| Title:
|
Improvement of prediction for a larger number of steps in discrete stationary processes (English) |
| Author:
|
Cipra, Tomáš |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
27 |
| Issue:
|
2 |
| Year:
|
1982 |
| Pages:
|
118-127 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\{W_t\}=\{(X'_{t'}, Y'_t)'\}$ be vector ARMA $(m,n)$ processes. Denote by $\hat{X}_t(a)$ the predictor of $X_t$ based on $X_{t-a}, X_{t-a-1}, \ldots$ and by $\hat{X}_t(a,b)$ the predictor of $X_t$ based on $X_{t-a}, X_{t-a-1}, \ldots, Y_{t-b},Y_{t-b-1}, \ldots$. The accuracy of the predictors is measured by $\Delta_X(a)=\text{E}[X_t-\hat{X}_t(a)][X_t-\hat{X}_t(a)]'$ and $\Delta_X(a,b)=\text{E}[X_t-\hat{X}_t(a,b)][X_t-\hat{X}_t(a,b)]'$. A general sufficient condition for the equality $\Delta_X(a)=\Delta_X(a,a)]$ is given in the paper and it is shown that the equality $\Delta_X(1)=\Delta_X(1,1)]$ implies $\Delta_X(a)=\Delta_X(a,a)]$ for all natural numbers $a$. (English) |
| Keyword:
|
improvement of prediction |
| Keyword:
|
discrete stationary process |
| MSC:
|
60G10 |
| MSC:
|
60G25 |
| MSC:
|
62M20 |
| idZBL:
|
Zbl 0489.60047 |
| idMR:
|
MR0651049 |
| DOI:
|
10.21136/AM.1982.103952 |
| . |
| Date available:
|
2008-05-20T18:18:45Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103952 |
| . |
| Reference:
|
[1] J. Anděl: Measures of dependence in discrete stationary processes.Math. Operationsforsch. Statist., Ser. Statistics 10 (1979), 107-126. MR 0542367 |
| Reference:
|
[2] J. Anděl: On extrapolation in two-dimensional stationary processes.To appear in Math. Operationsforsch. Statist., Ser. Statistics. MR 0596515 |
| Reference:
|
[3] J. Anděl: Some measures of dependence in discrete stationary processes.Doctoral dissertation (Department of Statistics, Charles University, Prague, 1980) (in Czech). MR 0542367 |
| Reference:
|
[4] T. Cipra: Correlation and improvement of prediction in multivariate stationary processes.Ph. D. dissertation (Department of Statistics, Charles University, Prague, 1980) (in Czech). |
| Reference:
|
[5] T. Cipra: Improvement of prediction in multivariate stationary processes.Kybernetika 17 (1981), 234-243. MR 0628211 |
| Reference:
|
[6] T. Cipra: On improvement of prediction in ARMA processes.Math. Operationsforsch. Statist., Ser. Statistics 12(1981), 567-580. Zbl 0514.62103, MR 0639253 |
| Reference:
|
[7] W. A. Fuller: Introduction to statistical time series.Wiley, New York, 1976. Zbl 0353.62050, MR 0448509 |
| Reference:
|
[8] C. W. J. Granger: Investigating causal relations by econometric models and cross-spectral methods.Econometrica 37 (1969), 424-438. 10.2307/1912791 |
| Reference:
|
[9] D. A. Pierce L. D. Haugh: Causality in temporal systems.Journal of Econometrics 5 (1977), 265-293. MR 0443261, 10.1016/0304-4076(77)90039-2 |
| Reference:
|
[10] Yu. V. Rozanov: Stationary random processes.Gos. izd., Moskva, 1963 (in Russian). |
| Reference:
|
[11] C. A. Sims: Money, income and causality.American Economic Review 62 (1972), 540-552. |
| . |
