Combining long memory and level shifts in modeling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean- and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in high-frequency measures of volatility whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes, and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons

Realized Volatility Risk

In this paper we document that realized variation measures constructed from high- frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation measures are nearly gaussian, this unpredictability brings considerably more uncertainty to the empirically relevant ex ante distribution of returns. Carefully modeling this volatility risk is fundamental. We propose a dually asymmetric realized volatility (DARV) model, which incorporates the important fact that realized volatility series are systematically more volatile in high volatility periods. Returns in this framework display time varying volatility, skewness and kurtosis. We provide a detailed account of the empirical advantages of the model using data on the S&P 500 index and eight other indexes and stocks.Realized volatility; volatility of volatility; volatility risk; value-at-risk; forecasting; conditional heteroskedasticity

Financial markets as a complex system: A short time scale perspective

In this paper we want to discuss macroscopic and microscopic properties of financial markets. By analyzing quantitatively a database consisting of 13 minute per minute recorded financial time series, we identify some macroscopic statistical properties of the corresponding markets, with a special emphasize on temporal correlations. These analysis are performed by using both linear and nonlinear tools. Multivariate correlations are also tested for, which leads to the identification of a global coupling mechanism between the considered stock markets. The application of a new formalism, called transfer entropy, allows to measure the information flow between some financial time series. We then discuss some key aspects of recent attemps to model financial markets from a microscopic point of view. One model, that is based on the simulation of the order book, is described more in detail, and the results of its practical implementation are presented. We finally address some general aspects of forecasting and modeling, in particular the role of stochastic and nonlinear deterministic processes. --time series analysis,econophysics,simulated markets,temporal correlations,high-frequency data

Forecasting Irregularly Spaced UHF Financial Data: Realized Volatility vs UHF-GARCH Models

A very promising literature has been recently devoted to the modeling of ultra-high-frequency (UHF) data. Our first aim is to develop an empirical application of Autoregressive Conditional Duration GARCH models and the realized volatility to forecast future volatilities on irregularly spaced data. We also compare the out sample performances of ACD GARCH models with the realized volatility method. We propose a procedure to take into account the time deformation and show how to use these models for computing daily VaR.Realized volatility, Ultra High Frequency GARCH, time deformation, financial markets, Daily VaR.