It is now 20 years since the publication of Engle's (1982) seminal paper, which introduced ARCH to the world. The ARCH paper had an enormous influence on both theoretical and applied econometrics, and was influential in the establishment of the discipline of Financial Econometrics. In this paper...

Theoretical and practical interest in non-linear time series models, particularly regime switching models, have increased substantially in recent years. Given the abundant research activity in analysing time-varying volatility through Generalized Autoregressive Conditional Heteroscedasticity...

Investor risk is a complicated concept in practice and is not well captured by measures of volatility as is well understood by uncertainty theory. Rather than asking statisticians to attempt to measure risk, it may be better to listen to decision theorists, but their suggestions are not very...

This paper looks at some recent work on estimating quadratic variation using realized variance (RV)-that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process is a...

In this paper we present an exact maximum likelihood treatment for the estimation of a Stochastic Volatility in Mean (SVM) model based on Monte Carlo simulation methods. The SVM model incorporates the unobserved volatility as an explanatory variable in the mean equation. The same extension is...

In this paper we suggest using a modified version of the time reversibility (TR) test of Chen, Chou and Kuan (2000) as a complementary diagnostic test for time series models. The modified CCK test is easy to compute and requires weaker moment conditions than existing tests. Our simulations...

This paper bridges the gap between traditional ARCH modelling and recent advances on realized volatilities. Based on a ten-year sample of five-minute returns for the ECU basket currencies versus the US dollar, we find that the realized volatilities constructed from the summation of the...

In this paper we provide both qualitative and quantitative measures of the precision of measuring integrated volatility by realized volatility for a fixed frequency of observation. We start by characterizing for a general diffusion the difference between realized and integrated volatility for a...