Thesis Defense: A Treatise on Econometric Forecasting

Alfredo Martinez

We investigate the effects of model misspecification and stochastic  dynamics in the problem of forecasting.  In economics and many fields of engineering, many researchers are guilty of the dangerous practice of treating their mathematical models as the  true data generating mechanisms responsible for the observed phenomena and  downplaying or omitting all together the important step of model verification.

In recent years, econometricians have acknowledged the need to account for model misspecification in the problems of estimation and forecasting. In particular, a large body of work has emerged to address properties of estimators under model misspecification, along with a plethora of misspecification testing methodologies.

In this work, we investigate the combined effects of model misspecification and various types of stochastic dynamics  on forecasts based on linear regression models. The data generating process (DGP) is assumed unknown to the forecaster except for the nature of process dependencies, i.e., independent identically distributed, covariance stationary, or nonstationary.

Estimation is carried out by means of ordinary least squares, and forecasts are evaluated with the mean squared forecast error (MSFE) or mean square error of prediction. We investigate the sample size dependence of the MSFE. For this purpose, we develop an algorithm to approximate the MSFE by  an expression depending only on the sample size $n$ and  moments of the processes.

The approximation is constructed by Taylor series expansions of the squared forecast error which do not require knowledge of the functional form of the DGP.

The approximation can be used to determine the existence of optimal observation windows which result in the minimum MSFE.

We assess the accuracy of the approximating algorithm with Monte Carlo experiments.