A comparison of some autocovariance-based methods of arma model selection: a simulation study

Abstract

In this paper statistical methods are considered that use certain second moment properties in order to identify stationary autoregressive moving average models. In particular, the performance of the corner method, the vector autocorrelations, the smallest canonical correlations and the extended autocorrelations are investigated and the usefulness of the involved statistics as model specification tools in time series analysis is compared by means of Monte Carlo studies using some simple automatic model selection procedures. The simulation results indicate some similarities between these methods. For instance, they are less powerful in identifying moving average than autoregressive structures and for high order models and small sample sizes between 30 and 100 observations they tend frequently to select more parsimonious parametrizations, underestimating the true orders. In these cases, other approaches based on order selection criteria seem to be superior. However, the ability of the autocovariance-based methods in identifying the true order increases with the sample size and for 200 observations some of these methods perform fairly well also for the high order models considered.

Keywords:

• Autoregressive moving average models
• canonical correlations
• corner method
• extended autocorrelations
• generalized autocorrelations
• generalized partial autocorrelations
• order identification
• vector autocorrelations

¹Adress for correspondence:Technische Universität Berlin, Institut für Quantitative Methoden, FB20,Sekr. FR 6-4, Franklinstr.28/29,D-1000 berlin 10, Federal Republic of Germany.

¹Adress for correspondence:Technische Universität Berlin, Institut für Quantitative Methoden, FB20,Sekr. FR 6-4, Franklinstr.28/29,D-1000 berlin 10, Federal Republic of Germany.

Notes

¹Adress for correspondence:Technische Universität Berlin, Institut für Quantitative Methoden, FB20,Sekr. FR 6-4, Franklinstr.28/29,D-1000 berlin 10, Federal Republic of Germany.