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I have a model that uses autoregressive multidimensional time series to make a prediction.

I use a smoothed X’X and a smoothed X’Y (of the recent past) to do an in-sample regression: B = (X’X)^-1 X’Y. When I create a prediction F = X B, I then determine R2 in the recent past by looking at the smoothed F’F the smoothed F’Y_test. In the single-dimensional setting R2 = (2F’Y_test - F’F) / Y_test’Y_test. And the optimal gain = (F’F)^-1 F’Y_test. It occurred to me that I could use this R2 matrix to update the gains on my model: B = (X’X)^-1 X’Y (F’F)^-1 F’Y_test. And I could do it even when the data is multidimensional.

Is this a common technique? Does it have a name? You could even apply this technique recursively. It feels like a Kalman filter or like back-prop, but I don’t fully understand the relations.

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