I have developed a SARIMA model for a large dataset (hourly data over several years). I have been trying to take the results of my model and hand calculate (validate) a few of the hourly results, and I have been unable to do so. I just want to be able to take the table of generated values and actuals, and calculate what one hour was predicted to be based on the inputs to the model and the (already estimated) parameters and residuals. I am not trying to recalculate the parameters, the residuals, any error calculations, or fitting results, as I know these are a result of an iterative convergence on this solution that cannot be replicated with a simple one-off calculation.
Attached to this post is the exported results from JMP along with my manual calculations (attempts at validation).
Columns A through G are the results of a SARIMA (1,1,1) (0,1,0) [24] No Intercept model. the model is not ideal (I use a more complex one for my own purposes) but for purposes of validating the way the predictions are calculated, it should suffice. (If I can get this one to work, I can get the other one to work).
Columns J through N are my attempts to manually calculate a given prediction based on the model parameter information and the relevant previous actual and residual values. To do so, I calculate the double differenced y in column J, then calculate the AR part of the prediction in K, the MA part of the Prediction in part L, and then put them together and undo the double difference in M to get the calculated prediction. Column N has the residual as calculated using this manual prediction and the actual target value.
The two applicable parameters are in the table starting in P4. The original fit was forced to calculate with no intercept, so it is just the two.
For the life of me, I cannot figure out why they wouldn't tie out. I am not trying to iteratively calculate the error term, I just want to see how a given prediction was calculated from the information in the file, and I cannot. When I force this to run even simpler models (MA(1) for example) I still can't get the thing to tie out. I assumed for a while that it was just a simple calculation error on my end, but I no longer believe it is. If anyone could tell me what calculations I am doing incorrectly, or why this task is not possible, I would greatly appreciate it. I suspect it is something simple, but I tried reversing the sign on the MA terms and that didn't help, and I believe my differencing and un-differencing calculations are correct.
Full disclosure: This work is neither for a homework/exam/project or for a work project, this is just a personal project, and the data is public information. The goal of this was to be able to show the excel sheet validation to an old colleague, so that he can see the use case and the power of SARIMA models.
Any help is greatly appreciated!
