Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/242010 
Year of Publication: 
2021
Citation: 
[Journal:] Journal of Time Series Analysis [ISSN:] 1467-9892 [Volume:] 42 [Issue:] 5-6 [Publisher:] John Wiley & Sons, Ltd [Place:] Oxford, UK [Year:] 2021 [Pages:] 653-684
Publisher: 
John Wiley & Sons, Ltd, Oxford, UK
Abstract: 
We estimate the parameter of a stationary time series process by minimizing the integrated weighted mean squared error between the empirical and simulated characteristic function, when the true characteristic functions cannot be explicitly computed. Motivated by Indirect Inference, we use a Monte Carlo approximation of the characteristic function based on i.i.d. simulated blocks. As a classical variance reduction technique, we propose the use of control variates for reducing the variance of this Monte Carlo approximation. These two approximations yield two new estimators that are applicable to a large class of time series processes. We show consistency and asymptotic normality of the parameter estimators under strong mixing, moment conditions, and smoothness of the simulated blocks with respect to its parameter. In a simulation study we show the good performance of these new simulation based estimators, and the superiority of the control variates based estimator for Poisson driven time series of counts.
Subjects: 
Asymptotic normality
characteristic function
control variates
indirect inference estimation
time series of counts
SLLN
variance reduction
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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