# Transforming Series with 2nd Moment Nonstationarity

I am trying to induce stationarity in this series. I have graphed a range-mean plot to detect 1st and 2nd moment nonstationarity. Can anyone suggest a transformation that will remedy the 2nd moment nonstationarity? My professor covered 3 Box-Cox transformations, but they applied to linear range-mean plots.

• We can't see the series. What is this plot supposed to tell you about nonstationarity? Why do you think Box-Cox transformations could yield stationarity? What does CPI mean? (This is an interdisciplinary and international forum; I can guess, but we should not have to.) Feb 16, 2015 at 23:06
• The range mean plot can help detect 1st and 2nd moment nonstationarity. The range is used as an alternative to the variance. Since the variance and mean are both changing throughout the series (displayed on the scatter plot) then we suspect 1st and 2nd moment nonstationarity. I was using Box-Cox transformation to attempt to fix the 2nd moment nonstationarity. The CPI is the consumer price index. I apologize for not mentioning that. Feb 17, 2015 at 0:02
• I see your plot as implying that range doesn't really depend on the mean. As I distrust ranges any way -- and fail to see why you can't show variances if they are the real quantities of interest -- the graph seems underwhelming to me. How many values is each point based on, any way? Why not show us a plot of the original time series? I still fail to see why Box-Cox is pertinent. Feb 17, 2015 at 0:05
• You don't really have enough data to conclude there is second order nonstationarity from this plot, for several reasons. First, the range is an unstable surrogate for the variance. Second, your data surely have strong serial correlation. Third, there are few points within each visible segment of the plot, casting doubt on any trends. Although you can cure some of these problems by using robust statistics (choose median and IQR), overall the plot is unreadable due to these deficiencies and because we have no idea what subset of the data each individual point corresponds to!
– whuber
Feb 17, 2015 at 0:06
• I added the original time series to the question. What is another method for detecting 2nd moment nonstationarity? If it is detected, how should it be handled? I was instructed to utilize Box-Cox transformations. Feb 17, 2015 at 0:38