# Improvement of prediction for a larger number of steps in discrete stationary processes

Aplikace matematiky (1982)

- Volume: 27, Issue: 2, page 118-127
- ISSN: 0862-7940

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topCipra, Tomáš. "Improvement of prediction for a larger number of steps in discrete stationary processes." Aplikace matematiky 27.2 (1982): 118-127. <http://eudml.org/doc/15230>.

@article{Cipra1982,

abstract = {Let $\lbrace W_t\rbrace =\lbrace (X^\{\prime \}_\{t^\{\prime \}\}, Y^\{\prime \}_t)^\{\prime \}\rbrace $ 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 $\Delta _X(a)=\text\{E\}[X_t-\hat\{X\}_t(a)][X_t-\hat\{X\}_t(a)]^\{\prime \}$ and $\Delta _X(a,b)=\text\{E\}[X_t-\hat\{X\}_t(a,b)][X_t-\hat\{X\}_t(a,b)]^\{\prime \}$. 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 $a$.},

author = {Cipra, Tomáš},

journal = {Aplikace matematiky},

keywords = {improvement of prediction; discrete stationary process; improvement of prediction; discrete stationary process},

language = {eng},

number = {2},

pages = {118-127},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Improvement of prediction for a larger number of steps in discrete stationary processes},

url = {http://eudml.org/doc/15230},

volume = {27},

year = {1982},

}

TY - JOUR

AU - Cipra, Tomáš

TI - Improvement of prediction for a larger number of steps in discrete stationary processes

JO - Aplikace matematiky

PY - 1982

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 27

IS - 2

SP - 118

EP - 127

AB - Let $\lbrace W_t\rbrace =\lbrace (X^{\prime }_{t^{\prime }}, Y^{\prime }_t)^{\prime }\rbrace $ 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 $\Delta _X(a)=\text{E}[X_t-\hat{X}_t(a)][X_t-\hat{X}_t(a)]^{\prime }$ and $\Delta _X(a,b)=\text{E}[X_t-\hat{X}_t(a,b)][X_t-\hat{X}_t(a,b)]^{\prime }$. 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 $a$.

LA - eng

KW - improvement of prediction; discrete stationary process; improvement of prediction; discrete stationary process

UR - http://eudml.org/doc/15230

ER -

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