We introduce the multivariate Ornstein-Uhlenbeck and discuss how it generalizes a vast class of continuous-time and discrete-time multivariate processes. Relying on the simple geometrical interpretation of the dynamics of the Ornstein-Uhlenbeck process we introduce cointegration and its...

We analyze the impact of the estimation frequency - updating parameter estimates on a daily, weekly, monthly or quarterly basis - for commonly used GARCH models in a large-scale study, using more than twelve years (2000-2012) of daily returns for constituents of the S&P 500 index. We assess the...

A novel simulation-based methodology is proposed to test the validity of a set of marginal time series models, where the dependence structure between the time series is taken "directly" from the observed data. The procedure is useful when one wants to summarize the test results for several time...

We investigate the direct connection between the uncertainty related to estimated stable ratios of stock prices and risk and return of two pairs trading strategies: a conditional statistical arbitrage method and an implicit arbitrage one. A simulation-based Bayesian procedure is introduced for...

We test the presence of regime changes in the GARCH volatility dynamics of Bitcoin log-returns using Markov-switching GARCH (MSGARCH) models. We also compare MSGARCH to traditional single-regime GARCH specifications in predicting one-day ahead Value-at-Risk (VaR). The Bayesian approach is used...

We perform a large-scale empirical study to compare the forecasting performance of single-regime and Markov-switching GARCH (MSGARCH) models from a risk management perspective. We find that, for daily, weekly, and ten-day equity log-returns, MSGARCH models yield more accurate Value-at-Risk,...