Estimation of Layered Periodic Autoregressive Moving Average Models

Title & Authors
Estimation of Layered Periodic Autoregressive Moving Average Models
Lee, Sung-Duck; Kim, Jung-Gun; Kim, Sun-Woo;

Abstract
We study time series models for seasonal time series data with a covariance structure that depends on time and the periodic autocorrelation at various lags $\small{k}$. In this paper, we introduce an ARMA model with periodically varying coefficients(PARMA) and analyze Arosa ozone data with a periodic correlation in the practical case study. Finally, we use a PARMA model and a seasonal ARIMA model for data analysis and show the performance of a PARMA model with a comparison to the SARIMA model.
Keywords
Periodic correlation;SARIMA;PARMA;layered model;
Language
Korean
Cited by
1.
A study on parsimonious periodic autoregressive model, Korean Journal of Applied Statistics, 2016, 29, 1, 133
References
1.
Cipra, T. (1985). Periodic moving average process, Aplikace Matematiky, 30, 218-229.

2.
Lund, R. B. and Basawa, I. V. (1999). Modeling for periodically correlated time series, Asymptotics, Nonparametrics, and Time Series, 37-62.

3.
McLeod, A. I. (1993). Parsimony, model adequacy and periodic correlation in time series forecasting, International Statistical Review, 61, 387-393.

4.
Osborn, D. R. (1991). The implications of periodically varying coefficients for seasonal time series process, Journal of Econometrics, 48, 373-384.

5.
Pagano, M. (1978). On periodic and multiple autoregressions, The Annals of Statistics, 6, 1310-1317.

6.
Tiao, G. C. and Grupe, M. R. (1980). Hidden periodic autoregressive moving average models in time series data, Biometrika, 67, 365-373.

7.
Vecchia, A. V. (1985). Maximum likelihood estimation for Periodic Autoregressive Moving-Average process, Technometrics, 27, 375-384.