3

I was always under the impression that differencing and Box-Cox were two ways to achieve the same goal: Making a time series stationary so that it can be modeled using an ARMA process.

However, looking at the code for auto.arima(), I notice that there is an option to include a Box-Cox transformation, which if my idea about redundancy is correct, doesn't make sense.

Now I am questioning whether that was correct to start with:

  • Is it correct that Box-Cox and differencing are two means to the same end?
  • If not, what does Box-Cox do exactly, since it seems that differencing already makes the time series stationary?
  • Does the combination of ARMA + Box-Cox still count as ARIMA (based on the inclusion of Box-Cox in the auto.arima() function) - since the "I" is no longer necessary? Or does it count as an ARIMA-like approach, but not ARIMA strictly speaking?
kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
Akaike's Children
  • 1,251
  • 7
  • 15
  • Box-Cox transformations are used to transform variables, for ex. log, to get your variables in a "prettier" form. Differencing is done to make a series stationary. These two concepts are not necessarily related. – user2974951 Jul 09 '19 at 13:09
  • 1
    Box-Cox transformations are used to transform a series to make to make the variance stationary http://stats.stackexchange.com/questions/18844/when-and-why-to-take-the-log-of-a-distribution-of-numbers. Differencing and arma is done to transform the series to make the expected value stationary – IrishStat Jul 09 '19 at 14:39
  • @IrishStat: does the order matter? Should I use a Box-Cox transformation first to stabilize the variance and then first-difference to stabilize the mean or vice versa? What is the best practice? – ColorStatistics Sep 15 '21 at 18:17
  • the preferred order is to deal with the expected value first. "ARIMA MODELS AND THE BOX-JENKINS METHODOLOGY" by MAKRIDAKIS & Hibon laid out the flaws of using differencing when linear detrending was more appropriate. If you can't find the paper send me an email and I will respond (dave@autobox.com_ – IrishStat Sep 16 '21 at 12:59
  • When dealing with non-constant error variance be aware that untreated pulses and other untreated latent deterministic structure can falsely suggest either Box-Cox or deterministic break-points. – IrishStat Sep 16 '21 at 13:05
  • https://stats.stackexchange.com/questions/461014/stochastic-vs-deterministic-trend-in-time-series MIGHT BE OF INTEREST – IrishStat Sep 16 '21 at 19:35

0 Answers0