Geodesic
QMLE of periodic bilinear models and of PARMA models with periodic bilinear innovations
Kybernetika, Tome 54 (2018) no. 2, pp. 375-399 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper develops an asymptotic inference theory for bilinear $\left( BL\right) $ time series models with periodic coefficients $\left( PBL\text{ for short}\right) $. For this purpose, we establish firstly a necessary and sufficient conditions for such models to have a unique stationary and ergodic solutions (in periodic sense). Secondly, we examine the consistency and the asymptotic normality of the quasi-maximum likelihood estimator $\left( QMLE\right) $ under very mild moment condition for the innovation errors. As a result, it is shown that whenever the model is strictly stationary, the moment of some positive order of $PBL$ model exists and is finite, under which the strong consistency and asymptotic normality of $QMLE$ for $PBL$ are proved. Moreover, we consider also the periodic $ARMA$ $\left( PARMA\right) $ models with $PBL$ innovations and we prove the consistency and the asymptotic normality of its $QMLE$.
This paper develops an asymptotic inference theory for bilinear $\left( BL\right) $ time series models with periodic coefficients $\left( PBL\text{ for short}\right) $. For this purpose, we establish firstly a necessary and sufficient conditions for such models to have a unique stationary and ergodic solutions (in periodic sense). Secondly, we examine the consistency and the asymptotic normality of the quasi-maximum likelihood estimator $\left( QMLE\right) $ under very mild moment condition for the innovation errors. As a result, it is shown that whenever the model is strictly stationary, the moment of some positive order of $PBL$ model exists and is finite, under which the strong consistency and asymptotic normality of $QMLE$ for $PBL$ are proved. Moreover, we consider also the periodic $ARMA$ $\left( PARMA\right) $ models with $PBL$ innovations and we prove the consistency and the asymptotic normality of its $QMLE$.
DOI : 10.14736/kyb-2018-2-0375
Classification : 62M10, 62M15
Keywords: periodic bilinear model; periodic $ARMA$ model; strict and second-order periodic stationarity; strong consistency; asymptotic normality 
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     author = {Bibi, Abdelouahab and Ghezal, Ahmed},
     title = {QMLE of periodic bilinear models and of {PARMA} models with periodic bilinear innovations},
     journal = {Kybernetika},
     pages = {375--399},
     year = {2018},
     volume = {54},
     number = {2},
     doi = {10.14736/kyb-2018-2-0375},
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     zbl = {06890427},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-2-0375/}
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Bibi, Abdelouahab; Ghezal, Ahmed. QMLE of periodic bilinear models and of PARMA models with periodic bilinear innovations. Kybernetika, Tome 54 (2018) no. 2, pp. 375-399. doi: 10.14736/kyb-2018-2-0375

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