You are given an annual time series with 40 consecutive values and asked to fit a fifth-order autoregressive model. State the fifth order autoregressive model.
The fifth-order autoregressive model can be stated as:
yt = β0 + β1 * yt-1 + β2 * yt-2 + β3 * yt-3 + β4 * yt-4 + β5 * yt-5 + εt
where:
- yt is the time series variable at time t
- β0, β1, β2, β3, β4, β5 are the autoregressive coefficients to be estimated
- yt-1, yt-2, yt-3, yt-4, yt-5 are the lagged values of the time series variable up to the fifth order
- εt is the residual or error term at time t