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Hello,

I'm currently forecasting a time series with an AR(2) model with seasonality and trend, and I'm trying to figure out the calculation from the equation to actual forecast values so I can recreate it in an excel spreadsheet. I saw your post 'ARMA Estimation and Forecasting' and was able to go from equation to forecast values if I used an AR(1) model without trend and seasonality using the equation yt = (1-r)c + r * yt-1.

Would really appreciate it if someone could help me figure out how to find the mathematical representation when seasonal dummies and a trend factor is included.

Thanks so much

Seasonal dummies and trends are just X values, and work as indicated in the example.

Thanks for the quick response, I'm a bit confused because for seasonal dummies Xt-1 would be 0, and Xt would just be 1. For example (monthly data, with just seasonality and no trend):

The forecast value for July is: 136.2407
The forecast value for June is: 136.4862
AR Coeff: 0.999667
July Dummy Coeff: 0.850561
June Dummy Coeff: 1.089980
C: 117.2447

Using the equation we get: 117.2447 + 0.850561+0.999667(136.4682-117.2447) = 137.3304 which is not 136.4682

Seems you're missing the June dummy in the AR part.