Eduardo Rossi

Estimation of Long Memory in Integrated Variance

A stylized fact is that realized variance has long memory. We show that, when the instantaneous volatility is a long memory process of order d, the integrated variance is characterized by the same long-range dependence. We prove that the spectral density of realized variance is given by the sum of the spectral density of the integrated variance plus that of a measurement error, due to the sparse sampling and market microstructure noise. Hence, the realized volatility has the same degree of long memory as the integrated variance. The additional term in the spectral density induces a finite-sample bias in the semiparametric estimates of the long memory. A Monte Carlo simulation provides evidence that the corrected local Whittle estimator of Hurvich et al. (2005) is much less biased than the standard local Whittle estimator and the empirical application shows that it is robust to the choice of the sampling frequency used to compute the realized variance. Finally, the empirical results suggest that the volatility series are more likely to be generated by a nonstationary fractional process.

Model and distribution uncertainty in multivariate GARCH estimation: A Monte Carlo analysis

Multivariate GARCH models are in principle able to accommodate the features of the dynamic conditional correlations processes, although with the drawback, when the number of financial returns series considered increases, that the parameterizations entail too many parameters.In general, the interaction between model parametrization of the second conditional moment and the conditional density of asset returns adopted in the estimation determines the fitting of such models to the observed dynamics of the data. This paper aims to evaluate the interactions between conditional second moment specifications and probability distributions adopted in the likelihood computation, in forecasting volatilities and covolatilities. We measure the relative performances of alternative conditional second moment and probability distributions specifications by means of Monte Carlo simulations, using both statistical and financial forecasting loss functions.

A No Arbitrage Fractional Cointegration Analysis of the Range Based Volatility

The no arbitrage relation between futures and spot prices implies an analogous relation between futures and spot volatilities as measured by daily range. Long memory features of the range-based volatility estimators of the two series are analyzed, and their joint dynamics are modeled via a fractional vector error correction model (FVECM), in order to explicitly consider the no arbitrage constraints. We introduce a two-step estimation procedure for the FVECM parameters and we show the properties by a Monte Carlo simulation. The out-of-sample forecasting superiority of FVECM, with respect to competing models, is documented. The results highlight the importance of giving fully account of long-run equilibria in volatilities in order to obtain better forecasts.

Chasing Volatility: A Persistent Multiplicative Error Model with Jumps

The realized volatility of financial returns is characterized by persistence and occurrence of unpredictable large increments. To capture those features, we introduce the Multiplicative Error Model with jumps (MEM-J). When a jump component is included in the multiplicative specification, the conditional density of the realized measure is shown to be a countably infinite mixture of Gamma and K distributions. Strict stationarity conditions are derived. A Monte Carlo simulation experiment shows that maximum likelihood estimates of the model parameters are reliable even when jumps are rare events. We estimate alternative specifications of the model using a set of daily bipower measures for 7 stock indexes and 16 individual NYSE stocks. The estimates of the jump component confirm that the probability of jumps dramatically increases during the financial crises. Compared to other realized volatility models, the introduction of the jump component provides a sensible improvement in the fit, as well as for in-sample and out-of-sample volatility tail forecasts.

Efficient importance sampling maximum likelihood estimation of stochastic differential equations

Maximum likelihood estimation (MLE) of stochastic differential equations (SDEs) is difficult because in general the transition density function of these processes is not known in closed form, and has to be approximated somehow. An approximation based on efficient importance sampling (EIS) is detailed. Monte Carlo experiments, based on widely used diffusion processes, evaluate its performance against an alternative importance sampling (IS) strategy, showing that EIS is at least equivalent, if not superior, while allowing a greater flexibility needed when examining more complicated models.

Independent Factor Autoregressive Conditional Density Model

In this article, we propose a novel Independent Factor Autoregressive Conditional Density (IFACD) model able to generate time-varying higher moments using an independent factor setup. Our proposed framework incorporates dynamic estimation of higher comovements and feasible portfolio representation within a non-elliptical multivariate distribution. We report an empirical application, using returns data from 14 MSCI equity index iShares for the period 1996 to 2010, and we show that the IFACD model provides superior VaR forecasts and portfolio allocations with respect to the Conditionally Heteroskedastic Independent Component Analysis of Generalized Orthogonal (CHICAGO) and DCC models.

Conditional Jumps in Volatility and Their Economic Determinants

The volatility of financial returns is affected by rapid and large increments. Such movements can be hardly generated by a pure diffusive process for stochastic volatility. On the contrary jumps in volatility are important because they allow for rapid increases, like those observed during stock market crashes. We propose an extension of HAR model for estimating the presence of jumps in volatility, using the realized-range measure as a volatility proxy. By focusing on a set of 36 NYSE stocks, we show that, once that squared jumps in prices are disentangled from integrated variance, then there is a positive probability of jumps in volatility, conditional on the past information set. We then focus on the contribution of jumps during periods of financial turmoil. We analyze the dependence between the first principal component of the volatility jumps with a set of financial covariates including VIX, S&P500 volume, CDS, and Federal Fund rates. We observe that CDS captures large part of the expected jumps moves, verifying the common interpretation that large and sudden increases in volatility in stock markets over some days in the recent financial crisis have been caused by credit deterioration of US bank sector. Finally, we extend the model incorporating the credit-default swap in the dynamics of the jump size and intensity. The estimates confirm the significant contribution of the credit-default swap to the dynamics of the volatility jump size.

Artificial regression testing in the GARCH-in-mean model

The issue of finite-sample inference in Generalised Autoregressive Conditional Heteroskedasticity (GARCH)-like models has seldom been explored in the theoretical literature, although its potential relevance for practitioners is obvious. In some cases, asymptotic theory may provide a very poor approximation to the actual distribution of the estimators in finite samples. The aim of this paper is to propose the application of the so-called double length regressions (DLR) to GARCH-in-mean models for inferential purposes. As an example, we focus on the issue of Lagrange Multiplier tests on the risk premium parameter. Simulation evidence suggests that DLR-based Lagrange Multiplier (LM) test statistics provide a much better testing framework than the more commonly used LM tests based on the outer product of gradients (OPG) in terms of actual test size, especially when the GARCH process exhibits high persistence in volatility. This result is consistent with previous studies on the subject. Copyright 2005 Royal Economic Society

Long memory and periodicity in intraday volatilities of stock index futures

This paper investigates the intraday volatility pattern of the E-mini SP500 hourly returns. In order to account for the observed long memory and periodicity in returns volatility we introduce the Fractionally Integrated Periodic EGARCH and the Seasonal Fractional Integrated Periodic EGARCH. For both models we compute the population kurtosis and the autocorrelation function of power transformations of absolute returns. The results confirm that volatility of hourly returns sampled over the 24 hours across different markets are characterized by strong seasonal pattern with a statistically significant persistence.

Long Memory in Integrated and Realized Variance

The long memory properties of the integrated and realized volatility are investigated under the assumption that the instantaneous volatility is driven by a fractional Brownian motion. The equality of their long memory degrees is proved in the ideal situation when prices are observed continuously. In this case, the spectral density of the integrated and realized volatility coincide.