

ce pt

ed

Notes: The likelihood ratio test investigates the null hypothesis of constant correlations (Bollerslev, 1990) against the alternative of time-varying correlations (Bollerslev et al., 1988). The p-values are in parenthesis. *** denotes statistical significance at the 1% level. Source: Authors’ calculations.

26 Page 26 of 34

ip t

AUS

CHN

2.5

3

1.0

et ar ht w or g P D G

4 0 -4

0.5 0.0 96

98

00

02

04

06

08

10

12

0

-1

-3

94

96

98

00

JPN

02

04

06

08

10

12

94

3

98

00

02

04

06

08

10

94

-1 -2

1 0

-2

-3

-3 94

96

98

00

02

04

06

08

10

et ar ht w or g P D G

-1

12

94

96

98

00

02

04

06

10

-2

04

06

08

10

12

04

06

08

10

12

06

08

10

12

1

0

-1 94

96

98

00

02

04

06

08

10

12

94

96

98

00

THA

8

02

2 et ar ht w or g P D G

0

12

00

NZL

-4 08

98

3

SGP

3

ce pt

PHL

ed

0

96

MYS

2

et ar ht w or g P D G

-8

12

4

2

1

0 -4

-12 96

KOR

2

et ar ht w or g P D G

-2

-8 94

4

1

M an

1.5

IDN 8

2

8 et ar ht w o gr P D G

2.0

et ar ht w or g P D G

HKG

12

us

3.0

et ar ht w or g P D G

cr

Figure 1: Quarterly Real GDP Growth Rates

02

TWN

10

4

6

2 et ar ht w or g P D G

et ar ht w or g P D G

1

0

0 et ar ht w -10 or g P D G -20

4 2 0

2 et ar ht w or g P D G

0

-2

-2

-1

-4

96

98

00

02

04

06

08

10

12

94

96

98

00

02

-30 04

06

08

10

12

-4 94

96

98

00

02

04

06

08

10

12

94

96

98

00

02

04

Ac

94

USA 2 1 et ar ht w or g P D G

0 -1 -2 -3 94

96

98

00

02

04

06

08

10

12

Notes: Quarterly Real GDP Growth Rates in 13 Countries over the period 1993:2-2012:4. Source: Authors’ calculations.

27 Page 27 of 34

ip t

Figure 2: Comovement between the growth cycles of China and other Asia-Pacific countries. CHN vs HKG 0.7 0.6 0.4

us

0.5 1

1

0.2 0.1 0 2

-0.1 -0.2 -0.3 -0.4

) sr a ey n(i y c n e uq er F

-0.5

4

M an

0.3 ) sr a ey n(i y c n e uq er F

2

4

-0.6 -0.7 -0.8 2000

2005

2010

1995

Time CHN vs JPN

1

2

Ac

) sr a ey n(i y c n e qu er F

2005

4

1995

2000

2005 Time

2010

0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

) sr a ey n(i y c n e uq er F

2

4

1995

2000

2005 Time

CHN vs KOR

CHN vs MYS

2010

0.7

0.6

0.6

0.5

0.5

0.4 1

0.4 0.3 0.2 0.1

2

0 -0.1 -0.2 -0.3

4

1995

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

1

2010

1

) sr a ey n(i y c n e qu er F

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9

Time

ce pt

0.8 0.7 0.6 0.5 0.4 0.3 0.2

2000

ed

1995

CHN vs IDN

cr

CHN vs AUS

2000

2005 Time

2010

) sr a ey n(i y c n e qu er F

0.3 0.2 0.1 0

2

-0.1 -0.2 -0.3 -0.4

4

-0.4

-0.5

-0.5

-0.6 1995

2000

2005

2010

Time

Notes: The vertical axis denotes the frequency, which is measured in time units, i.e., years. The horizontal axis represents the time period of the analysis: 1993:2-2012:4. The final dimension – the grayscale – evaluates the strength of comovement between the two time series. Thus, a rise in the darkness in the grayscale refers to a higher value of the wavelet-based measure of comovement between the growth cycles. Source: Authors’ calculations.

