Modeling financial volatility is an important part of empirical finance. This paper provides a literature review of the most relevant volatility models, with a particular focus on forecasting models. We firstly discuss the empirical foundations of different kinds of volatility. The paper, then, analyses the non-parametric measure of volatility, named realized variance, and its empirical applica...

For financial assets whose best quotes almost always change by jumping by the market’s price tick size (one cent, five cents, etc.), this paper proposes an estimator of Quadratic Variation which controls for microstructure effects. It measures the prevalence of alternations, where quotes jump back to their just-previous price. It defines a simple property called “uncorrelated alternation”, whic...

The performance of a kernel HAC estimator depends on the accuracy of the estimation of the normalized curvature, an unknown quantity in the optimal bandwidth represented as the spectral density and its derivative. This paper proposes to estimate it with a general class of kernels. The AMSE of the kernel estimator and the AMSE-optimal bandwidth are derived. It is shown that the optimal bandwidth...

The purpose of this paper is to investigate the ability of parameter instability tests in regressions with I(1) processes to discriminate between changes in the cointegrating relationship and changes in the marginal distribution of the regressors. Using annual data for the G-7 countries and the Purchasing Power Parity, we conclude that the regression coefficient between the price level differen...

This paper employs Hamilton’s (1989) original Markov-switching model and time-varying Markov-switching model developed by Filardo (1994), respectively, to investigate the business cycle and evaluate the usefulness of the coincident and leading indexes in dating the business cycle and in predicting future GDP in Taiwan. The empirical results do suggest that these two indexes help date the busine...

Alternative strategies for predicting stock market volatility are examined. In out-of-sample forecasting experiments implied-volatility information, derived from contemporaneously observed option prices or history-based volatility predictors, such as GARCH models, are investigated, to determine if they are more appropriate for predicting future return volatility. Employing German DAX-index retu...

In Markov-switching regression models, we use Kullback–Leibler (KL) divergence between the true and candidate models to select the number of states and variables simultaneously. Specifically, we derive a new information criterion, Markov switching criterion (MSC), which is an estimate of KL divergence. MSC imposes an appropriate penalty to mitigate the overretention of states in the Markov chai...

In this paper Efficient Importance Sampling (EIS) is used to perform a classical and Bayesian analysis of univariate and multivariate Stochastic Volatility (SV) models for financial return series. EIS provides a highly generic and very accurate procedure for the Monte Carlo (MC) evaluation of high-dimensional interdependent integrals. It can be used to carry out ML-estimation of SV models as we...

This paper presents a novel characterization of continuous time processes that captures the primary idiosyncratic features of many financial time series. We extend the analysis of unit root behaviors to incorporate series that have continuous sampling, but do so in such a way that the overall series does not tend towards explosive paths, as is implied by many unit root setups. In doing so, we e...

The outcome of popular unit root tests depends heavily on the initial condition, i.e. on the difference between the initial observation and the deterministic component. In some applications it is difficult to rule out small or large values of the initial condition a priori, so this dependence can be quite difficult to deal with in practice. We explore a number of methods for constructing unit r...