AR(1) Models with AR(1) or MA(1) Coefficients: Evidence on Micro and Financial Applications

In the present study we consider autoregressive models with autoregressive and moving average coefficients of order 1, denoted by AR(1)/AR(1) and AR(1)/MA(1) respectively. We obtain useful sufficient conditions for the second-order stability of the AR(1)/AR(1) process and necessary and sufficient conditions for the second-order stability of the AR(1)/MA(1) process. Then, we investigate the problem of model selection within a class of models containing AR(1)/AR(1), AR(1)/MA(1), as well as the random and the constant coefficient models. In particular, by means of Monte Carlo experiments we examine the frequency at which the usual information criteria of Akaike (AIC), Swzartz (SIC) and Hannan-Quinn (HQ) select the correct model under a variety of alternative data generation processes and sample sizes. Finally, we provide evidence supporting the view that many financial time series are best described by either AR(1)/AR(1) or AR(1)/MA(1) models.