Forecasting with time-varying vector autoregressive models

TL;DR

This paper introduces a flexible time-varying vector autoregressive (TV-VAR) model for multivariate time series forecasting, utilizing Bayesian inference and state-space representation to improve prediction accuracy over traditional VAR models.

Contribution

The paper develops a novel TV-VAR model with Bayesian inference for multivariate forecasting, including multi-step prediction and model selection techniques, demonstrated on financial data.

Findings

TV-VAR outperforms traditional VAR in empirical tests

Bayesian methods effectively select model order and evaluate forecasts

Model provides accurate multi-step forecasts for financial time series

Abstract

The purpose of this paper is to propose a time-varying vector autoregressive model (TV-VAR) for forecasting multivariate time series. The model is casted into a state-space form that allows flexible description and analysis. The volatility covariance matrix of the time series is modelled via inverted Wishart and singular multivariate beta distributions allowing a fully conjugate Bayesian inference. Model performance and model comparison is done via the likelihood function, sequential Bayes factors, the mean of squared standardized forecast errors, the mean of absolute forecast errors (known also as mean absolute deviation), and the mean forecast error. Bayes factors are also used in order to choose the autoregressive order of the model. Multi-step forecasting is discussed in detail and a flexible formula is proposed to approximate the forecast function. Two examples, consisting of bivariate data of IBM shares and of foreign exchange (FX) rates for 8 currencies, illustrate the methods. For the IBM data we discuss model performance and multi-step forecasting in some detail. For the FX data we discuss sequential portfolio allocation; for both data sets our empirical findings suggest that the TV-VAR models outperform the widely used VAR models.