Access Restriction

Author Lux, Thomas
Source EconStor
Content type Text
Publisher Kiel University, Department of Economics
File Format PDF
Language English
Subject Domain (in DDC) Social sciences ♦ Economics
Subject Keyword Multifractal ♦ Forecasting ♦ Volatility ♦ GMM estimation ♦ Markov-switching ♦ Kapitalertrag ♦ Börsenkurs ♦ Volatilität ♦ Prognoseverfahren ♦ Physik ♦ Markovscher Prozess ♦ Zeitreihenanalyse ♦ Theorie ♦ Single Equation Models; Single Variables: General ♦ Asset Pricing; Trading Volume; Bond Interest Rates
Abstract Multi-fractal processes have recently been proposed as a new formalism for modelling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns - a feature that has been found in virtually all financial data. Initial difficulties stemming from non-stationarity and the combinatorial nature of the original model have been overcome by the introduction of an iterative Markov-switching multi-fractal model in Calvet and Fisher (2001) which allows for estimation of its parameters via maximum likelihood and Bayesian forecasting of volatility. However, applicability of MLE is restricted to cases with a discrete distribution of volatility components. From a practical point of view, ML also becomes computationally unfeasible for large numbers of components even if they are drawn from a discrete distribution. Here we propose an alternative GMM estimator together with linear forecasts which in principle is applicable for any continuous distribution with any number of volatility components. Monte Carlo studies show that GMM performs reasonably well for the popular Binomial and Lognormal models and that the loss incured with linear compared to optimal forecasts is small. Extending the number of volatility components beyond what is feasible with MLE leads to gains in forecasting accuracy for some time series.
Part of series Economics Working Paper x2004-11
Learning Resource Type Article
Publisher Date 2004-01-01
Publisher Place Kiel
Rights Holder