Conditional sum of squares estimation of k-factor GARMA models

We analyze issues related to estimation and inference for the constrained sum of squares estimator (CSS) of the k-factor Gegenbauer autoregressive moving average (GARMA) model. We present theoretical results for the estimator and show that the parameters that determine the cycle lengths are asymptotically independent, converging at rate T, the sample size, for finite cycles. The remaining parameters lack independence and converge at the standard rate. Analogous with existing literature, some challenges exist for testing the hypothesis of non-cyclical long memory, since the associated parameter lies on the boundary of the parameter space. 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.