COMMON PERSISTENCE IN CONDITIONAL VARIANCES

A common finding in many of the recent empirical studies with the ARCH class of models applied to high frequency financial data concerns the apparent persistence of shocks for forecast of the future conditional variances. It is likely that several different variables share this same implied long-run component, however. In that situation, the variables are defined to be copersistent in variance. Conditions for copersistence to occur in the linear multivariate GARCH model are presented. These conditions parallel the conditions for linear cointegration in the mean. A simple empirical example with foreign exchange rate data illustrates the ideas. Copyright 1993 by The Econometric Society.

[1]  C. Nelson,et al.  A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the ‘business cycle’☆ , 1981 .

[2]  J. Wooldridge,et al.  Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances , 1992 .

[3]  G. William Schwert,et al.  Effects of model specification on tests for unit roots in macroeconomic data , 1987 .

[4]  P. Bougerol,et al.  Stationarity of Garch processes and of some nonnegative time series , 1992 .

[5]  R. Baillie,et al.  Common Stochastic Trends in a System of Exchange Rates , 1989 .

[6]  Robert F. Engle,et al.  A multi-dynamic-factor model for stock returns , 1992 .

[7]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[8]  R. Baillie,et al.  The Message in Daily Exchange Rates , 1989 .

[9]  P. Perron,et al.  Trends and random walks in macroeconomic time series : Further evidence from a new approach , 1988 .

[10]  J. Wooldridge,et al.  A Capital Asset Pricing Model with Time-Varying Covariances , 1988, Journal of Political Economy.

[11]  S. Ross.  The arbitrage theory of capital asset pricing , 1976 .

[12]  Christopher G. Lamoureux,et al.  Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects , 1990 .

[13]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[14]  Daniel B. Nelson.  Stationarity and Persistence in the GARCH(1,1) Model , 1990, Econometric Theory.

[15]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[16]  Tim Bollerslev,et al.  Quasi-maximum likelihood estimation of dynamic models with time varying covariances , 1988 .

[17]  Peter E. Rossi,et al.  Stock Prices and Volume , 1992 .

[18]  H. Iemoto.  Modelling the persistence of conditional variances , 1986 .

[19]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[20]  Peter Schmidt,et al.  Unit root tests with conditional heteroskedasticity , 1993 .

[21]  M. Rothschild,et al.  Asset Pricing with a Factor Arch Covariance Structure: Empirical Estimates for Treasury Bills , 1988 .

[22]  Christopher G. Lamoureux,et al.  Persistence in Variance, Structural Change, and the GARCH Model , 1990 .

[23]  T. Anderson.  Statistical analysis of time series , 1974 .

[24]  Mark W. Watson,et al.  Univariate detrending methods with stochastic trends , 1986 .

[25]  T. Bollerslev,et al.  A CONDITIONALLY HETEROSKEDASTIC TIME SERIES MODEL FOR SPECULATIVE PRICES AND RATES OF RETURN , 1987 .

[26]  R. Chou,et al.  ARCH modeling in finance: A review of the theory and empirical evidence , 1992 .

[27]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[28]  A. Gallant,et al.  On Fitting A Recalcitrant Series: The Pound/Dollar Exchange Rate, 1974- 83 , 1988 .