This paper proposes the Lagrange multiplier test for the null hypothesis thatthe bivariate time series has only a single common stochastic volatility factor and noidiosyncratic volatility factor. The test statistic is derived by representing the model in alinear state-space form under the...

This paper employs weighted least squares to examine the risk-return relation by applying high-frequency data from four major stock indexes in the US market and finds some evidence in favor of a positive relation between the mean of the excess returns and expected risk. However, by using...

This work develops change-point methods for statistics of high-frequency data. The main interest is the volatility of an Itô semi-martingale, which is discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate different smoothness classes of the...

We consider the problem of estimating the fractional order of a Lévy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two...

Empirical studies have shown that a large number of financial asset returns exhibit fat tails and are often characterized by volatility clustering and asymmetry. Also revealed as a stylized fact is Long memory or long range dependence in market volatility, with significant impact on pricing and...

The effects of temporal aggregation and choice of sampling frequency are of great interest in modeling the dynamics of asset price volatility. We show how the squared low-frequency returns can be expressed in terms of the temporal aggregation of a high-frequency series. Based on the theory of...

This paper examines the volatility of cryptocurrencies, with particular attention to their potential long memory properties. Using daily data for the three major cryptocurrencies, namely Ripple, Ethereum, and Bitcoin, we test for the long memory property using, Rescaled Range Statistics (R/S),...

This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the corresponding statistical properties of this model,...

This paper offers a new method for estimation and forecasting of the linear and nonlinear time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient parametric models, such as AR or GARCH, whose coefficients...

In this paper, we review the most common specifications of discrete-time stochastic volatility (SV) models and illustrate the major principles of corresponding Markov Chain Monte Carlo (MCMC) based statistical inference. We provide a hands-on ap proach which is easily implemented in empirical...