Computational Aspects of Maximum Likelihood Estimation of Autoregressive Fractionally Integrated Moving Average Models

We discuss computational aspects of likelihood-based estimation of univariate ARFIMA (p,d,q) models. We show how efficient computation and simulation is feasible, even for large samples. We also discuss the implementation of analytical bias corrections.Long memory, Bias, Modified profile likelihood, Restricted maximum likelihood estimator, Time-series regression model likelihood

Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models

In recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of 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 statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model

Analyzing Sunspot Number via Gegenbauer Long Memory Process with Correlated Additive Noise

It is known that the the sunspot number is well described by a Gegenbauer long memory process. Recent development on the field of time series analysis enable us to consider and estimate more flexible specification. The purposes of this paper are to extend the conventional specification for sunspot numbers to accommodate correlated additive noise and to estimate the new model by the Bayesian Markov chain Monte Carlo technique. The empirical result shows that the newspecification improves the model fitness

The volatility of realized volatility

Using unobservable conditional variance as measure, latent-variable approaches, such as GARCH and stochastic-volatility models, have traditionally been dominating the empirical finance literature. In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. By constructing "observable" or realized volatility series from intraday transaction data, the use of standard time series models, such as ARFIMA models, have become a promising strategy for modeling and predicting (daily) volatility. In this paper, we show that the residuals of the commonly used time-series models for realized volatility exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance when modeling and forecasting realized volatility. In an empirical application for S&P500 index futures we show that allowing for time-varying volatility of realized volatility leads to a substantial improvement of the model's fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting. Klassifikation: C22, C51, C52, C5

Density Forecasts Based on Disaggregate Data: Nowcasting Polish Inflation

The paper investigates gains in performance of density forecasts from models using disaggregate data when forecasting aggregate series. The problem is considered within a restricted VAR framework with alternative sets of exclusion restrictions. Empirical analysis of Polish CPI m-o-m inflation rate (using its 14 sub-categories for disaggregate modelling) is presented. Exclusion restrictions are shown to improve density forecasting performance (as evaluated using log-score and CRPS criteria) relatively to aggregate and also disaggregate unrestricted models

The Volatility of Realized Volatility

Using unobservable conditional variance as measure, latent–variable approaches, such as GARCH and stochastic–volatility models, have traditionally been dominating the empirical finance literature. In recent years, with the availability of high–frequency financial market data modeling realized volatility has become a new and innovative research direction. By constructing “observable” or realized volatility series from intraday transaction data, the use of standard time series models, such as ARFIMA models, have become a promising strategy for modeling and predicting (daily) volatility. In this paper, we show that the residuals of the commonly used time–series models for realized volatility exhibit non–Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance when modeling and forecasting realized volatility. In an empirical application for S&P500 index futures we show that allowing for time–varying volatility of realized volatility leads to a substantial improvement of the model’s fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.Finance, Realized Volatility, Realized Quarticity, GARCH, Normal Inverse Gaussian Distribution, Density Forecasting

Long Memory on the German Stock Exchange

In this study, the contributors present the results of their investigations into the long-memory properties of trading volume and the volatility of stock returns (given by absolute returns and alternatively by square returns). Their database is daily stock data of German companies in the DAX segment of the German Stock Exchange. The purpose of these investigations is the calculation of memory parameters and to determine whether there exists the same degree of long memory for trading-volume and return-volatility data. Calculations are performed on daily results from January 1994 to November 2005 and in three sub-periods: January 1994 to December 1997, January 1998 to December 2001, and January 2002 to November 2005.DAX 30; trading volume; univariate and bivariate long memory

Periodic Heteroskedastic RegARFIMA models for daily electricity spot prices

In this paper we consider different periodic extensions of regression models with autoregressive fractionally integrated moving average disturbances for the analysis of daily spot prices of electricity. We show that day-of-the-week periodicity and long memory are important determinants for the dynamic modelling of the conditional mean of electricity spot prices. Once an effective description of the conditional mean of spot prices is empirically identified, focus can be directed towards volatility features of the time series. For the older electricity market of Nord Pool in Norway, it is found that a long memory model with periodic coefficients is required to model daily spot prices effectively. Further, strong evidence of conditional heteroskedasticity is found in the mean corrected Nord Pool series. For daily prices at three emerging electricity markets that we consider (APX in The Netherlands, EEX in Germany and Powernext in France) periodicity in the autoregressive coefficients is also stablished, but evidence of long memory is not found and existence of dynamic behaviour in the variance of the spot prices is less pronounced. The novel findings in this paper can have important consequences for the modelling and forecasting of mean and variance functions of spot prices for electricity and associated contingent assetsGARCH, Long Memory

Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes

In order to assess the effect of jumps on realised variance calculations, we study some of the econometric properties of time-changed Levy processes. We show that in general we can derive the second order properties of realised variances and use these to estimate the parameters of such models. Our analytic results give a first indication of the degrees of inconsistency of realised variance as an estimator of the time-change in the non-Brownian case. Further, our results suggest volatility is even more predictable than has been shown by the recent econometric work on realised variance.Kalman filter, Levy process, Long-memory, Quasi-likelihood, Realised variance, Stochastic volatility, Time-change.