Minxian Yang

Asymmetric Volatility in the Foreign Exchange Markets

We examine the presence or absence of asymmetric volatility in the exchange rates of Australian dollar (AUD), Euro (EUR), British pound (GBP) and Japanese yen (JPY), all against US dollar. Our investigation is based on a variant of the heterogeneous autoregressive realized volatility model, using daily realized variance and return series from 1996 to 2004. We find that a depreciation against USD leads to significantly greater volatility than an appreciation for AUD and GBP, whereas the opposite is true for JPY. Relative to volatility on days following a positive one-standard-deviation return, volatility on days following a negative one-standard-deviation return is higher by 6.6% for AUD, 6.1% for GBP, and 21.2% for JPY. The realized volatility of EUR appears to be symmetric. These results are robust to the removal of jump component from realized volatility and the sub-samplings defined by structural-changes. The asymmetry in AUD, GBP and JPY appears to be embedded in the continuous component of realized volatility rather than the jump component.

SOME PROPERTIES OF VECTOR AUTOREGRESSIVE PROCESSES WITH MARKOV-SWITCHING COEFFICIENTS

Some statistical properties of a vector autoregressive process with Markov-switching coefficients are considered. Sufficient conditions for this nonlinear process to be covariance stationary are given. The second moments of the process are derived under the conditions. The autocovariance matrix decays at exponential rate, permitting the application of the law of large numbers. Under the stationarity conditions, although sharing the “mean-reverting†property with conventional linear stationary processes, the process offers richer short-run dynamics such as conditional heteroskedasticity, asymmetric responses, and occasional nonstationary behavior.

On The Size And Power Of System Tests For Cointegration

System tests for cointegration proposed by Stock and Watson (1988), Johansen (1988), and Bewley and Yang (1995) are compared using Monte Carlo experiments that include overspecification of the lag length and data-generating processes with moving average disturbances. Both AIC and SIC are used to select the lag length of the approximating vector autoregressions. The three tests considered are found to have very different characteristics, and each dominates in some portion of the parameter space.

Comparison of Box--Tiao and Johansen canonical estimators of cointegrating vectors in VEC(1) models

Abstract The Box—Tiao (1977) and Johansen (1988) approaches to estimating cointegrating vectors are compared and small-sample properties of the estimators are evaluated in Monte Carlo experiments for bivariate first-order models. In models without drift, the distributions of the Box—Tiao estimator are found to be less dispersed and leptokurtic in a variety of interesting cases. The presence of drift induces asymptotic normality in both estimators and again the distributions of the Box—Tiao estimator are often less dispersed in small samples.

Tests for Cointegration Based on Canonical Correlation Analysis

Abstract Critical values are provided for four new tests for cointegration based on the canonical correlations and variates of a development of the Box-Tiao procedure. It is found that in finite samples the power of three of these tests, unlike the power of Johansens and Engle and Yoos tests, is highly robust to the correlation between the disturbances in the cointegrating relationships and those generating the common trends. The proposed tests perform well against these alternatives, but neither set of tests dominates over the entire parameter space.

Normal log-normal mixture, leptokurtosis and skewness

The normal log-normal mixture (NLNM) is considered for modelling leptokurtosis and skewness. The moment of the mixture is shown to be finite for any positive order. The expectations of exponential functions of the NLNM variable are also investigated. The kurtosis and skewness of the NLNM are explicitly shown to be determined by the variance of the log normal and the correlation between the normal and log normal. A set of cross-sectional data is fitted to the NLNM to illustrate that idiosyncratic variances may be modelled by the mixture.

On identifying permanent and transitory shocks in VAR models

Abstract A simple procedure to identify the groups of permanent and transitory shocks in a cointegrated VAR model is suggested and a method for inverting the cointegrated VAR is provided.

Moving average conditional heteroskedastic processes

Abstract MACH processes are proposed to model volatile time series where effects of shocks on conditional variance are transitory.

On Identifying Structural VAR Models via ARCH Effects

In the framework of structural VAR models with ARCH effect, we show that a sufficient condition for the local identification of a structural model is that at most one structural shock is homoskedastic. Our approach is based on a result of Rothenberg (1971).

On cointegration tests for VAR models with drift

Abstract Following Bewley and Yang ( Journal of the American Statistical Association , 1995, 90, 990–996), this paper considers cointegration tests that are based on the canonical correlation analysis (CCA) of Box and Tiao ( Biometrika , 1977, 64, 355–365), for VAR models with drift. The critical values of the test statistics are shown to depend on the presence of drift. In addition, it is shown that the maximum eigenvalue from the CCA may be used as an indicator for the presence of drift. Tables of critical values are also presented.