Empirical aspects of the Whittle-based maximum likelihood method in jointly estimating seasonal and non-seasonal fractional integration parameters

This paper addresses the efficiency of the maximum likelihood (ML) method in jointly estimating the fractional integration parameters ds and d, respectively associated with seasonal and non-seasonal long-memory components in discrete stochastic processes. The influence of the size of non-seasonal parameter over seasonal parameter estimation, and vice versa, was analyzed in the space d×ds∈(0,1)×(0,1) by using mean squared error statistics MSE(dˆs) and MSE(dˆ). This study was based on Monte Carlo simulation experiments using the ML estimator with Whittle’s approximation in the frequency domain. Numerical results revealed that efficiency in jointly estimating each integration parameter is affected in different ways by their sizes: as ds and d increase simultaneously to 1, MSE(dˆs) and MSE(dˆ) become larger; however, effects on MSE(dˆs) are much stronger than the effects on MSE(dˆ). Moreover, as each parameter tends individually to 1, MSE(dˆ) becomes larger, but MSE(dˆs) is barely influenced.