Using simulation to compare the two estimation methods (ML) and (FGNLS) of the RCPAR periodic autoregressive model with random coefficient (1)


  • Hussein Ali Hussein



RCPAR (1) model, , PAR (1) model, FGNLS estimator, ML estimator


      The first-order random coefficient periodic autoregressive model RCPAR(1) was introduced by researchers (Frances and Paap, 2011), due to its importance in the field of seasonal time series applications, and its reduction of the number of parameters in the unrestricted periodic autoregressive model PAR(1). , as the increasing number of parameters results in a problem in the estimation stage. Thus, this stage was studied using the method of greatest possibility (ML) and the method of possible nonlinear least squares (FGNLS) and comparing them through the application of three simulation experiments using the Monte-Carlo method. It was concluded that there is a clear bias for small samples in the estimators of (ML), and then the preference of the (FGNLS) method in estimating the parameters of the RCPAR (1) model over the (ML) method for all samples used.


Abdelhakim Aknouche,A and Guerbyenne,H.(2009).” Periodic stationarity of random coefficient periodic autoregressions.”, Statistics and Probability Letters 79, pp. 990-996.

Abdullah, N.A., Mohamed ,I. , Peiris, S. & Azizan ,A.A.(2011). ” A New Iterative Procedure for Estimation of RCA Parameters Based on Estimating Functions.”, Applied Mathematical Sciences, Vol. 5, No. 4, pp. 193 - 202

Araveeporn,A.(2020).” Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist, Method.”, Mathematics 8(1),62.

Basawa ,I.R, Lund ,R. and Shao, Q.(2004).” First - order Seasonal Autoregressive Processes with Periodically Varying Parameters.”, Statistics and Probability Letters, 67, pp. 299-306.

Bloomfield, P., H. L. Hurd and R. B. Lund (1994), Periodic correlation in stratospheric ozone data, Journal of Time Series Analysis 15, 127–150.

Franses,P.H. and Paap,R.(2011).” Random-coefficient periodic autoregressions.”, Statistica Neerlandica , Vol. 65, No.1, pp. 101–115.

Jones, R. H. and W. M. Brelsford (1967), Time series with periodic structure, Biometrika 54, 403–407.

Nicholls, D.F. and Quinn, B.G. (1981).” The Estimation of Random Coefficient Autoregressive Models. II, Journal of Time Series Analysis, 2, 185-203.