Abstract
In this paper we elaborate an algorithm to estimate p-order Random Coefficient Autoregressive Model (RCA(p)) parameters. This algorithm combines quasi-maximum likelihood method, the Kalman filter, and the simulated annealing method. In the aim to generalize the results found for RCA(1), we have integrated a subalgorithm which calculate the theoretical autocorrelation. Simulation results demonstrate that the algorithm is viable and promising.
Highlights
In the aim to generalize the results found for Random Coefficient Autoregressive (RCA)(1), we have integrated a subalgorithm which calculate the theoretical autocorrelation
Random Coefficient Autoregressive (RCA) processes have been widely studied in the literature for modeling time series exhibiting nonlinear behavior
The RCA process was introduced by Andel (1976) who studied its properties
Summary
Random Coefficient Autoregressive (RCA) processes have been widely studied in the literature for modeling time series exhibiting nonlinear behavior. For a detailed early study, we refer to Nicholls and Quinn [1] On their side, Thavaneswaran and Abraham [2] apply Godambe’s theorem (1985) to obtain optimal estimates for RCA models. Aue and Horvath (2011) propose a unified quasi-likelihood procedure for the estimation of the unknown parameters of RCA(1) models that works for both stationary and nonstationary processes. They establish the weak consistency and the asymptotic normality for this procedure. A new algorithm was proposed by Allal and Benmoumen [3] to estimate first-order RCA’s parameters This algorithm combines quasi-maximum likelihood method, the Kalman filter, and the Powell’s method.
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