Silvano Bordignon

Long memory and nonlinearities in realized volatility: A Markov switching approach

Realized volatility is studied using nonlinear and highly persistent dynamics. In particular, a model is proposed that simultaneously captures long memory and nonlinearities in which level and persistence shift through a Markov switching dynamics. Inference is based on an efficient Markov chain Monte Carlo (MCMC) algorithm that is used to estimate parameters, latent process and predictive densities. The in-sample results show that both long memory and nonlinearities are significant and improve the description of the data. The out-sample results at several forecast horizons show that introducing these nonlinearities produces superior forecasts over those obtained using nested models.

Comparing stochastic volatility models through Monte Carlo simulations

Stochastic volatility models are important tools for studying the behavior of many financial markets. For this reason a number of versions have been introduced and studied in the recent literature. The goal is to review and compare some of these alternatives by using Bayesian procedures. The quantity used to assess the goodness-of-fit is the Bayes factor, whereas the ability to forecast the volatility has been tested through the computation of the one-step-ahead value-at-risk (VaR). Model estimation has been carried out through adaptive Markov chain Monte Carlo (MCMC) procedures. The marginal likelihood, necessary to compute the Bayes factor, has been computed through reduced runs of the same MCMC algorithm and through an auxiliary particle filter. The empirical analysis is based on the study of three international financial indexes.

Estimation of Cpm when Measurement Error is Present

In this paper we study the properties of the estimator of Cpm when the observations are affected by measurement errors. We compare the performances of the estimator in the error case with those of the estimator in the error-free case. The results indicate that the presence of measurement errors in the data leads to different behavior of the estimator according to the entity of the error variability. We finally show how to use our results in practice. Copyright

Periodic Long-Memory GARCH Models

A distinguishing feature of the intraday time-varying volatility of financial time series is given by the presence of long-range dependence of periodic type, due mainly to time-of-the-day phenomena. In this work, we introduce a model able to describe the empirical evidence given by this periodic long-memory behaviour. The model, named PLM-GARCH (Periodic Long-Memory GARCH), represents a natural extension of the FIGARCH model proposed for modelling long-range persistence of volatility. Periodic long memory versions of EGARCH (PLM-EGARCH) and of Log-GARCH (PLM-LGARCH) models are also examined. Some properties and characteristics of the models are given and finite sample performance of quasi-maximum likelihood estimation are studied with Monte Carlo simulations. Further possible extensions of the model to take into account multiple sources of periodic long-memory behaviour are proposed. Two empirical applications on intra-day financial time series are also provided.

Generalised long-memory GARCH models for intra-daily volatility

The class of fractionally integrated generalised autoregressive conditional heteroskedastic (FIGARCH) models is extended for modelling the periodic long-range dependence typically shown by volatility of most intra-daily financial returns. The proposed class of models introduces generalised periodic long-memory filters, based on Gegenbauer polynomials, into the equation describing the time-varying volatility of standard GARCH models. A fitting procedure is illustrated and its performance is evaluated by means of Monte Carlo simulations. The effectiveness of these models in describing periodic long-memory volatility patterns is shown through an empirical application to the Euro-Dollar intra-daily exchange rate.

The Optimal Use of Provisional Data in Forecasting With Dynamic Models

Timely economic forecasts by means of dynamic models rely on updated time series, the last figure(s) of which are provisional and will be typically subjected to a number of revisions. A general approach to the efficient use of provisional observations in dynamic models is presented, based on the state-space methodology and the Kalman filter. Suitable adaptations are introduced, chiefly involving the measurement equations. Some applications are carried out for Italy, concerning (a) the monthly index of industrial production and (b) a small dynamic simultaneous-equation model of the aggregate economy. Kalman-filter estimates and predictions are compared with more traditional procedures.

Monitoring algorithms for detecting changes in the ozone concentrations

The quality of data collected by air pollution monitoring networks is often affected by inaccuracies and missing data problems, mainly due to breakdowns and/or biases of the measurement instruments. In this paper we propose a statistical method to detect, as soon as possible, biases in the measurement devices, in order to improve the quality of collected data on line. The technique is based on the joint use of stochastic modelling and statistical process control algorithms. This methodology is applied to the mean hourly ozone concentrations recorded from one monitoring site of the Bologna urban area network. We set up the monitoring algorithm through Monte Carlo simulations in such a way to detect anomalies in the data within a reasonable delay. The results show several out of control signals that may be caused by problems in the measurement device.

k -Factor GARMA models for intraday volatility forecasting

This paper studies the ability of the k -factor GARMA processes to model and forecast the volatility of an intraday financial time series. Forecasting results from the k -factor GARMA model are obtained and compared with those produced by a conventional SARIMA model.

Predictive accuracy for chaotic economic models

Abstract In this work we present a technique to obtain prediction intervals for chaotic data. Using nearest neighbors method we give estimates of local variance and percentiles of the prediction error distribution. This allows to define an interval containing a future value with a given probability. Its effectiveness is shown with data generated by a chaotic economic model.

Nonlinear models for ground--level ozone forecasting

One of the main concerns in air pollution is excessive tropospheric ozone concentration. The aim of this work is to develop statistical models giving shortterm forecasts of future ground-level ozone concentrations. Since there are few physical insights about the dynamic relationship between ozone, precursor emissions and/or meteorological factors, a nonparametric and nonlinear approach seems promising in order to specify the forecast models. First, we apply four nonparametric procedures to forecast daily maximum 1-hour and maximum 8-hour averages of ozone concentrations in an urban area. Then, in order to improve the forecast performances, we combine the time series of the forecasts. This idea seems to give encouraging results.