Traden4Alpha
Senior Member
Posts: 14107
Joined: Sep 2002
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Fri Mar 07, 08 12:01 PM
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The residuals of the correlation are what you have when you subtract the predicted value of dependent variable from the measured value of the dependent variable. This forms a dataset that one can plot or analyze. Standard approaches to correlation assume that the residuals are i.i.d. with zero mean and constant variance and we can perform various tests. If the residuals contain structure (e.g., time series of them contains significant runs of the same sign) then we might wonder if our correlation is really valid.
Regarding "....each price being a sum of price returns" the issue here is to express the price series algebraically as an initial price P0 and the sum of returns, Rn. Thus the price series [P1, P2, P3,..., Pn] becomes [P0+R1, P0+R1+R2, P0+R1+R2+R3, ...., P0+SUM[R1,R2,R3,....,Rn] ]. Notice that the value of R1 (the OLDEST value in the return series) contributes to every value of the price series and that Rn (the most recent value of the return series) only contributes to a single value of the price series. Thus, with a price series, the older data has more influence than the newer data which seems rather counterintuitive in most models of market action.
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"It often happens that a player carries out a deep and complicated calculation, but fails to spot something elementary right at the first move." -- grandmaster Alexander Kotov --inscribed on gift chess sets given by Amaranth hedge fund.
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