Sparse vector autoregression with application to multivariate cryptocurrency time series

Abstract

The vector autoregressive (VAR) model as proposed by Christopher A. Sims ( l980b) has been widely used in the context of high dimensional time series. It has been praised for its ability to capture temporal and cross-sectional dependencies which may exist between different time series. However, over the years, improvements were made to address the problem of noisy estimates caused by correlations which are insignificant. We mention the Least Absolute Shrinkage Selection Operator (LASSO) method of simultaneously estimating and regularizing the VAR models with the aim of reducing the insignificant parameters of the V AR coefficient matrices. We will look into the estimation procedures and properties of unregularized VAR and see how they compare to unregularized VAR models, also known as Sparse-VAR. Amongst the properties, we discuss Granger causality and its implications on the multivariate time series. The performance of these models is illustrated by applying them to the scenario of time series of cryptocurrency prices. We study the main differences between the unregularized and regularized VAR models and, for the latter, analyse the effects different values of the LASSO shrinkage parameter have on the estimated VAR transition matrices. We also see how the different models interpret the dependencies between different cryptocurrencies and confirm whether historical values of one cryptocurrency have any impact on predicting other cryptocurrency prices. We proceed with applying time series cross-validation on the available dataset for the purpose of comparing the predictive performance of the unregularized and regularized models. The findings indicate that sparse-VAR is able to make slight improvements in the quality of the forecasts produced. We also see how the method of estimating the LASSO shrinkage parameter also plays an important part in the improvement of prediction errors.