Abstract

Multivariate time series (MTS) data are widely available in different fields. Modelling MTS data effectively is important for many decision-making activities. A multivariate time series has more than one-time dependent variable. Each variable depends not only on its past values but also has some dependency on other variables. For example, Consumption and income/ interest rates, money growth, income, and inflation. There are many occupations where univariate time series is not enough, and multivariate time series is needed.
Real world problems are mainly based on multiple objectives rather than single objective. Multi-objective optimization is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. This paper explores the usage of Goal Programming (GP) as a tool to estimate the parameters of multivariate time series and forecast future observations. GP is the most well-known tool in the field of operational research and it has been used for a wide range of optimization problems. Nonetheless, there are very few applications in forecasting and all of them are limited to causal modelling. The rationale behind this study is that time series forecasting problems can be treated as optimization problems, where the objective is to minimize the forecasting error. GP will give to forecasters the opportunity to do accurate forecasts quickly and easily. In addition, the flexibility of GP can help analysts to deal with situations that other methods cannot deal with such not normally distribution and outliers.
In this paper, a goal programming is presented for estimating and forecasting multivariate auto regressive time series (VAR) models. To accomplish this, we utilize goal programming. The aim of employing the GP is to estimate the VAR model. To evaluate the effectiveness of the proposed GP approach, we conducted a simulation study. In the simulation study, we generate 1000 time series datasets from each of the different VAR models with different orders, number of variables, series length, error distribution. Compare MAE of GP with OLS method. The results obtained from the simulation study demonstrate the effectiveness of GP in accurately estimating and forecasting VAR models. These findings support the applicability and reliability of the proposed method in practical scenarios. Overall, our research contributes to the field of time series analysis by providing a new approach for estimating and forecasting VAR models using GP, paving the way for improved forecasting and decision-making in various domains.
Keywords Vector Autoregressive Model, Goal Programming, multivariate time series.