Introduction to Time Series Modeling with Applications in R by Kitagawa Genshiro;

Author:Kitagawa, Genshiro;
Language: eng
Format: epub
Publisher: CRC Press LLC
Published: 2020-07-20T00:00:00+00:00

(9.17)

(9.18)

As indicated previously, the predictive distribution of yn+j based on the observation Yn of the time series becomes a normal distribution with mean yn+j|n and variance covariance matrix dn+j|n. These are easily obtained by (9.17) and (9.18). That is, the mean of the predictor of yn+j is given by yn+j|n, and the standard error is given by (dn+j|n)1/2. It should be noted that the one-step-ahead predictors yn|n−1 and dn|n−1 of the time series yn have already been obtained and were applied in the algorithm for the Kalman filter (9.13).

Example (Long-term prediction of BLSALLFOOD data)

The function tsmooth of the package TSSS performs long-term prediction by the state-space representation of time series model. The following arguments are required

f:

the state transition matrix Fn.

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