Estimation and Prediction for the Modulated Power Law Process

Abstract

The modulated power law process has been proposed by Lakey and Rigdon in 1992 as a compromise between the non-homogeneous Poisson process and the renewal process model. It is useful in analyzing duration dependence in economic and financial cycles. In this paper we consider a problem of estimation and prediction for the modulated power law process. Using the estimating functions approach we propose new estimators of the parameters of the modulated power law process. The estimators proposed we apply to construct predictors of the next event time. We also present algorithms for effective calculating the values of estimators and predictors proposed. In the simulation study conducted we compare the accuracy of the estimators proposed with the maximum likelihood ones and examine the precision of predictors presented. The results obtained we apply in analysing a real data set of U.S. stock market cycles.