I want to determine the parameter(s) which produce the optimum (minimised
sum-squared error )
weighted average for a dependent variable with the complication that the
'weighting' variable (say time)
intervals are not constant. I also have multiple runs of data and the
lengths of the runs vary. It is valid to use subsets of the data too eg
predict value 4 after 3 measurements.
eg
#1
weighting variable(days ago) 1 ,7,12,20,22,56
measured value 80,76,76,80,70,60
#2
weighting variable(days ago) 12 ,16,22,30,42,60,90,96
measured value 62,60,65,54,66,82,80,82
(note the above is 'rubbish' data just used for illustration)
So I want to calculate the optimim alpha with 0< alpha >1 to minimise the
sum squared
error of the predictions (alpha defined below).
All the time series literature I've read only seem to deal with fixed time
periods.
Any help and/or code examples (pref matlab) appreciated.
TIA
In the constant period case the formula is (I think):
Ft=F(t-1) + alpha*(A(t-1)-F(t-1))
where:
Ft =forecast made in period t
F(t-1) =forecast made in period t-1
alpha = smoothing constant
A(t-1)= actual value in period t-1
.
.
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