Beaumont, Paul and Smallwood, Aaron (2019): Inference for likelihoodbased estimators of generalized longmemory processes.

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Abstract
Despite a recent proliferation of research using cyclical long memory, surprisingly little is known regarding the asymptotic properties of likelihoodbased methods. Estimators have been studied in both the time and frequency domains for the Gegenbauer autoregressive moving average process (GARMA). However, a full set of asymptotic results for all parameters has only been proposed by Chung (1996a,b), who present somewhat tenuous results without an initial consistency proof. In this paper, we review the GARMA process and the properties of frequency and time domain likelihoodbased estimators using Monte Carlo analysis. The results demonstrate the strong efficacy of both estimators and generally sup port the proposed theory of Chung for the parameter governing the cycle length. Important caveats await. The results show that asymptotic confidence bands can be unreliable in very small samples under weak long memory, and the distribution theory under the null of an infinitely long cycle appears to be unusable. Possible solutions are proposed, including the use of narrower confidence bands and the application of theory under the alternative of finite cycles.
Item Type:  MPRA Paper 

Original Title:  Inference for likelihoodbased estimators of generalized longmemory processes 
English Title:  Inference for likelihoodbased estimators of generalized longmemory processes 
Language:  English 
Keywords:  long memory, GARMA, CSS estimator, Whittle estimator 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C40  General C  Mathematical and Quantitative Methods > C5  Econometric Modeling 
Item ID:  96313 
Depositing User:  Dr Aaron Smallwood 
Date Deposited:  12 Oct 2019 04:31 
Last Modified:  12 Oct 2019 04:31 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/96313 