Modelling multivariate financial time series using vector autoregressive processes

Abstract

Time series analysis is used to predict future behaviour of processes and is widely used in the finance sector. In this paper we will analyse the modelling of multivariate time series of financial data using vector autoregressive processes. The goal is that the reader will understand the presented models and could theoretically perform time series analysis by himself. Two specific models will be explained: the Vector Autoregressive model (VAR model) and the Vector Error Correction Model (VECM). We will describe various methods to analyse multivariate time series using these models, such as forecasting the process, variance decomposition of the forecast error, causality analysis and impulse response analysis. Examples of these models and analysis methods will be presented and investigated. Finally, we will perform a time series analysis with these models on Dutch indices and stock data. We conclude that real-world data often does not fit the VAR model and VECM requirements and that further improved models should be considered as well.