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Asymptotic Inference for the Weak Stationary Double AR(1) Model
Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada. M3J 1P3
Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada. M3J 1P3
Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada. M3J 1P3
- 1 Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada. M3J 1P3
- 2 Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada. M3J 1P3
- 3 Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada. M3J 1P3
Open Journal of Statistics·Volume 02 (2012)·Pages 141–152·Published 23 April 2012·DOI10.4236/ojs.2012.22016
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Abstract
An AR(1) model with ARCH(1) error structure is known as the first-order double autoregressive (DAR(1)) model. In this paper, a conditional likelihood based method is proposed to obtain inference for the two scalar parameters of interest of the DAR(1) model. Theoretically, the proposed method has rate of convergence O(n -3/2 ). Applying the proposed method to a real-life data set shows that the results obtained by the proposed method can be quite different from the results obtained by the existing methods. Results from Monte Carlo simulation studies illustrate the supreme accuracy of the proposed method even when the sample size is small.
KeywordsCanonical ParameterDouble Autoregressive Modelp-Value FunctionSigned Log-Likelihood Ratio Statistic
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