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seen Nov 16 '12 at 12:30

Nov
14
comment Combining Mulitple Forecasts? Budged Constraints?
BTW, thanks for your patience John. I think I'm starting to get it.
Nov
14
comment Combining Mulitple Forecasts? Budged Constraints?
What if we knew that E[x(t)] = E[y(t)] = 0 and E[e(1,t)] = E[e(2,t)] = 0 and B(1,0) = B(2,0) = 0? (E[] being the expected value)
Nov
13
comment Combining Mulitple Forecasts? Budged Constraints?
Thanks John. This is the bit that I am puzzing over. Let's say that we knew nothing about the construction, only that we are trying to predict z(t). If we were only given x(t) and knew nothing of y(t) then we would consider x(t) to be a completely valid prediction, and vice-versa. I have made this example contrived to demonstrate that two independent predictions x(t) and y(t) of z(t) may form a better combined estimate if they are added rather than averaged. Contrived yes, but only to demonstrate the point.
Nov
13
comment Combining Mulitple Forecasts? Budged Constraints?
@John - I agree this is more like a regression model. In some ways combining multiple forecasts is usually, isn't it? However each of the two predictions time series is a valid prediction in it's own right, is it not?
Nov
13
comment Combining Mulitple Forecasts? Budged Constraints?
@John: In your example with 10% and 15% please consider this example and tell me where I am misunderstanding. Mum and Dad each pay me a weekly pocket money or charge me board. It varies from week to week and the two amounts are independent (they don't speak nor live together). All up the expected amount that Mum pays me (pocket money-board) each week is 0. Same with Dad. So, both income streams have no bias. Now, I ask Mum and Dad separately how much my pocket money less board is likely to be? Mum says £10, Dad says £15. Clearly the best estimate for my weekly income is £25 not £12.50, right?
Nov
13
comment Combining Mulitple Forecasts? Budged Constraints?
Yes, I kind of agree tentatively. If you have time, do you mind taking a look at the spreadsheet I provided. In that example there are two predictions of a time series. The optimal combination it turns out is them added not averaged. Any ideas?