Is there any way to convert a non-stationary signal to a stationary one, perform operations on it meant for a stationary signal and then convert it back to the non-stationary one?
$\begingroup$
$\endgroup$
5
-
1$\begingroup$ differencing the series can sometimes work. that's pretty much the only one if the non-stationarity is in the mean. if the non-stationarity is only in the variance, the transformations such as log or sine can sometimes help. $\endgroup$– mark leedsCommented Sep 24, 2018 at 5:49
-
$\begingroup$ What sort of signal are you dealing with? $\endgroup$– A_ACommented Sep 24, 2018 at 5:59
-
$\begingroup$ Its a time series data for a country's GDP for about 100 years. $\endgroup$– CuriosityCommented Sep 24, 2018 at 6:35
-
$\begingroup$ Best way is to partition the non-stationary signal to the duration you can assume its stationary and perform the operation you require on it. But depends on what you want to do? $\endgroup$– learnerCommented Sep 24, 2018 at 7:53
-
$\begingroup$ I want to use the discrete Wiener estimation method of Levinson to predict the next value in the series using the available ones. $\endgroup$– CuriosityCommented Sep 24, 2018 at 8:47
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
2
Strict sense stationarity relates to hypothesis that the statistical law $f_{\omega(t)}$ behind the process does not change over time. Even in that case, it is difficult to access to the law from a few realizations, unless you add an ergodicity assumption (possibility to estimate sample properties from past and future data).
Strict sense non-stationarity can offer such a variety of behaviors that a stationarization is unlikely: all $f_{\omega(t)}$ should be cast to a single $f_{\omega}$. Would it exist, non-stationary processing would be a paradise, as we could apply all stationary methods.
In a lighter sense, one can consider wide-sense non-stationarity, where only the first and second moments (expectation and variance) are allowed to vary. In Nonstationary Models for Time Series, one can explore either what is "Nonstationary in the Variance" and "Nonstationarity in the Mean".
In the mean, several methods can be applied for deterministic trends and stochastic trends. Differentiation, parametric modeling or ARMA, ARIMA, random walk techniques can be used.
In the variance, one can look for Variance-stabilizing transformations (Anscombe, Box-Cox) aiming at:
creating new values such that the variability of the values y is not related to their mean value
answered Sep 24, 2018 at 18:10
-
1$\begingroup$ Thanks Laurent: Note that the ARIMA class of models still require that a difference of some order ( which could be greater than 1 but generally 1 is common ) be stationary ( in the mean ) and it requires stationary variance. $\endgroup$ Commented Sep 25, 2018 at 5:20
-
$\begingroup$ Nice, I will be more specific $\endgroup$ Commented Sep 25, 2018 at 8:19