A study on parsimonious periodic autoregressive model Lee, Jiho; Seong, Byeongchan;
This paper proposes a parsimonious periodic autoregressive (PAR) model. The proposed model performance is evaluated through an analysis of Korean unemployment rate series that is compared with existing models. We exploit some common features among each seasonality and confirm it by LR test for the parsimonious PAR model in order to impose a parsimonious structure on the PAR model. We observe that the PAR model tends to be superior to existing seasonal time series models in mid- and long-term forecasts. The proposed parsimonious model significantly improves forecasting performance.
seasonal time series model;parsimony of principle;seasonality;ARIMA model;Holt-Winters model;unemployment rate;
Boswijk, H. P., Franses, P. H., and Haldrup, N. (1997). Multiple unit roots in periodic autoregression, Journal of Econometrics, 80, 167-193.
Box, G. E. P. and Jenkins, G. (1976). Time Series Analysis: Forecasting and Control, Francisco Holden-Day.
Franses, P. H. and McAleer, M. (1998). Cointegration analysis of seasonal time series, Journal of Economic Survey, 12, 651-678.
Franses, P. H. and Paap, R. (2004). Periodic Time Series Models, Oxford University Press.
Holt, C. C. (1957). Forecasting trends and seasonals by exponentially weighted averages, ONR memorandum no. 52. Carnegie Institute of Technology, Pittsburgh, USA published in International Journal of Forecasting 2004, 20, 5-10.
Lee, S. D., Kim, J. G., and Kim, S. W. (2012). Estimation of layered periodic autoregressive moving average models, Communications for Statistical Applications and Methods, 19, 507-516.
Lund, R., Shao, Q., and Basawa, I. (2006). Parsimonious periodic time series modeling, Australian & New Zealand Journal of Statistics, 48, 33-47.
Lutkepohl, H. (2005). New Introduction to Multiple Time Series Analysis, Springer Science & Business Media.
Matas-Mir, A. and Osborn, D. R. (2004). Does seasonality change over the business cycle? an investigation using monthly industrial product series, European Economic Review, 48, 1309-1332.
McLeod, A. I. (1993). Parsimony, model adequacy and periodic correlation in time series forecasting, International Statistical Review/Revue Internationale de Statistique, 387-393.
Osborn, D. R. (1991). The implications of periodically varying coefficients for seasonal time-series processes, Journal of Econometrics, 48, 373-384.
Osborn, D. R. and Smith, J. P. (1989). The performance of periodic autoregressive models in forecasting seasonal U.K. consumption, Journal of Business & Economic Statistics, 7, 117-127.
Pagano, M. (1978). On periodic and multiple autoregressions, The Annals of Statistics, 1310-1317.
Troutman, B. M. (1979). Some results in periodic autoregression, Biometrika, 66, 219-228.
Ursu, E. and Turkman, K. F. (2012). Periodic autoregressive model identification using genetic algorithms, Journal of Time Series Analysis, 33, 398-405.
Winters, P. R. (1960). Forecasting sales by exponentially weighted moving averages, Management Science, 6, 324-342.