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Statistica Sinica 23 (2013), 1573-1594




Tze Leung Lai and Haipeng Xing

Stanford University and SUNY at Stony Brook

Abstract: This paper shows that the commonly encountered volatility persistence in fitting GARCH models to financial time series can arise if the possibility of structural changes is not incorporated in the time series model. To avoid spurious long memory in modeling volatilities of econometric time series, we consider two time-scales and use the ``short'' time-scale to define GARCH dynamics and the ``long'' time-scale to incorporate parameter jumps. This leads to a Bayesian change-point ARX-GARCH model, whose unknown parameters can undergo occasional changes at unspecified times and can be estimated by explicit recursive formulas when the hyperparameters of the Bayesian model are specified. Efficient estimators of the hyperparameters of the Bayesian model are developed, yielding empirical Bayes estimates of the piecewise constant parameters in the stochastic change-point model. The empirical Bayes approach is applied to the frequentist problem of partitioning the time series into segments under sparsity assumptions on the change-points. Simulation and empirical studies of its performance are also given.

Key words and phrases: ARX-GARCH models, empirical Bayes, long memory, multiple change-points, recursive adaptive filters, segmentation.

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