Simultaneous prediction of functionally dependent random variables by maximum likelihood estimation

Article type: Research Article

Authors: Moiseev, Nikita A.

Affiliations: Plekhanov Russian University of Economics, Moscow, Russia | E-mail: moiseev.na@rea.ru

Correspondence: [*] Corresponding author: Plekhanov Russian University of Economics, Moscow, Russia. E-mail: moiseev.na@rea.ru.

Abstract: The paper presents a fundamental parametric approach to simultaneous forecasting of a vector of functionally dependent random variables. The motivation behind the proposed method is the following: each random variable at interest is forecasted by its own model and then adjusted in accordance with the functional link. The method incorporates the assumption that models’ errors are independent or weekly dependent. Proposed adjustment is explicit and extremely easy-to-use. Not only does it allow adjusting point forecasts, but also it is possible to adjust the expected variance of errors, that is useful for computation of confidence intervals. Conducted thorough simulation and empirical testing confirms, that proposed method allows to achieve a steady decrease in the mean-squared forecast error for each of predicted variables.

Keywords: Simultaneous prediction, time series, economic indicators, seemingly unrelated regressions, maximum likelihood estimation, linearly dependent random variables

DOI: 10.3233/MAS-210526

Journal: Model Assisted Statistics and Applications, vol. 16, no. 2, pp. 143-150, 2021