Fitting Time Series Models
Tucker McElroy, Dimitris N. Politis · 2019
The theory of linear models in statistics is centered around the basic ideas of linear regression, namely describing the conditional distribution of a dependent variable in terms of a linear function of the (possibly transformed) independent variables. This chapter focused on linear time series, describing methods of identification, estimation, computation, and evaluation of linear models. It examines the case of determining the model order q of a moving average. The EXP model can be identified by directly examining the cepstral coefficients. The basic estimation strategy results from another application of nonlinear spectral means. Examining the autocorrelations, a strong cyclical pattern is apparent, ruling out a moving average model. However, the partial autocorrelations also decay slowly, indicating either a high order AR model, or perhaps an autoregressive moving average or EXP model can be used.