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Suppose I have a time series. After looking at the PACF plot, it largely decreases to zero after 3 lags, but there is also a PACF value that "pokes out" of the significant bounds at a far lag, say at lag 20. I want to include this lag in my model as a subset to the primary AR(3) model. So the model will look like all the co-efficients from AR(3) + the co-efficient at lag 20 of AR(20).

or in other words

$Z_t = \sum\limits_{i=1}^3 \phi_iZ_{t-i} + \phi_{20}Z_{t-20} + a_t$ where $a_t$ is white noise.

How do I obtain the coefficients $\phi_i$ in R?

Should I simply fit the entire time series to AR(20) and manually suppress all $\phi_i, i\in[4,19] = 0$, regardless of what values it return?

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1 Answer 1

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You can fit the model with all 20 coefficients and then retrieve the coefficients from your model by calling:

model_name$coef

However, if you have a/several significant lags at higher lags in your PACF, it could be because there's still autocorrelation left in your data. Could also be seasonality or some random elements. I'm guessing you have checked if your data is stationary?

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