This paper proposes a logarithmic version of the two-component ACD (LogCACD) model with no restrictions on the sign of the model parameters while allowing the expected durations to be decomposed into the long- and short-run components to capture the dynamics of these durations. The extended generalised inverse Gaussian (EGIG) distribution is used for the error distribution as its hazard function consists of a roller-coaster shape for certain parameters’ values. An empirical application from the trade durations of International Business Machines stock index has been carried out to investigate this proposed model. Extensive comparisons are carried out to evaluate the modelling and forecasting performances of the proposed model with several benchmark models and different specifications of error distributions. The result reveals that the LogCACD_EGIG(1,1) model gives the best in-sample fit based on the Akaike information criterion and other criteria. Furthermore, the estimated parameters obtained through the maximum likelihood estimation confirm the existence of the roller-coaster-shaped hazard function. The examination of LogCACD_EGIG(1,1) model also provides the best out-of-sample forecasts evaluated based on the mean square forecast error using the Hansen’s model confidence set. Lastly, different levels of time-at-risk forecasts are provided and tested with Kupiec likelihood ratio test.

Time series of counts occur in many different contexts, the counts being usually of certain events or objects in specified time intervals. In this paper we introduce a model called parameter-driven state-space model to analyse integer-valued time series data. A key property of such model is that the distribution of the observed count data is independent, conditional on the latent process, although the observations are correlated marginally. Our simulation shows that the Monte Carlo Expectation Maximization (MCEM) algorithm and the particle method are useful for the parameter estimation of the proposed model. In the application to Malaysia dengue data, our model fits better when compared with several other models including that of Yang et al. (2015)

This paper aims to investigate the efficiency of the value-at-risk (VaR) backtests in the model selection from different types of generalised autoregressive conditional heteroskedasticity (GARCH) models with skewed and non-skewed innovation distributions. Extensive simulation is carried out to compare the model selection based on VaR backtests and Akaike Information Criteria (AIC). When the model is given but the innovation distribution is one of the six selected distributions which may be skewed or non-skewed, the simulation results show that both AIC and the VaR backtests succeed in selecting the correct innovation distribution from the set of six distributions under consideration. This indicates that both AIC and the VaR backtests are able to distinguish between skewed and non-skewed distributions when the innovation distribution is misspecified. Using an empirical data from NASDAQ index, we observe that the selected combination of model and innovation distribution based on the smallest AIC does not agree with that selected by using the in-sample VaR backtests. Examination of confidence limits for VaR and the expected shortfall forecasts under various loss functions provides evidence that the selected combination of model and innovation distribution using the VaR backtests tends to possess smaller mean absolute percentage error and logarithmic loss.

Bitcoin (BTC), as the dominant cryptocurrency, has attracted tremendous attention lately due to its excessive volatility. This paper proposes the time-varying transition probability Markov-switching GARCH (TV-MSGARCH) models incorporated BTC logarithmic daily trading volume or Google daily searches as exogenous factors to model the volatility dynamics of BTC return series. Extensive comparisons were carried out to evaluate the modelling and forecasting performances of TV-MSGARCH models with the benchmark models such as GARCH, GJRGARCH, threshold GARCH and constant transition probability MSGARCH. Results reveal that the TV-MSGARCH models predominate other models for the in-sample model fitting based on log-likelihood function and other benchmark criteria. Furthermore, the TV-MSGARCH model with Google daily searches offers the best out-of-sample forecast evaluated based on quasi-likelihood loss function and also using Hansen’s model confidence set. In addition, the Filardo’s weighted transition probabilities is computed and the results show the existence of time-varying effect on transition probabilities. Lastly, new approach for computing different levels of long and short positions of value-at-risk forecasts based on TV-MSGARCH models are also provided and tested.