28 Page 28 of 34

CHN vs NZL

CHN vs PHL 0.7

us

0.6 0.5 0.4

1

1

0.2 0.1 0

2

-0.1 -0.2 -0.3

) sr a ey n(i y c n e qu er F

M an

0.3 ) sr a ey n(i y c n e qu er F

2

-0.4 4

4

-0.5 -0.6

2000

2005

2010

1995

Time CHN vs THA

2000

2005

Ac

2

4

1995

2000

2005 Time

2010

0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9

CHN vs SGP 0.8 0.7 0.6 0.5

1

0.4 ) sr a ey n(i y c n e qu er F

0.3 0.2 0.1 2

0 -0.1 -0.2 -0.3 -0.4

4

-0.5 -0.6 -0.7 1995

2000

2005

2010

Time

CHN vs TWN 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9

2

4

1995

0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

2010

1

) sr a ey n(i y c n e uq er F

0.8 0.7 0.6 0.5 0.4 0.3 0.2

Time

ce pt

0.7 0.6 0.5 0.4 0.3 0.2 0.1

1 ) sr a ey n(i y c n e uq er F

ed

-0.7 1995

ip t

cr

Figure 2: (continued)

2000

2005

2010

Time

29 Page 29 of 34

ip t

Figure 3: Comovement between the growth cycles of Japan and other Asia-Pacific countries. JPN vs HKG

2

4

1995

2000

2005

) sr a ey n(i y c n e qu er F

2

4

2010

1995

Time JPN vs KOR

2000

2005

Ac

2

4

1995

2000

2005 Time

2010

0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7

0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7

0.7 0.6 0.5

1

0.4 ) sr a ey n(i y c n e qu er F

0.3 0.2 0.1 2

0 -0.1 -0.2 -0.3 -0.4

4

-0.5 -0.6 -0.7 1995

2000

2005 Time

JPN vs MYS

JPN vs NZL 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7

2

4

1995

0.8

2010

1

) sr a ey n(i y c n e qu er F

0.9 0.8 0.7 0.6 0.5 0.4 0.3

Time

ce pt

0.9 0.8 0.7 0.6 0.5 0.4 0.3

1 ) sr a ey n(i y c n e qu er F

1

ed

) sr a ey n(i y c n e qu er F

us

1

M an

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9

JPN vs IDN

cr

JPN vs AUS

2000

2005 Time

2010

2010

0.8 0.7 0.6 0.5

1

0.4 ) sr a ey n(i y c n e qu er F

0.3 0.2 0.1 2

0 -0.1 -0.2 -0.3 -0.4

4

-0.5 -0.6 -0.7 1995

2000

2005

2010

Time

Notes: The vertical axis denotes the frequency, which is measured in time units, i.e., years. The horizontal axis represents the time period of the analysis: 1993:2-2012:4. The final dimension – the grayscale – evaluates the strength of comovement between the two time series. Thus, a rise in the darkness in the grayscale refers to a higher value of the wavelet-based measure of comovement between the growth cycles. Source: Authors’ calculations.

30 Page 30 of 34

JPN vs SGP

2

4

1995

2000

2005

2010

) sr a ey n(i y c n e qu er F

2

4

1995

Time JPN vs TWN 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

0.6

0.8

0.5

2000

2005 Time

2010

0.4

0.6

0.3

1

0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4

0.2 ) sr a ey n(i y c n e qu er F

0.1 0 -0.1 2

-0.2 -0.3 -0.4 -0.5 -0.6

4

-0.7

-0.5

-0.8

-0.6

-0.9 1995

2000

2005

2010

Time

ce pt

1

2

Ac

) sr a ey n(i y c n e qu er F

us

) sr a ey n(i y c n e qu er F

1

ed

1

0.9 0.7

M an

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

JPN vs THA

cr

JPN vs PHL

ip t

Figure 3: (continued)

