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Results tagged with autoregressive
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user 309015
The autoregressive (AR) model is a stochastic process modelling time series, which specifies the value of the series linearly in terms of the previous values.
1
vote
Accepted
Forecasting $X_{t+2}$ for causal AR(p)
Consider $X_{t+2}$ term:
\begin{equation}
\begin{split}
X_{t+2} & = \sum_{i=1}^p \psi_iX_{t+2-i} \,+Z_{t+2} = \psi_1X_{t+1} + \sum_{i=2}^p\psi_iX_{t+2-i} \,+Z_{t+2} \\
& = \psi_1\left(\sum_{i=1}^p \ps …
1
vote
Accepted
Prediction error for ARMA process
Remark: Mind, that we can solve this only is $(X_t)$ is casual. A sufficient condition for that is $|\varphi|<1$. Using the representation with a lag operator $B$
\begin{equation}
(1-\varphi B^{12})X_ …