| Title:
|
QMLE of periodic bilinear models and of PARMA models with periodic bilinear innovations (English) |
| Author:
|
Bibi, Abdelouahab |
| Author:
|
Ghezal, Ahmed |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
375-399 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $QMLE$. (English) |
| Keyword:
|
periodic bilinear model |
| Keyword:
|
periodic $ARMA$ model |
| Keyword:
|
strict and second-order periodic stationarity |
| Keyword:
|
strong consistency |
| Keyword:
|
asymptotic normality |
| MSC:
|
62M10 |
| MSC:
|
62M15 |
| idZBL:
|
Zbl 06890427 |
| idMR:
|
MR3807722 |
| DOI:
|
10.14736/kyb-2018-2-0375 |
| . |
| Date available:
|
2018-05-30T16:14:21Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147201 |
| . |
| Reference:
|
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| . |
