# The importance of stationary time series

I am a bit confused with stationary time series. Data transformations (detrending, difference etc) are used to seek stationary time series so that we can treat correlation as a constant over time. Using the ACF to compare before and after data transformed. But is the stationary really important? This question comes from two sides: first if no transformation can find satisfied ACF, we still need to analyze the series. Second is that various models can handle different ACFs like long tails, cutoff lags etc so that the ACF can help pick the right model and model orders.

Therefore, stationary seems not very needed but it is a "good-to-have". Does this make sense?

Thanks.

Data transformations (detrending, demeaning, differencing, ARMA structure ,power, constancy of variance considerations, elimination of pulses/level shifts/seasonal pulses/local time trends ) are used to convert an observed series to a white noise series/process . The parameters of this white-noise process ( the errors from these suitable transformations) i.e. the mean , variance and covarince for all lags should be constant for all sub-intervals of time.

• Including ARMA structure in data transformation is a better way to help me. The textbooks I read often treat data transformations be pre-req to ARMA modeling. Feb 11, 2015 at 1:26
• I should also have added that a series is stationary if it's probability distribution is invariant over time which is a rephrasing of the last sentence in my response. Feb 11, 2015 at 2:11

Stationarity is vital to have. A short outline of why:

1. Nonstationary (aka integrated, and sometimes unit root) data have undefined means and infinite variance.

2. All estimates of population means and variances from finite samples are thus badly biased.

3. Spurious correlations are very likely to obtain in nonstationary data.

• I didn't mean stationarity is optional if achievable. What I meant was when you can't get stationary series after all means. Even you don't get a stationary series, the model would still "help" to analyze, right? Feb 11, 2015 at 1:23
• @visitor99999 Perhaps, except for that bit about spurious correlations. Feb 11, 2015 at 6:07