Albert K. Tsui

A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations

In this article we propose a new multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) model with time-varying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. Whereas each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analog. Our new model retains the intuition and interpretation of the univariate GARCH model and yet satisfies the positive-definite condition as found in the constant-correlation and Baba–Engle–Kraft–Kroner models. We report some Monte Carlo results on the finite-sample distributions of the maximum likelihood estimate of the varying-correlation MGARCH model. The new model is applied to some real data sets.

Evaluating the hedging performance of the constant-correlation GARCH model

This paper compares the performances of the hedge ratios estimated from the OLS (ordinary least squares) method and the constant-correlation VGARCH (vector generalized autoregressive conditional heteroscedasticity) model. These methods are evaluated based on the out-of-sample optimal hedge ratio forecasts. A systematic comparison is provided by examining ten spot and futures markets covering currency futures, commodity futures and stock index futures. Using a recently proposed test (Tse, 2000) for the constant-correlation assumption, it is found that the assumption cannot be rejected for eight of the ten series. To gain the maximum benefit of a time-varying hedging strategy the estimation data is kept up-to-date for the re-estimation of the hedge ratios. Both the constant hedge ratio (using OLS) and the timevarying hedge ratio (using constant-correlation VGARCH) are re-estimated on a day-by-day rollover, and the post-sample variances of the hedged portfolios are examined. It is found that the OLS hedge ratio performs better than the VGARCH hedge ratio. This result may be another indication that the forecasts generated by the VGARCH models are too variable.

Constant conditional correlation in a bivariate GARCH model: evidence from the stock markets of China

In this paper we examine the behaviour of stock returns in two emerging markets of China. These are the Shanghai and Shenzhen markets. It is found that both markets suffer from negative mean returns on Monday and Tuesday, but positive returns on Friday. In addition, we employ the bivariate GARCH model of Bollerslev [T. Bollerslev, Review of Economics and Statistics 72 (1990) 498–505] to capture the co-movements of stock returns between the markets. However, the information matrix test statistic does not support the null hypothesis of a constant conditional correlation in the stock returns.

Conditional Volatility in Foreign Exchange Rates: Evidence from the Malaysian Ringgit and Singapore Dollar

Abstract In this paper we examine the conditional volatility of the exchange rates of two Asia-Pacific currencies. These are the Malaysian ringgit-US dollar and the Singapore dollar-US dollar exchange rates. Both currencies are under relatively intervention-free managed-float systems. We employ the new class of APARCH model of Ding et al. (1993) to capture the possibly asymmetric effects of exchange shocks on future volatilities. In addition, we take account of the nonnormality in the residuals by using f-distributed errors . Similar to the findings for the major currencies under flexible exchange rate systems, the exchange rates of the two Asia-Pacific currencies demonstrate conditional heteroscedasticity and are adequately described by the APARCH model. We also find that a depreciation shock in the Malaysian ringgit against the US dollar has a greater effect on future volatilities than an appreciation shock of the same magnitude. However, such asymmetric effects are not significant in the Singapore market.

A Note on Diagnosing Multivariate Conditional Heteroscedasticity Models

In this paper we consider several tests for model misspecification after a multivariate conditional heteroscedasticity model has been fitted. We examine the performance of the recent test due to Ling and Li (J. Time Ser. Anal. 18 (1997), 447–64), the Box–Pierce test and the residual‐based F test using Monte Carlo methods. We find that there are situations in which the Ling–Li test has very weak power. The residual‐based diagnostics demonstrate significant under‐rejection under the null. In contrast, the Box–Pierce test based on the cross‐products of the standardized residuals often provides a useful diagnostic that has reliable empirical size as well as good power against the alternatives considered.

Procuring honest responses indirectly

Abstract We propose a new method for obtaining truthful answers to sensitive survey questions indirectly from a dichotomous population. In the proposed method, each sample respondent is asked to report a numerical value chosen from two parallel set of multiple outcomes generated by arbitrary randomizing devices. We show that the proposed estimator of the population proportion is more efficient and general than those put forward by Warner (1965. J. Amer. Statist. Assoc. 60, 63–69), Franklin (1989. Survey Methodol. 15, 225–235) and Kuk (1990. Biometrika 77, 436–438). Intuitively, our approach creates a remarkably respondent-friendly environment for each interviewee to discharge honest answers without the fear of exposing ones identity. Two illustrative cases using the normal and exponential distributions as randomizing devices are performed to demonstrate the superiority of the proposed estimator.

Life annuities of compulsory savings and income adequacy of the elderly in Singapore

Singapore has a publicly managed central provident fund (CPF) system, which is compulsory and based on individual accounts with an explicit link between contribution and benefits. This paper assesses the adequacy of the CPF saving to meet the retirement needs of the elderly in Singapore. Instead of emphasizing the mechanism of accumulation, we focus on the expenditure side of the lifetime budget of the elderly and estimate the present value of retirement consumption (PVRC). The estimated PVRC is obtained by simulations through three major components: calibration of subsistence and medical expenses of the elderly; forecast of cohort survival probability by age and by sex; and generation of yield curves to discount the future cash flows. Our results indicate that the existing CPF-decreed minimum sum is inadequate to meet the future consumption needs of the female elderly. The inadequacy becomes more severe when medical expense is set at higher growth rates. Moreover, the monthly payouts of a single premium deferred annuity are computed as illustrative examples.

Asymmetric volatility of real GDP: some evidence from Canada, Japan, the United Kingdom and the United States

Abstract The recent empirical investigation of conditional volatility in real GDP growth rates of Japan, the United Kingdom, and the United States by Hamori [Jpn. World Econ. 12 (2000) 143] finds no evidence of asymmetry. This paper re-visits the issue of asymmetric volatility using a similar approach with some modifications. We find statistically significant evidence of asymmetric volatility in the real growth rates of the United States and Canada. As such, it may be premature to conclude that business cycle indicators generally do not exhibit volatility asymmetry.

Monetary services and money demand in China

Abstract Using Barnetts methodology, we construct a monetary services index (MSI) for China. Compared to the traditional simple money aggregates, this index has solid microeconomic foundations, and has consistent variables. With Chinas on-going economic reforms in full swing, this index may provide a more appropriate indication of the current rapid process of economic monetization and financial innovations. In addition, we that it is capable of using the MSI to replace the conventional simple-sum aggregates in estimating long-term money demand. This may provide attractiveness for the Peoples Bank of China (PBC) to include the index as an alternative target variable in concluding its monetary policy during the period of rapid economic transition.

Exact distributions, density functions and moments of the least squares estimator in a first-order autoregressive model

Abstract This paper investigates the finite sample distributions of the least squares estimator in a first order autoregressive model. Distributions of the least squares estimator o are computed numerically from an alternative approach for both stationary and nonstationary cases. Convenient expressions are also obtained to compute the density functions and moments of the least squares estimator o. It is found that the limiting distributions of o are inadequate approximations to the exact distributions.