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Needing some help with verbiage and opinions on how I am approaching this model.

I have counts of people over the past 24 months.

month count
1 100
2 105
... ...
24 200

First, I reverse the months to this:

month count
24 100
23 105
... ...
1 200

I create multiple custom periods from month 24...

period month
3 1
3 2
3 3
6 1
... ...
6 6
9 1
9 ...
9 9
... ...
24 24

For each period I calculate the Linear Regression and forecast next value

period lr_slope lr_intercept lr_r2 forcast_next period_weight* contrib
3 4.543 903 .4499 900 1/3* 300
6 44.67 309 .9944 903 1/6* 150.5
9 990.33 33.990 .9494 910 1/9* 101.11
... ... ... ... 980 ...
24 776.677 77.09 .0009 990 1/24* 41.5

For this example, assume SUM(period_weight) = 1

The contrib is the period_weight * forecast_next

I sum up all the contrib above to get the final forecast value.

Is this a valid regression model? Does it mimic current models?

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    $\begingroup$ Let me try to understand what you are doing. You use expanding windows and from each one you estimate the regression and then forecast from it. Then you average (or sum? but why?) the forecasts to obtain your final forecast. If that is so, what you might be looking for is weighted regression where more recent observations receive higher weights. I think it might be a safer approach. (Perhaps your approach amounts to it in the end, but some algebra is needed to verify that.) $\endgroup$
    – Richard Hardy
    Commented Feb 15 at 10:49
  • $\begingroup$ So the forecasts from each expanding period are assigned a diminishing weight. The forecast for each period is multiplied by the period weight. That results in a contribution that is then summed across all periods to obtain the final forecast. The thought process is that the expanding windows with weights will 'smooth' some of the volatility. $\endgroup$
    – Tyler Brown
    Commented Feb 15 at 13:42
  • $\begingroup$ OK, so I was not too far off. Anyway, the forecasts are probably equivalent to ones from some form of weighted least squares regression – or perhaps not. Regarding your question, I do not think this is a valid regression model, as I do not see how it is a model at all. It may be a valid mechanism for generating forecasts, however, but I strongly suspect your emphasis on the shortest samples that are just a few observations long. You may get very noise forecasts from that. $\endgroup$
    – Richard Hardy
    Commented Feb 15 at 15:14

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