Abstract
This study investigates the existence of long-run comovement in the returns of local-currency-denominated bonds of ASEAN-5 countries (Indonesia, Malaysia, the Philippines, Singapore, and Thailand). We explore the pairwise cointegration between Asian local currency bond returns indices using stepwise multiple testing. This helps to identify which pairs of bond indices are cointegrated, while avoiding over-rejection of the null hypothesis or the multiplicity problem. This method is adjusted to deal with possible cross-sectional correlation among the countries. In addition, we assume linear as well as nonlinear models in order to capture potential gradual and asymptotic adjustment of a linear combination of bond indices toward its mean. We find long-term stable relationships among local currency bond returns for some pairs of countries. Specifically, close interlinkages captured as nonlinear cointegration are evident for at least four pairs of countries, namely Indonesia and the Philippines, Malaysia and the Philippines, the Philippines and Thailand, and Singapore and Thailand. In addition, a relatively weak but significant relationship between Malaysia and Thailand is found. Although the adjustment process toward long-run market equilibrium is characterized by the linear model, comovement in bond returns is observed between Malaysia and Singapore.
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Notes
The ABMI is the brainchild of the finance ministers of the ASEAN+3, which includes the ASEAN-5 countries (Indonesia, Malaysia, the Philippines, Thailand, and Singapore), Japan, China, and Korea. The purpose of the ABMI is to build the required financial infrastructure to serve both government and nongovernment bond markets in the region. The ABF 1 is a project launched by the 11 member countries of the Executives’ Meeting of East Asia and Pacific Central Banks (EMEAP), which is a cooperative organization of central banks and monetary authorities in the region. To make Asian bonds more liquid in Asian bond markets, the EMEAP has developed investment trusts based on sovereign bonds and quasi-sovereign bonds of its member economies. In addition, the ABF 2 was established as an extension of the ABF 1 in mid-2005. While the ABF 1 focuses on dollar-denominated bonds, the ABF 2 develops local-currency-denominated bonds (see also Chan et al. 2012).
The Asian bond returns index is based on the HSBC Asian Local Bond Index (ALBI).
For example, Im et al.’s (2003) panel unit root test permits heterogeneous coefficients under the alternative model. However, its acceptance only reveals that at least one of the series being tested is stationary. In addition, in Pedroni’s (2004) group mean cointegration test, the heterogeneity of coefficients is assumed under the alternative; however, the rejection of the null hypothesis means only that cointegration occurs for some cross-sectional units.
For example, there are 10 individual tests, and each test is conducted independently at the 5 % significance level. Let \(T_i \) and \(c_i \) (\(i=1,\ldots ,10\)) be the test statistics, being mutually independent and critical values corresponding to the 10 null hypotheses, respectively, where \(\Pr (T_i \ge c_i)=0.05\) for all i. In this case, if \(T_i \ge c_i \), the corresponding null hypothesis is rejected. If all the null hypotheses are true, the probability of rejecting at least one hypothesis in the entire test is
$$\begin{aligned}&\Pr \left\{ {(T_1 \ge c_1 )\cup (T_2 \ge c_2)\cup \cdots \cup (T_{10} \ge c_{10})} \right\} \\&\quad =1-\Pr \left\{ {(T_1 <c_1)\cap (T_2 <c_2)\cap \cdots \cap (T_{10} <c_{10})} \right\} \\&\quad =1-\Pr (T_1 <c_1)\Pr (T_2 <c_2)\cdots \Pr (T_{10} <c_{10})\\&\quad =1-0.95^{10}=0.4013. \end{aligned}$$The familywise error rate (= 0.4013) is much higher than the nominal size of each individual test (= 0.05).
Kim et al. (2009) applied a similar concept to Asian stock price indices.
One example of the failure of the transitivity property is as follows. Consider markets A and B, which are cointegrated with market C. The bilateral cointegration between markets A and B is not detected by the Johansen test when market C is not included. This issue may be caused by the enhanced variance of error terms contained in the series of markets A and B. See Ferré (2004).
