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I want to test stationarity of variants using Box-Cox Lambda for Time series assumption (Stationarity).

Null-Hypothesis : Lambda is not zero (Data is stationarity of variants)

Alternative-Hypothesis : Lambda is zero (Data is not stationarity of variants)

But I got confused to obtain that lambda. Do you know the formula to obtain that lambda?

Thankyou

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You might want to read Guerrero, V.M. (1993) Time-series analysis supported by power transformations. Journal of Forecasting, 12, 37–48.

The above paper is the only paper that I know of have developed automatic technique to determine box cox transformation parameter lambda and importantly this procedure is model independent. This is done by minimizing coeficient of variation of time series. This is implemented in the forecast package in R software. See example below:

library('forecast')
lambda <- BoxCox.lambda(AirPassengers,lower=0)

There are better ways to test stationarities. Box cox transformation is used for stabilizing variance not to check stationarity. You might want to use specific procedures such as Ljung-Box test, augmented Dickey-Fuller test, ACF, PACF and others to check stationarity. See this website for a nice summary of methods and how to apply in $R$.

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  • $\begingroup$ Thanks for respond, Actually I've used that code of R and I got Lambda = 1. But I need the exact formula for literature review of my research. I've already used the augmented Dickey-Fuller test for stationary test towards mean. $\endgroup$
    – Shieryn
    Commented Aug 21, 2016 at 5:33
  • $\begingroup$ The exact formula is found in the paper and the R function BoxCox.Lambda. Again, this is not the right approach to test for stationarity. $\endgroup$
    – forecaster
    Commented Aug 22, 2016 at 1:19
  • $\begingroup$ Yeah i know. Which paper? $\endgroup$
    – Shieryn
    Commented Aug 22, 2016 at 6:15

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