% url = {https://www.semanticscholar.org/paper/Parameter-Estimation-of-ARMA-Models-with-GARCH-%2F-An-W%C3%BCrtz-Chalabi/a36c8a229960c7e6a47c2c060d94b780399ab065}

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@PhdThesis{mary2013,
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@article{10.2307/20445243,
 ISSN = {03195724},
 DOI = {10.1002/cjs.5550350112},
 abstract = {The authors show how to extend univariate mixture autoregressive models to a multivariate time series context. Similar to the univariate case, the multivariate model consists of a mixture of stationary or nonstationary autoregressive components. The authors give the first and second order stationarity conditions for a multivariate case up to order 2. They also derive the second order stationarity condition for the univariate mixture model up to arbitrary order. They describe an EM algorithm for estimation, as well as a diagnostic checking procedure. They study the performance of their method via simulations and include a real application. /// Les auteurs montrent comment les mod�les de m�lange autor�gressifs univari�s peuvent �tre �tendus au cas de s�ries chronologiques multivari�es. � l'instar du cas univari�, le mod�le multivari� est compos� d'un m�lange de processus autor�gressifs, stationnaires ou non. Les auteurs donnent les conditions de stationnarit� de premier et de deuxi�me ordre des mod�les multivari�s de degr� 1 et 2. Ils pr�cisent aussi les conditions de stationnarit� du deuxi�me ordre pour un mod�le de m�lange univari� de degr� arbitraire. Ils d�crivent un algorithme de type EM aux fins d'estimation, ainsi qu'un test diagnostic. Ils examinent la performance de leur proc�dure au moyen de simulations et pr�sentent une application concr�te.},
 author = {P. W. Fong and W. K. Li and C. W. Yau and C. S. Wong},
 journal = {The Canadian Journal of Statistics / La Revue Canadienne de Statistique},
 number = {1},
 pages = {135--150},
 publisher = {[Statistical Society of Canada, Wiley]},
 title = {On a Mixture Vector Autoregressive Model},
 volume = {35},
 year = {2007}
}

@article{Smith1985,
author = {Smith, J. Q.},
title = {Diagnostic checks of non-standard time series models},
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keywords = {Time-series analysis, Diagnostic checks, Non-normal models, Cusum},
doi = {10.1002/for.3980040305},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/for.3980040305},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/for.3980040305},
abstract = {Abstract Diagnostic checks have become a standard tool for helping to assess the adequacy of a forecasting system since Box and Jenkins' (1970) ARIMA modelling technique became popular. However, most of the research has developed checks for normal or second-order stationary models. This paper gives various diagnostic checks that can be performed simply on nonnormal, non-standard models such as the class of multiprocess models (Harrison and Stevens, 1976), where residuals are definitely not normal. The performance to date of these models can then be objectively scrutinized on-line. Examples, including a generalized cusum technique, are given to illustrate the effectiveness of the techniques on specific series.},
year = {1985}
}
