Maximum Likelihood Estimation and Unit Root Test for First Order Random Coefficient AutoRegressive Models

• Published in: Journal of statistical theory and practice Vol. 4; no. 2; pp. 261 - 278
• Main Authors: Wang, Dazhe, Ghosh, Sujit K., Pantula, Sastry G.
• Format: Journal Article
• Language: English
• Published: Cham Taylor & Francis Group 01.01.2010; Springer International Publishing
• Subjects: Ergodicity; Hypothesis testing; Mathematics and Statistics; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Statistics; Strict stationarity; Time series; 62M10; Hypothesis testing; Strict stationarity; Time series; Ergodicity; 65F12; 62F03
• ISSN: 1559-8608; 1559-8616
• DOI: 10.1080/15598608.2010.10411985

Random Coefficient AutoRegressive (RCAR) models are obtained by introducing random coefficients to an AR or more generally AutoRegressive Moving Average (ARMA) model. For a weakly stationary first order RCAR model, it has been shown that the Maximum Likelihood Estimators (MLEs) are strongly consistent and satisfy a classical Central Limit Theorem. A broader class of first order RCAR models allowing the parameters to lie in the region of strict stationarity and ergodicity is developed. Asymptotic properties are established for this extended class of models which includes the unit root first order RCAR model as a special case. The existence of a unit root in a first order RCAR process has practical impact on data analysis especially in the context of model forecasting. A Wald type criterion based on the MLEs is also developed to test unit root hypothesis. The asymptotic normality of the Wald statistic under the null hypothesis is validated using a simulation study.