On periodic time-varying bilinear processes: structure and asymptotic inference

Abdelouahab Bibi () and Ahmed Ghezal ()
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Abdelouahab Bibi: UMC(1)
Ahmed Ghezal: UMC(1)

Statistical Methods & Applications, 2016, vol. 25, issue 3, No 4, 395-420

Abstract: Abstract This paper is devoted to the bilinear time series models with periodic-varying coefficients $$\left( { PBL}\right) $$ P B L . So, firstly conditions ensuring the existence of periodic stationary solutions of the $${ PBL}$$ P B L and the existence of higher-order moments of such solutions are given. A distribution free approach to the parameter estimation of $${ PBL}$$ P B L is presented. The proposed method relies on minimum distance estimator based on the first and second order empirical moments of the observed process. Consistency and asymptotic normality of the estimator are discussed. Examples and Monte Carlo simulation results illustrate the practical relevancy of our general theoretical results are presented.

Keywords: Periodic bilinear model; Strict and second-order periodic stationarity; Minimum distance estimator; Consistency; Asymptotic normality; Primary 62M10; Secondary 62M15 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10260-015-0344-5

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