Obtaining the coefficients of a Vector Autoregression Model through minimization of parameter criteria

VAR models [13] are a type of multi-equation model that linearly describe the simultaneous interactions and behaviour among a group of variables using only their own past. More specifically, a VAR is a model of simultaneous equations formed by a system of equations in which the contemporary values of model variables do not appear in any explanatory variable in the equations. The set of explanatory variables in each equation is a block consisting of lags of each of the model variables, and the block is the same for all the equations. VAR models have been traditionally used in finance and econometrics [2, 15]. With the arrival of Big Data, huge amounts of data are being collected in numerous fields. Our group is studying the application of statistical models in health problems which, traditionally, have been applied in econometrics [8]. To model time series we use Vector Autoregression Models (VAR). Tools exist to tackle this problem [14], but the large amount of data, along with the availability of computational techniques and high performance systems, advise an in-depth analysis of the computational aspects of VAR, so large models can be solved efficiently with today’s computational systems. To solve the model, Ordinary Least Squares (OLS) are used equation by equation. However, the practical challenge of its design lies in selecting the optimal length of the lag of the model. There are different strategies to solve this problem [9, 10]: one of them is to examine some information criteria, for example Akaike (AIC) [1], Schwarz (BIC) [12] or Hannan-Quinn (HQC) [6] (these are the most well-known and used criteria but not the only ones). This work aims to solve a VAR model by obtaining the coefficients through heuristic and metaheuristic algorithms, minimizing one parameter criterion, and also to compare with those coefficients obtained by OLS.