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- algebraic transformation of series,
- transformation of non-equidistant series into equidistant series,
- creation of accumulative series, and
- error spreading.
These transformation options are dealt with in the next Sections.
Algebraic Transformations
The following algebraic transformations are available to create a series Y by some function of series X~p~ , p=1,2,...
1. | linear equation: | Y~i,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 |
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Y~i~ = X~1,j~ * X~2,k~ | |
3. | division |
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Y~i~ = X~1,j~ /X~2,k~ | |
4. | involution |
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Y~i~ = X~1,j~ X2,k | |
5. | natural logarithm |
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Y~i~ = ln(X~j~ ) | |
6. | common logarithm |
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Y~i~ = 10 log(X~j~ )) | |
7. | exponential |
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Y~i~ = exp(X~j~ ) | |
8. | power of 10 |
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Y~i~ = 10^Xj^ | |
9. | power |
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Y~i~ = |
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X~j~C~l~ | |
10. | power of constant |
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Y~i~ = |
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C 1Xj | ||
11. | polynomial | Y~i~ = C~0~ + C~1~ X~1,j~ + C~2~ X~1,j~ 2 + C~3~ X~1,j~ 3 + C~4~ X~1,j~ 4 |
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12. | conditional | Y~i~ = max (X~1,j~ , X~2,k~ , X~3,l~ , X~4,m~ , C) |
13. | conditional | Y~i~ = min (X~1,j~ , X~2,k~ , X~3,l~ , X~4,m~ , C) |
14. | conditional | Y~i~ = mean (X~1,j~ , X~2,k~ , X~3,l~ , X~4,m~ ) |
15. |
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drift | Y~i~ = X~1~ + C~1~ dt +C~0~ | |
16. |
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conditional | if X~i~ < C~1~ then Yi = C~0~ else Yi = X~i~ | |
17. |
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conditional | if X~i~ > C~1~ then Yi = C~0~ else Yi = X~i~ | |
18. |
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conditional | if |
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X~i~ |
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< C~1~ then Yi = C~0~ else Yi = X~i~ |
19. |
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conditional | if X~i~ = missing then Yi = C~0~ else Yi = X~i~ | |
20. |
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conditional | if X~1~ = missing then Y = X~2~ else Y = X~1~ |
where:
X~p~ = equidistant time series p
C~p~ = coefficients
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