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Parameter estimation and subset selection for separable lower triangular bilinear models. (English) Zbl 1091.62091

The time series $X\left(t\right)$ is described by the separable lower triangular bilinear model:

$X\left(t\right)+\sum _{m=1}^{p}{a}_{m}X\left(t-m\right)=\epsilon \left(t\right)+\sum _{m=1}^{q}{b}_{m}\epsilon \left(t-m\right)+\sum _{m=1}^{r}{c}_{m}\epsilon \left(t-m\right)\left[\sum _{m=0}^{s}{d}_{n}X\left(t-m-n\right)\right]$

with i.i.d. Gaussian $\epsilon \left(t\right)$. An EM algorithm with non-informative prior is proposed for estimation of parameters. Akaike’s and Bayesian information criteria are considered for selection of the optimal subset model. Results of simulations and application to weekly egg prices at a German agricultural market are presented.

MSC:
 62M10 Time series, auto-correlation, regression, etc. (statistics) 62F10 Point estimation