An estimator for parameters of a nonlinear nonnegative multidimensional AR(1) process

Anděl, Jiří

Applications of Mathematics, Tome 43 (1998) no. 5, pp. 389-398.

Résumé

Let $\mathbb{e}_t=(e_{t1},\dots ,e_{tp})^{\prime }$ be a $p$-dimensional nonnegative strict white noise with finite second moments. Let $h_{ij}(x)$ be nondecreasing functions from $[0,\infty )$ onto $[0,\infty )$ such that $h_{ij}(x)\le x$ for $i,j=1,\dots ,p$. Let $\mathbb{U}=(u_{ij})$ be a $p\times p$ matrix with nonnegative elements having all its roots inside the unit circle. Define a process $\mathbb{X}_t=(X_{t1},\dots ,X_{tp})^{\prime }$ by \[ X_{tj}=u_{j1}h_{1j}(X_{t-1,1})+\dots +u_{jp}h_{pj}(X_{t-1,p})+ e_{tj} \] for $j=1,\dots ,p$. A method for estimating $\mathbb{U}$ from a realization $\mathbb{X}_1,\dots ,\mathbb{X}_n$ is proposed. It is proved that the estimators are strongly consistent.

Détail

DOI : 10.1023/A:1022290419411

Classification : 62M09, 62M10
Keywords: autoregressive process; estimating parameters; multidimensional process; nonlinear process; nonnegative process