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This paper investigates tests for multiple structural changes with non-homogeneous regressors, such as polynomial trends. We consider exponential-type, supremum-type and average-type tests as well as the corresponding weighted-type tests suggested in the literature. We show that the limiting distributions depend on regressors in general, and we need to tabulate critical values depending on them. Then, we focus on the linear trend case and obtain the critical values of the test statistics. The Monte Carlo simulations are conducted to investigate the finite sample properties of the tests proposed in the paper, and it is found that the specification of the number of breaks is an important factor for the finite sample performance of the tests. Since it is often the case that we cannot prespecify the number of breaks under the alternative but can suppose only the maximum number of breaks, the weighted-type tests are useful in practice.

A new bootstrap procedure for unit root testing based on the tapered block bootstrap is introduced. This procedure is similar to previous tests that were based on the block bootstrap and stationary bootstrap, but it has the advantage of the tapering procedure that has been previously shown to reduce the bias of the variance estimator by an order of magnitude. In this paper, the procedure is defined including a specific data-driven method for choosing the block size. Both theoretical results for the asymptotic behavior of the test and simulations that address the small-sample properties and are used for comparison to other methods are given.

We propose a fractionally integrated matrix-exponential dynamic conditional correlation (FIEDCC) model to capture the asymmetric effects and long- and short-range dependence of a correlation process. We also propose employing an inverse Wishart distribution for the disturbance of a covariance structure, which gives an alternative interpretation for a multivariate t conditional distribution. Using the inverse Wishart distribution, we present a three-step procedure to obtain initial values for estimating a high-dimensional conditional covariance model with a multivariate t distribution. We investigated the finite-sample properties of the ML estimator. Empirical results for nine assets from chemical firms, banks, and oil and gas producers in the US indicate that the new FIEDCC model outperforms the other dynamic correlation models for the AIC and BIC and for forecasting value-at-risk thresholds. Furthermore, the new FIEDCC model captures the stronger connection among the nine assets for the period right after the global financial crisis.

The GARCH class of models for dynamic conditional covariances trades off flexibility with parameter parsimony. The unrestricted BEKK GARCH dominates its restricted scalar and diagonal versions in terms of model fit, but its parameter dimensionality increases quickly with the number of variables. Covariance targeting has been proposed as a way of reducing parameter dimensionality, but for the BEKK with targeting the imposition of positive definiteness on the conditional covariance matrices presents a significant challenge. In this article, we suggest an approach based on Constrained Hamiltonian Monte Carlo that can deal effectively both with the nonlinear constraints resulting from BEKK targeting and the complicated nature of the BEKK likelihood in relatively high dimensions. We perform a model comparison of the full BEKK and the BEKK with targeting, indicating that the latter dominates the former in terms of marginal likelihood. Thus, we show that the BEKK with targeting presents an effective way of reducing parameter dimensionality without compromising the model fit, unlike the scalar or diagonal BEKK. The model comparison is conducted in the context of an application concerning a multivariate dynamic volatility analysis of a foreign exchange rate returns portfolio.