A self-exciting switching model
In this research, a self-exciting switching model where the switch depends on the past realizations of the process is proposed. The model can be used to capture the cluster pattern driven by the self-exciting mechanism and trace the "turning point" of the regime switching. Closed-form likelihood function and maximum likelihood estimation are presented when the underlying distribution comes from general exponential family. A modified likelihood ratio test is considered when conventional regularity conditions of asymptotic theory for likelihood ratio test is violated. A new test is also developed to distinguish between data with cluster pattern where the variables are dependent in a self-exciting fashion versus independently identically distributed random variables. We also developed asymptotic distribution of the test statistic with closed-form covariance structure. Comparison with scan statistics is discussed in the context of simulated earthquake data. Application on the residential burglary data is also considered. Our test is easy to implement because they do not require the estimation of the model under the alternative. To demonstrate the applicability of the model, we conduct the following studies: In the first study, we investigate the daily coalition casualties data in Iraq from time period: January 2004 to March 2006. In this study, our model assumption is that we have two states of terrorist activity in Iraq: low and high. The self-exciting nature of the terrorism phenomena is straightforward: violence typically triggers more violence. A moving-sum/threshold type of switching mechanism is implemented and comparisons with Hidden Markov Model (HMM) are discussed. In the second study, we apply the self-exciting switching model to US GNP data to study the asymmetric business cycles. The data is seasonally adjusted U.S. GNP quarterly growth from January 1947 to March 2006. Self-exciting switching models with various switching mechanisms and dynamics are considered. Finally comparisons of forecasting performance with Self-Exciting Threshold AutoRegressive (SETAR) model are discussed. The prediction of U.S. business cycle dates using our model are extremely close to the results provided by NBER. (National Bureau of Economic Research).
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Dissertations Collection for University of Connecticut