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What is prewhitening?
Situations in which the input amplitude spectrum has zeroes rarely occur. However, to ensure numerical stability, an artificial level of white noise is added to the amplitude spectrum of the input seismogram before deconvolution. This is called prewhitening and is referred to in Figure 2.3-3.
What is pre whitening filter?
A pre-whitening filter takes a signal that is not white and produces a white signal. This is performed by a predictor, as you mentioned. The way the predictor whitens the signal is that itl attempts to predict sample n based on the information from the previous samples.
Why is prewhitening important in a time series?
A simple filter (2,1,0) was used to prewhiten creating “adjusted cross-correlations or prewhitened cross-correlations” suggesting/identifying a three period delay culminating in this useful equation . Note clearly that Y is not CONDITIONALLY a function of X contemporarily (or lag 1 or lag 2) given the model form.
Why is it important to pre whiten y and X?
The reason that you pre-whiten X is to identify a filter that can transform Y and X into y and x where x is white noise i.e. serially independent or free of autocorrelation in order to IDENTIFY an appropriate model. Note that one filter (ARMA developed on X ) is used on both the Y and X.
What is the purpose of prewhitening in Proc Arima?
Note that prewhitening is done to estimate the cross-correlation function; the unfiltered series are used in any subsequent ESTIMATE or FORECAST statements, and the correlation functions of Y with its own lags are computed from the unfiltered Y series.
Why is prewriting important in the writing process?
The more time and effort you put into prewriting, the less time you will have to spend on the rest of the writing process. If you develop a plan before you start writing, your writing will start with a purpose and a structure.