Efficient estimation method for generalized ARFIMA models

Abstract

This paper focuses on pretest and shrinkage estimation strategies for generalized autoregressive fractionally integrated moving average (GARFIMA) models when some of the regression parameters are possible to restrict to a subspace. These estimation strategies are constructed on the assumption that some covariates are not statistically significant for the response. To define the pretest and shrinkage estimators, we fit two models: one includes all the covariates and the others are subject to linear constraint based on the auxiliary information of the insignificant covariates. The unrestricted and restricted estimators are then combined optimally to get the pretest and shrinkage estimators. We enlighten the statistical properties of the shrinkage and pretest estimators in terms of asymptotic bias and risk. We examine the comparative performance of pretest and shrinkage estimators with respect to unrestricted maximum partial likelihood estimator (UMPLE). We show that the shrinkage estimators have a lower relative mean squared error as compared to the UMPLE when the number of significant covariates exceeds two. Monte Carlo simulations are conducted to examine the relative performance of the proposed estimators to the UMPLE. An empirical application is used for the usefulness of our proposed estimation strategies.

Keywords:

• ARFIMA
• asymptotic distributional bias and risk
• Monte Carlo simulation
• partial likelihood
• shrinkage and pretest estimators

Acknowledgements

The authors are thankful to the editor, associate editor and referee for their insightful comments that have greatly improved this manuscript.

Additional information

Funding

Natural Sciences and Engineering Research Council of Canada.