Dynamic and sequential update for time series forecasting

Abstract

Two different sciences, physics and statistics, have worked, from the foundations of each, on the explanation and modelling of stochastic processes characterized by the succession of random variables whose realizations at each instant of time give rise to time series. From Physics we have worked with the Fourier transform to explain the dynamics of time series, a similar case occurs from statistics where dynamic models of time series are worked to explain the variations of the series and, in both cases, to make reliable forecasts. The main objective of this research is to adjust a model, using the methodology framed in the sequential update procedure of the forecast, to a time series of coal production observed quarterly during the years 2007 to 2011, in order to disaggregate quarterly the annual production for the years 2012 to 2018. Once the process has been carried out and validated, a quarterly production model is estimated which allows valid and reliable forecasts to be made for each quarter in subsequent years.