Parameter Estimation for Periodically Stationary Time Series

The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper, we compute the asymptotic distribution for these estimates in the case, where the innovations have a finite fourth moment. These asymptotic results are useful to determine which model parameters are significant. In the process, we also develop asymptotics for the Yule-Walker estimates. Copyright 2005 Blackwell Publishing Ltd.

[1]  Marcello Pagano,et al.  On Periodic and Multiple Autoregressions , 1978 .

[2]  K. Berk.  Consistent Autoregressive Spectral Estimates , 1974 .

[3]  G. C. Tiao,et al.  Hidden Periodic Autoregressive-Moving Average Models in Time Series Data, , 1980 .

[4]  G. Reinsel,et al.  Prediction of multivariate time series by autoregressive model fitting , 1985 .

[5]  Mark M. Meerschaert,et al.  Modeling river flows with heavy tails , 1998 .

[6]  Mark M. Meerschaert,et al.  Innovations algorithm for periodically stationary time series , 1999 .

[7]  R. Bhansali.  Linear Prediction by Autoregressive Model Fitting in the Time Domain , 1978 .

[8]  Graham C. Goodwin,et al.  PARAMETER ESTIMATION FOR PERIODIC ARMA MODELS , 1995 .

[9]  Richard A. Davis,et al.  Simple consistent estimation of the coefficients of a linear filter , 1988 .

[10]  Robert Lund,et al.  Recursive Prediction and Likelihood Evaluation for Periodic ARMA Models , 2000 .

[11]  Mark M. Meerschaert,et al.  PERIODIC MOVING AVERAGES OF RANDOM VARIABLES WITH REGULARLY VARYING TAILS , 1997 .

[12]  Jose D. Salas,et al.  APPROACHES TO MULTIVARIATE MODELING OF WATER RESOURCES TIME SERIES1 , 1985 .

[13]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[14]  T. Ula,et al.  FORECASTING OF MULTIVARIATE PERIODIC AUTOREGRESSIVE MOVING‐AVERAGE PROCESSES , 1993 .

[15]  Aldo V. Vecchia,et al.  ASYMPTOTIC RESULTS FOR PERIODIC AUTOREGRESSIVE MOVING‐AVERAGE PROCESSES , 1993 .

[16]  B. Troutman.  Some results in periodic autoregression , 1979 .

[17]  A. V. Vecchia,et al.  Testing for periodic autocorrelations in seasonal time series data , 1991 .

[18]  R H Jones,et al.  Time series with periodic structure. , 1967, Biometrika.

[19]  D. Tjøstheim,et al.  EMPIRICAL IDENTIFICATION OF MULTIPLE TIME SERIES , 1982 .