4

1995

2000

2005

2010

Time

31 Page 31 of 34

ip t

Figure 4: Comovement between the growth cycles of the United States and other Asia-Pacific countries. USA vs CHN 0.8

0.8 0.7

0.5

us

0.6 1

0.3 0.2 0.1 2

0 -0.1 -0.2 -0.3

) sr a ey n(i y c n e qu er F

-0.4

4

M an

0.4 ) sr a ey n(i y c n e qu er F

2

4

-0.5 -0.6 -0.7 2000

2005

2010

1995

Time USA vs IDN

2005

Ac

2

4

1995

2000

2005 Time

2010

0.4 0.3 0.2 0.1 0 -0.1 -0.2

) sr a ey n(i y c n e qu er F

-0.3

0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

2

4

-0.4 -0.5 -0.6

1995

2000

2005 Time

USA vs JPN

USA vs KOR 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

2

4

1995

1

0.5

2010

1

) sr a ey n(i y c n e qu er F

0.6

Time

ce pt

1 ) sr a ey n(i y c n e qu er F

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9

2000

ed

1995

0.8 0.7 0.6 0.5 0.4 0.3 0.2

0.9

0.7

1

USA vs HKG

cr

USA vs AUS

2000

2005 Time

2010

2010

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8

1 ) sr a ey n(i y c n e qu er F

2

4

1995

2000

2005

2010

Time

Notes: The vertical axis denotes the frequency, which is measured in time units, i.e., years. The horizontal axis represents the time period of the analysis: 1993:2-2012:4. The final dimension – the grayscale – evaluates the strength of comovement between the two time series. Thus, a rise in the darkness in the grayscale refers to a higher value of the wavelet-based measure of comovement between the growth cycles. Source: Authors’ calculations.

32 Page 32 of 34

USA vs NZL 0.7 0.6 0.4

1

0.2 0.1 0

2

-0.1 -0.2 -0.3

) sr a ey n(i y c n e qu er F

M an

0.3 ) sr a ey n(i y c n e qu er F

2

-0.4 4

4

-0.5 -0.6 -0.7 2000

2005

2010

1995

Time USA vs SGP

1

2

Ac

) sr a ey n(i y c n e qu er F

4

1995

2000

2005 Time

2010

0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7

0.8

0.6

0.7

2005

0.5

1

0.3 0.2 0.1 0 -0.1 -0.2 -0.3

0.4 ) sr a ey n(i y c n e qu er F

0.3 0.2 0.1

2

0 -0.1 -0.2

-0.4

-0.3 4

-0.5

-0.4

-0.6

-0.5

-0.7

-0.6

2010

1995

2000

2005

2010

Time

USA vs THA

USA vs TWN 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9

0.7 0.6 0.5 0.4

1

) sr a ey n(i y c n e qu er F

0.6

0.4

Time

ce pt

0.9 0.8 0.7 0.6 0.5 0.4 0.3

2000

ed

1995

0.7 0.5

us

0.5 1

USA vs PHL

cr

USA vs MYS

ip t

Figure 4: (continued)

1

0.3 0.2 0.1 0

2

-0.1 -0.2 -0.3 -0.4 -0.5

4

-0.6

) sr a ey n(i y c n e qu er F

2

4

-0.7 -0.8 1995

2000

2005 Time

2010

1995

2000

2005

2010

Time

33 Page 33 of 34

ip t

ce pt

ed

M an

us

cr

We study business cycle synchronization in Asia-Pacific. Specifically, we assess the comovement of growth cycles using wavelet analysis. The comovement between China, Japan, USA and other Asia-Pacific economies. We find that the degree of comovement fluctuates across frequencies and over time. We emphasize the importance of examining comovement using a time-frequency framework.

Ac

1. 2. 3. 4. 5.

34 Page 34 of 34