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The following algebraic transformations are available to create a series Y by some function of series X~p~ Xp , p=1,2,...
1. | linear equation | Y~i Yi,new~ = C~1~ Y~i,old~ + C~2~ X~2,j~ + C~3~ X~3,k~ + C~4~ X~4,l~ + C~5~ X~5,m~ + C~6~new = C 1 Y i,old + C 2 X 2,j + C 3 X 3,k + C 4 X 4,l + C 5 X 5,m + C 6 |
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2. | multiplication | Y~i~ Yi = X~1X1,j~ j * X~2X2,k~k |
3. | division | Y~i~ Yi = X~1X1,j~ j /X~2X2,k~k |
4. | involution | Y~i~ Yi = X~1X1,j~ j X2,k |
5. | natural logarithm | Y~i~ Yi = ln(X~j~ Xj ) |
6. | common logarithm | Y~i~ Yi = 10 log(X~j~ Xj )) |
7. | exponential | Y~i~ Yi = exp(X~j~ Xj ) |
8. | power of 10 | Y~i~ Yi = 10^Xj^ |
9. | power Y~i~ | = X~j~C~l~ Yi = XjCl |
10. | power of constant | Y~i~ Yi = C 1{}Xj |
11. | polynomial | Y~i~ Yi = C~0~ + C~1~ X~1,j~ + C~2~ X~1,j~ 2 + C~3~ X~1,j~ 3 + C~4~ X~1,j~ C0 + C1 X1,j + C2 X1,j 2 + C3 X1,j 3 + C4 X1,j 4 |
12. | conditional | Y~i~ Yi = max (X~1X1,j~ j , X~2X2,k~ k , X~3X3,l~ l , X~4X4,m~ m , C) |
13. | conditional | Y~i~ Yi = min (X~1X1,j~ j , X~2X2,k~ k , X~3X3,l~ l , X~4X4,m~ m , C) |
14. | conditional | Y~i~ Yi = mean (X~1X1,j~ j , X~2X2,k~ k , X~3X3,l~ l , X~4X4,m~ m ) |
15. | drift | Y~i~ Yi = X~1~ X1 + C~1~ C1 dt +C~0~C0 |
16. | conditional | if X~i~ Xi < C~1~ C1 then Yi = C~0~ C0 else Yi = X~i~Xi |
17. | conditional | if X~i~ Xi > C~1~ C1 then Yi = C~0~ C0 else Yi = X~i~Xi |
18. | conditional | if X~i~ Xi < C~1~ C1 then Yi = C~0~ C0 else Yi = X~i~Xi |
19. | conditional | if X~i~ Xi = missing then Yi = C~0~ C0 else Yi = X~i~Xi |
20. | conditional | if X~1~ X1 = missing then Y = X~2~ X2 else Y = X~1~X1 |
where:
X~p~ Xp = equidistant time series p
C~p~ Cp = coefficients
In the application of the above transformations different start dates can be applied for each of the series, i.e. i may differ from j, k, etc. This can be achieved by entering a value for the time shift per series.
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Under the accumulative series option a series Y is created which is a continuous summation of a basic series X as follows:
Series Codes
The series to accumulate can be selected or de-selected by clicking the checkbox of the series in the series list box. Only one series may be selected in one execution.
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Errors may have an accumulative character, when the phenomenon causing the error has to do e.g. with siltation, weed growth, etc. hymosoffers the possibility to correct for this type of error by applying a continuously growing adjustment from the time the error is thought to have commenced till the error was detected and quantified. Let the error be DX observed at time t=i+k and assumed to have commenced k intervals before, then the applied correction reads:
X~corr X corr,j~ j = X~measX meas,j~ j - ((j-i)/k)DX for j=i,i+1,....,i+k
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