Modelling Comovements of Selected Large Cap Cryptocurrencies: A Semi-Parametric Noncausal VAR Approach

This dissertation focuses on multivariate mixed causal noncausal models and their application to cryptocurrencies. The empirical application considered in the dissertation focuses on detecting comovements in the US dollar exchange rates of four prominent cryptocurrencies as well as on forecasting for multivariate mixed causal noncausal models. The dissertation explores forecasting methods which can be used when modelling data as mixed causal noncausal multivariate processes.

The dissertation is divided into three chapters. Chapter one is dedicated to the detection of comovements in four prominent cryptocurrency US dollar exchange rates by modelling the exchange rates as mixed causal noncausal processes. The cryptocurrency pairs Bitcoin/Ethereum and Ripple/Stellar are modelled as bivariate mixed causal noncausal processes and then estimated as a single mixed causal noncausal multivariate time series model of dimension four.

Chapter two contains forecasting methods and applications to the cryptocurrencies estimated in chapter one. Nonparametric predictive densities are calculated and a new linear approximation method is introduced and used to calculate one step ahead out of sample forecasts using a mixed causal noncausal vector autoregressive model estimated via the GCov estimator.

Chapter three extends theory for forecasting multivariate mixed causal noncausal processes. Theory pertaining to the calculation of predictive densities for mixed causal noncausal vector autoregressive models with three lags using the latent causal and noncausal components of the process is discussed. Theory pertaining to the calculation of predictive densities for causal noncausal vector autoregressive models with high dimensional data is also discussed.

Two experiments are conducted via simulation study. Firstly the coverage of the predictive density forecasting method is investigated. Secondly the predictive density forecasting method is compared with the linear approximation forecasting method in terms of their respective Mean Squared Errors.