A globally covariance stationary process is defined as follows. Let \(\{{y_t}\}\) be a random sequence such that \(E(y_t^2)<\infty \) for \(t=1,\ldots ,T\) and define \(\eta _T \equiv Var(T^{-1/2}\sum _{t=1}^T {y_t})\). If \(\eta \equiv \mathop {\lim }\nolimits _{T\rightarrow \infty } \eta _T \) exists and is finite, \(\{{y_t}\}\) is globally covariance stationary (see White 2001, p. 176).
On the other hand, Narayan’s (2005) threshold autoregressive specification was weakly supported in terms of rejection of the unit root null hypothesis for stock price indices.
The maximum lag order is determined by \(\bar{{k}}=[12(T/100)^{1/4}]\). The same definition is used to determine the maximum lag order in Eq. (4).
This discussion is only valid asymptotically under the null hypothesis because in this case, the p values are based on the asymptotic null distribution.
Paparoditis and Politis (2003) proposed a residual-based block bootstrap, which effectively generates unit root processes that consist of a wide class of weakly dependent processes. In addition, Palm et al. (2011) showed the validity of the multivariate extension of Paparoditis and Politis’ block bootstrap procedure for panel unit root tests in dependent panel settings. In contrast, Smeekes and Urbain’s (2014) simulation results suggested the occurrence of size distortion in panel unit root tests based on the autoregressive (AR) sieve bootstrap in cross-sectionally dependent panels. This study, however, follows Palm et al.’s (2011) bootstrap algorithm, the application of which seems to be more appropriate for our data. In addition, Hanck (2009) utilized the bootstrap method to conduct the Romano and Wolf (2005) stepwise multiple testing procedures and validly implemented the test. Furthermore, Matsuki and Sugimoto (2013) investigated the small sample performance (in terms of familywise error rates and average powers) of block bootstrap-based multiple tests for a unit root in nonstationary panels, showing the validity of the tests and improved performance compared with the repeated use of individual unit root tests.
\(y_{i^{\prime },t}^d =y_{i^{\prime },t} -{\hat{{\mathbf{a}}}_{i^{\prime }}}^{{\prime }} d_t \), where \(\hat{{\mathbf{a}}}_{i^{\prime }} \) is the estimated coefficient vector obtained by regressing \(y_{i^{\prime },t}\) on \(d_t =(1,\;t)^{\prime }\) (Smeekes (2013)). In addition, when the equation \(\Delta y_{i^{\prime },t}^d =\hat{{\pi }}_{i^{\prime }} y_{i^{\prime },t-1}^d +\varepsilon _{i^{\prime },t}^d \) is estimated, the lag variables \(\Delta y_{i^{\prime },t-p}^d (p=1,\ldots ,\bar{{p}}_{\max })\) are added to get rid of the serial correlation of \(\varepsilon _{i^{\prime },t}^d \), where the maximum lag order \(\bar{{p}}_{\max } \) is set at \([12(T/100)^{1/4}]\) and the optimum one is determined by the MAIC for each \(i^{\prime }\). Due to this augmentation, the actual sample size in the time dimension is \(T-\bar{{p}}_{\max } \). For the sake of simplicity, these descriptions are omitted from the text.
This is calculated as \(b_l =1.75T^{1/3}\), similar to Palm et al. (2011).
For the NEG test, when the series is assumed to have a nonzero mean or time trend, it is demeaned or detrended before the estimation of Eq. (1).
There are numerous other multiple testing procedures that control the familywise error rate at a prespecified significance level \(\alpha \) (e.g., 5 or 10 %), such as those based on the Bonferroni inequalities and improved by Holm (1979) and Simes (1986). One of the advantages of using multiple testing methods is to be able to consider an unknown correlation structure among data (or test statistics or their p values), controlling the familywise error rate. Further, Hochberg and Tamhane (1987) and Tamhane (1996) conducted comprehensive surveys on multiple testing methods and other related topics (see also Footnote 28).
