Conditional Heteroscedastic Time Series Models

Abstract Under the traditional linear time series or regression setting, the conditional variance of one-step-ahead prediction is time invariant. Experience in conjunction with data analysis, however, suggests that the variability of a process might well depend on the available information. This reality has motivated extensive research to relax the constant variance assumption imposed by the traditional linear time series model, and several classes of generalized parametric models designed specifically for handling nonhomogeneity of a process have been proposed recently. In particular, the random coefficient autoregressive (RCA) models were widely investigated by time series analysts and the autoregressive conditional heteroscedastic (ARCH) models were investigated by econometricians. The interesting fact is that the ARCH processes can be regarded as special cases of the RCA model. In this article, I first give the relationship between these two types of models and show that the special feature of these t...

[1]  Ruey S. Tsay,et al.  Order Selection in Nonstationary Autoregressive Models , 1984 .

[2]  A Further Note on Stability in a Random Coefficient Model , 1976 .

[3]  Hirotugu Akaike,et al.  On entropy maximization principle , 1977 .

[4]  G. Box,et al.  Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models , 1970 .

[5]  A. A. Weiss.  ARMA MODELS WITH ARCH ERRORS , 1984 .

[6]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[7]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[8]  B. G. Quinn,et al.  Multiple autoregressive models with random coefficients , 1981 .

[9]  Jostein Paulsen,et al.  ORDER DETERMINATION OF MULTIVARIATE AUTOREGRESSIVE TIME SERIES WITH UNIT ROOTS , 1984 .

[10]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[11]  George E. P. Box,et al.  Intervention Analysis with Applications to Economic and Environmental Problems , 1975 .

[12]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[13]  Stability in a Random Coefficient Model , 1974 .

[14]  G. C. Tiao,et al.  Consistent Estimates of Autoregressive Parameters and Extended Sample Autocorrelation Function for Stationary and Nonstationary ARMA Models , 1984 .

[15]  TESTING FOR THE RANDOMNESS OF AUTOREGRESSIVE COEFFICIENTS , 1982 .

[16]  Barry G. Quinn,et al.  THE ESTIMATION OF RANDOM COEFFICIENT AUTOGRESSIVE MODELS. II , 1981 .

[17]  A. Milhøj.  The moment structure of ARCH processes , 1985 .

[18]  Henry L. Gray,et al.  A New Approach to ARMA Modeling. , 1978 .

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

[20]  H. Akaike.  A new look at the statistical model identification , 1974 .

[21]  E. J. Hannan,et al.  On Limit Theorems for Quadratic Functions of Discrete Time Series , 1972 .

[22]  Jiří Anděl,et al.  Autoregressive series with random parameters , 1976 .

[23]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[24]  E. Hannan.  The Estimation of the Order of an ARMA Process , 1980 .

[25]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[26]  R. Shibata.  Selection of the order of an autoregressive model by Akaike's information criterion , 1976 .

[27]  P. Billingsley,et al.  The Lindeberg-Lévy theorem for martingales , 1961 .

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

[29]  B. G. Quinn,et al.  THE ESTIMATION OF RANDOM COEFFICIENT AUTOREGRESSIVE MODELS. I , 1980 .