Title: Unbiased estimation of autoregressive models in bounded series
Authors: Lola Gadea - University of Zaragoza (Spain) [presenting]
Antonio Montanes - University of Zaragoza (Spain)
Josep Lluis Carrion-i-Silvestre - Universitat de Barcelona (Spain)
Abstract: The standard analysis of time series consider that an stochastic process can vary freely in the limit . However, there are some important macroeconomic variables that are bounded by definition. In this case, the OLS estimation generates a biased estimate of the autoregressive parameters, which might affect the estimation of other relevant statistics, if the bounded nature of the time series is not accounted for. In order to overcome undesirable effects, we propose to implement different approaches in the literature that correct the estimation bias of autoregressive processes, taking into account the existence of bounds. First, we focus on the median-unbiased estimation procedure, which requires the computation of look-up tables to obtain a correspondence between the value of the OLS estimation of the autoregressive parameter. We have computed similar look-up tables for different values of the bounds to adapt his procedure for bounded stochastic processes. Secondly, we essay the performance of a modified estimator in bounded series and show, both theoretically and through a Monte Carlo experiment, its adequacy depending on the value of the limits. These results open a wide range of theoretical and empirical possibilities, given the abundance of economic bounded series and the multitude of procedures that require accurate estimation of the autoregressive parameters.