Ng (2008) proposed a new method for determining the ratio of I(0) to I(1) in mixed panels. This method is based on the existence of a time trend in the variances of nonstationary series. However, it does not consider nonlinearity in a series.
This replacement follows Remark 3.4 in Romano and Wolf (2005).
Two other cases \(( {\sigma _{13} ,\sigma _{23}})=( {-0.5, 0.0} )\) and \(( {0.0, -0.5})\) were simulated as well. The characteristics of the small sample properties were mostly unchanged.
This method takes only one bootstrap draw for each simulated sample in a Monte Carlo experiment to approximate the statistic of interest.
For the cases of \({N}^{\prime }\) = 3 and 7, the results are available on request for the author.
From the figures for the pairs of IND–MAL, IND–SIN, and IND–THA, there seems to be a temporary sharp drop of the mean in each residual in late 2008 or early 2009. However, asymptotically, as long as the magnitude of such a drop, which is normally expressed as the coefficient of a temporary dummy variable, is constant over time or at order O(1), this type of a temporary mean shift in a time series does not affect the limiting distribution of the linear and nonlinear EG tests under the null hypothesis. The proof is available on request. By contrast, the existence of such a shift in finite samples may not be negligible in the hypothesis test. Whether this could lead to over- or under-rejection of the null hypothesis by the tests depends on the stochastic property of the time series, that is, I(1) or I(0) (see Perron 1989; Leybourne et al. 1998). Therefore, we may have to interpret the results of the tests in the following subsections for the three above-mentioned pairs from a conservative viewpoint.
From Fig. 1, the bond returns index of Indonesia shows an obvious upward tendency, which means that it has a linear time trend; therefore, we draw the figures for the residuals of all pairs from Eq. (1) using the detrended bond index series. As a result, there is no trending movement in the pairs of the bond series. The figures are available on request.
In addition, as a preliminary investigation, we applied Terasvirta’s (1994) nonlinearity test to the residuals for the 10 pairs of bond indices. As a result, except for the IND–THA pair, for at least one of three types of data: raw, demeaned, or detrended data, the linearity hypothesis for the residuals was rejected at the 5 % or lower significance level for all country pairs.
The sample correlation matrices of the bootstrapped EG or NEG statistics calculated by Algorithm 1 indicate nonzero coefficients for all the pairs.
In addition, we apply Bonferroni’s and Holm’s (1979) multiple testing procedures to the same data. As a result, no null hypothesis is rejected in either test at the 10 % significance level. As Hanck (2013) discussed the validity of Simes’ (1986) method under general patterns of cross-sectional dependence, we also conduct this test. However, we obtain no rejection of the no-cointegration null hypothesis. These testing methods allow for an unknown or more general correlation structure among series in panels, but are conservative in the sense that they do not necessarily reach the predetermined bound of the familywise error rate (see Romano and Wolf 2005, pp. 1243–1244). However, as Westfall and Young (1993) and Romano and Wolf (2005) suggest that accounting for the underlying correlation structure should increase power, the bootstrap method, which is one of the effective ways of improvement, has been used in the multiple testing framework. This study follows this approach.
These amounts were small proportions of the total (i.e., 3.5 % for Indonesia and 3 % for Malaysia), but they were comparable to those of some developed countries, such as Germany, France, and Australia.
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I would like to thank the anonymous referees and Ming-Jen Chang for their helpful comments.
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Matsuki, T. Linear and nonlinear comovement in Southeast Asian local currency bond markets: a stepwise multiple testing approach. Empir Econ 51, 591–619 (2016). https://doi.org/10.1007/s00181-015-1020-1
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DOI: https://doi.org/10.1007/s00181-015-1020-1