Nonstationarity may imply the existence of trend and/or seasonality. Box and Jenkins (1976) proposed that differencing of the nonstationary series be done. First order nonseasonal differencing often gets rid of any trend and seasonal differencing often gets rid of any seasonal component thereby making the series stationary.
We proposed a technique for constructing mathematical models of non-linear stochastic differential systems in the form of non-linear stochastic differential equations. The first step of this technique is normalizing non-Gaussian stochastic processes into Gaussian ones (or approximate converting the non-stationary stochastic processes into stationary) on the basis of bijective normalizing transformations like the Johnson translation for Su family. We applied this technique for such non-Gaussian stochastic processes as speach signals, random waves, ship roll motion.
This technique is proposed in the paper (in Russian) on the link bellow
Article Application of normalizing transformations for constructing ...
Interesting answers...but I m interested to do this task with Matlab. If any one can guide?
In Google I typed your request with two corrections and added Matlab "Matlab How to convert non-stationary time series into stationary?" and I got the answer which seems very complete:
https://nl.mathworks.com/help/econ/data-transformations.html
Use ADF test in Matlab. If unit root is founded, take the first difference. repeat this procedure no unit root is founded.
The two standard approaches are to take time differences and/or logarithmic/power transformations. There are various guides that might or might not be helpful in identifying which type to use. Generally a logarithmic transformation followed by a 1st time difference works in many cases.
- Maybe some above above perfect answers consider cases of linear transforms of stationary processes (see the econometric literature or the excellent bopk by Peter Brockwell and Richard Davis).
- To my opinion the possibility of such a transformation relies on the fact that either the underlying dynamic is stationary or the observations are affine transforms of a stationary process.
- Recall that, eg, most of the markov chains with time varying coefficients dont fit this frame. I think this question is a really good one, indeed!
Thank you very much Dr Paul Doukhan for appreciation. You have pointed out many dimensions worth reading.
Stationarity is a fundamental concept in the study of series. It is therefore an unavoidable step and necessary to devote a central part in the analysis. In general, two reasons explain non-stationarity, when a series depends on its past values and when it has a tendency. The first is of type DS. To deprive and then obtain a stationary series, simply differentiate (type DS) one or more times and see if it is with at least two tests (Dickey-Fuller, Phill-Perron, KPSS, .. etc.). The second form of non-stationarity (TS) is the use of a filter, it exits the hodrick-Prescott filter, to identify the trend of the series, which is a long-term component. From these analyzes, one can easily reach the most suitable method for estimating the forecast values of the chronicle. Another thing to note is that there is also the notion of stationarity of a model in econometrics, which has common points and divergent points with that seen in statistics.
Comment: Maybe I am mis-understanding but filtering in a time series context usually means passing or blocking various frequency bands in the frequency domain. To me, non-stationary implies frequencies with an infinitely long period exist. If the frequency has a finite period, it is stationary over some suitably long period. Not sure how filters relate to the concept of stationarity. Of course, if one knows the true class of models underlying the time series, perhaps this perspective makes sense.
PS: The true model underlying most time series are unknowable because fundamentally they are many-bodied problems with extremely high dimensionality. At most we can hope for a reasonable approximation that is locally accurate in some sense. Complex strategies for modeling TS tend to produce nice statistics but poor forecasting ability outside the observed time period. My recommendation, keep it simple.
ADF test, see Hamilton "Time Series Analysis", and differentiate if ADF test is true.
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