Conditional sum of squares estimation of k-factor GARMA models. (Under Review)
Abstract
We review the k-factor Gegenbauer autoregressive moving average (GARMA) model, which can reproduce a wide range of autocorrelation functions. As emphasized by Hunt, Peiris, and Weber (2022), a full set of theoretical results for estimators of the model are generally unavailable, particularly in the time domain. For the single-factor model, proposed distribution results for a constrained sum of squares (CSS) estimator were presented by Chung (1996b), although Beaumont and Smallwood (2022) show concerns when the cycle length is infinite. Building on this work, we directly extend the analysis of Chung (1996b) for the CSS estimator to models with multiple spectral poles. With T denoting the sample size, we show that the parameters that determine the cycle lengths are asymp- totically independent, converging at rate-T for finite cycles. Remaining parameters lack independence and are Op(T^-1/2). We present simulation results to explore small sample properties of the estimator, which support most distributional results, while also highlighting areas that merit additional exploration. We demonstrate the applicability of the theory and estimator with an application to IBM trading volume.
