A Statistical Method for the Determination of the Appropriate Order in a General Class of Time Series Models

Abstract

We propose a method to determine the order q of a model in a general class of time series models. For the subset of linear moving average models (MA(q)), our method is compared with that of the sample autocorrelations. Since the sample autocorrelation is meant to detect a linear structure of dependence between random variables, it turns out to be more suitable for the linear case. However, our method presents a competitive option in that case, and for nonlinear models (NLMA(q)) it is shown to work better. The main advantages of our approach are that it does not make assumptions on the existence of moments and on the distribution of the noise involved in the moving average models. We also include an example with real data corresponding to the daily returns of the exchange rate process of mexican pesos and american dollars.

Keywords:

• Nonlinear moving average models
• Measures of stochastic dependence
• Sample autocorrelation
• Empirical distribution functions
• Moving average models

Acknowledgments

We want to thank the referee for useful comments which improved this paper. Research partially supported by Conacyt Grants 32256-E, 32705-E and PAPIIT Grant IN-101198.