A transformation to normality suggested by Box and Sir David Cox in 1964. They proposed a family of transformations that might be used to convert a general set of n observations into a set of n independent observations from a normal distribution with constant variance. The transformation involves a parameter λ that can be estimated from the data using the method of maximum likelihood. The transformed observation, y(λ), is related to the original observation, y, by
A transformation for time-series data of the form
where xt is the transformed series, yt is the original series, and λ is a number between 0 and 1. It is often used to stabilize the variance of the time series. λ = 0 corresponds to the logarithmic transformation, and λ = 1 is a mean reduction. The optimal λ can be estimated from the data, simultaneously with other parameters in a completely specified time series model for yt.
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- water
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