| Title:
|
An estimator for parameters of a nonlinear nonnegative multidimensional AR(1) process (English) |
| Author:
|
Anděl, Jiří |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
43 |
| Issue:
|
5 |
| Year:
|
1998 |
| Pages:
|
389-398 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
autoregressive process |
| Keyword:
|
estimating parameters |
| Keyword:
|
multidimensional process |
| Keyword:
|
nonlinear process |
| Keyword:
|
nonnegative process |
| MSC:
|
62M09 |
| MSC:
|
62M10 |
| idZBL:
|
Zbl 0953.62091 |
| idMR:
|
MR1644124 |
| DOI:
|
10.1023/A:1022290419411 |
| . |
| Date available:
|
2009-09-22T17:58:53Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134395 |
| . |
| Reference:
|
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| . |
