Abstract

Multivariate Time Series (MTS) is used to model and explain the interactions and co-movements among a group of time series variables. MTS is typically high dimensional and involves multiple time series which must be jointly analyzed. The rationale behind this is the possible presence of interdependencies, which, when quantified appropriately, could lead to better forecasting. In this research, an extension of the Vector Autoregressive (VAR) model, named Vector Autoregressive Moving Average (VARMA) model, was considered because the VARMA class has the advantage of being closed with respect to linear transformations, that is, a linearly transformed finite order VARMA representation. These transformations are very common and are useful to study problems of aggregation, marginal processes or averages of variables generated by VARMA processes. However, there are several good reason for choosing models from the more general VARMA class. VARMA permits more parsimonious representations and this in turn may lead to improvements in estimation and forecast precision. There are also theoretical reasons why the class of pure VAR models may be too small for many economic indicators data sets. A range of methods were explored for better forecasting in macro-economic based on the publicly available World Development Indicator database. The unit root and cointegration test of stationarity were studied. The dynamic relationship between some macroeconomics variables and the direction of causality among the variables were investigated. In particular, possible linear transformation of data was explored in combination with VARMA models, to derive at better forecasts of a range of macro-economic variables while keeping the requirements for implementation at level which does not deter applied researchers.