Improved interval estimation of long run response from a dynamic linear model: a highest density region approach


Jae H Kim, Iain Fraser, Rob J Hyndman


10 March 2011

Publication details

Computational Statistics and Data Analysis 55(8), 2477-2489



This paper proposes a new method of interval estimation for the long run response (or elasticity) parameter from a general linear dynamic model. We employ the bias-corrected bootstrap, in which small sample biases associated with the parameter estimators are adjusted in two stages of the bootstrap. As a means of bias-correction, we use alternative analytic and bootstrap methods. To take atypical properties of the long run elasticity estimator into account, the highest density region (HDR) method is adopted for the construction of confidence intervals. From an extensive Monte Carlo experiment, we found that the HDR confidence interval based on indirect analytic bias-correction performs better than other alternatives, providing tighter intervals with excellent coverage properties. Two case studies (demand for oil and demand for beef) illustrate the results of the Monte Carlo experiment with respect to the superior performance of the confidence interval based on indirect analytic bias-correction.

Keywords: ARDL model, bias-correction, bootstrapping, Highest density region, long run elasticity.