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This series is frequently called prewhitened entry series.
Transfer function models are used in series related to one or more entry series.
In the transfer function model, it is assumed that a t are independent, white noises of the entry series X t and, so, they are also independent from the prewhitened entry series a ^ t.
In a casual model, the system does not respond the entry series until it has really been applied into the system.
One may assume that the X t entry series follows an ARIMA process Φ L Y t d = Θ L e t. t.
In this case, the cross correlation test is carried out, in which for a proper mode the sampling CCF ρ ^ a a ^ k, between a ^ t and a t, must not show standards and must be within its two standard-errors, 2 (n − k)−1/2; in other words, the noise series a t and the X t entry series must be independent.
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The same effect was also observed for the isopropyl-substituted series (entry 11 versus entries 9 and 10).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com