I have three different linear, multi-variate time series models with a best fit against the same observed value $Y$ at 1 minute, 3 minutes and 10 minutes horizons respectively. Each model is using different predictors data. There is no serial correlation or ARIMA involved here.
I want to blend the three models to predict $Y$ every second, on a rolling base. The prediction for the three models is thus overlapping. For example, at time $t_3$ minutes, we'll have the prediction for the first and second model colliding (third prediction for the 1 minute model and first for the 3 minutes model).
How should I approach the problem?
Best Answer
Your problem looks like it's related to looking at time series aggregates on different frequencies. That is, one could look at daily sales data, build a model on that, forecast daily data... then aggregate historical data to weeks, build a model on weekly data and forecast weekly data... finally do the same exercise after aggregating to monthly data. Then finally one would combine the forecasts on different frequencies - and this last step seems to be what you are mainly interested in.
There is a recent very nice paper on the whole procedure by Kourentzes, Petropoulos and Trapero. I imagine that you could profit from looking at the final combination step in the paper.