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I needed to use SAS to find an adequate model for some data using time series analysis. To get the adequate model I needed to include first order and season differencing, then I used an ARIMA model along with autoregressive and moving average to find the adequate model.
Here is my adequate model: $\text{ARIMA } p=(1, 2, 3, 7) d=(1, 12) q=(8, 10, 12)$

I think I know what the equations are for each part, I need help with putting it together and creating one equation for the model.

Simple and Season diffeencing: $z_t=y_t^*-y_{t-1}^*-y_{t-L}^*+y_{t-L-1}^*$
I am not sure if $L$ means number of years or the frequency of my data, my data was monthly between 1959 and 1992.

Autoregressive: $z_t=\delta+\phi_1z_{t-1}+\phi_2z_{t-2}+\phi_3z_{t-3}+\phi_7z_{t-7}+a_t$

Moving Average: $z_t=\delta+a_t-\sigma_8a_{t-8}-\sigma_{10}a_{t-10}-\sigma_{12}a_{t-12}$

idknuttin
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  • I have previously commented on expressing the ARIMA equation as a pure right-hand side . Search on "user:3382 RIGHT HAND SIDE" for some commentaries that might help you. Your "adequate model" appears to me to be potentially inadequate as it seems to me to be way over-parameterized/fitted with adaptive structure. Many times omitted deterministic structure such as level shifts, time trends, seasonal pulses exist but are not identifiable with existing software thus chaos can reign in simply trying to use previous values. Additionally this often happens when you have data that has either error var – IrishStat Dec 13 '16 at 14:50
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    http://stats.stackexchange.com/questions/251336/statistics-for-time-series-trend-in-r/251354#251354 contains a recent presentation of a conversion from ARIMA notation to a Polynomial Distributed Lag (PDL) or ADL format. – IrishStat Dec 13 '16 at 19:11

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