COMPUTATION OF RELIABLE INTERVAL FORECAST FOR DYNAMIC AVERAGING OF ECONOMIC TIME SERIES REGRESSION MODELS

This paper presents a method of obtaining reliable confidence intervals when conducting the dynamic averaging procedure for linear regression models of economic time series. It is explicitly shown, that when we adapt models' weights each time new data occurs, the traditional approach to computing an unbiased estimator of errors' variance systematically underestimates the true variance. The traditional approach is valid only in case of static weights, when the optimization procedure is conducted just once. The same conclusion holds for dynamic and static specification procedure as well. However, when applying static weights to time series processes model accuracy is usually lower than for dynamically adapted weights. Thus, in this paper, the authors make an attempt to solve this conundrum concerning the choice between either better prediction (adaptive weights) or reliable confidence intervals (static weights). To achieve this goal, the authors work out a substantial solution for obtaining an adjusted estimator of true errors' variance that yields a reliable result. Such an estimator is proposed to be computed numerically by simulating the errors' variance-covariance matrix by Wishart distribution with a prior equal to a sample variance-covariance matrix and, thus, obtaining the average bias of traditional estimator. To prove the efficiency of the proposed approach, the authors also conduct rigorous out-of-sample simulation testing.