Recency weighted regression
Hi,
I wondered if anyone could help with the following:
(I'll make up a fictional example to explain in simple terms what I am trying to do):
If for example you created an extremely simple model that was to predict whether a share price was to rise or fall (for now we'll consider as a linear classification model) and the only inputs you had were:
X0 = 1
X1 = yesterday's share price
X2 = the share price the day before that in X1
X3 = the share price the day before that in X2
X4 = the share price the day before that in X3
it would seem sensible to apply more of a weighting to the more recent share prices so you may decide to do a transform before applying the learning i.e.,
you may create a new matrix Z = [X0 X1*0.9 X2*0.8 X3*0.7 X4*0.6]
and do the learning from Z.
Hope this makes sense so far?
My questions:
1) is this a sensible thing to do?
2) can the recency weights i.e., 0.9, 0.8, 0.7 and 0.6 be learned?
More Advanced:
Though this is a simple example, you may have more data each day for which you want to apply the same recency weighting i.e., you may have data for say (i) the minimum and (ii) the maximum price the share was on each day. In which case you may have a new model something like:
X0 = 1
X1 = yesterday's share price
X1_1 = the minimum price the share traded at yesterday
X1_2 = the maximum price the share traded at yesterday
X2 = the share price the day before that in X1
X2_1 = the minimum price the share traded the day before that in X1
X2_2 = the maximum price the share traded the day before that in X1
X3 = the share price the day before that in X2
X3_1 = the minimum price the share traded the day before that in X2
X3_2 = the maximum price the share traded the day before that in X2
X4 = the share price the day before that in X3
X4_1 = the minimum price the share traded the day before that in X3
X4_2 = the maximum price the share traded the day before that in X3
applying a new transform would be like this:
Z = [X0 X1*0.9 X1_1*0.9 X1_2*0.9 X2*0.8 X2_1*0.8 X2_3*0.8 X3*0.7 X3_1*0.7 X3_2*0.7 X4*0.6 X4_1*0.6 X4_2*0.6]
Hope this is still making sense?
Extra questions:
3) is this still (if it was before) a sensible thing to do?
4) can the recency weights i.e., 0.9, 0.8, 0.7 and 0.6 be learned?
Any pointers, discussion, answers much appreciated.
