For example price is non-stationary transfer to rate of return that is stationary .
No need to transfer ur series to stationary one.rather u can smoothen it in many ways which will help to find the trend of the series.
Depends on your data,to name it few u can try with exponential smoothening, least square method etc..
I suggest the following: Non stationary time series can be approximated by stationary ones over limited intervals - Or use a stochastic model with drift and noise driving term, as in stochastic diff eq, to model the series - Or fit data with a model depending on parameters which are random variables
It depends on the prediction model. If you use ARMA or ARMA GARCH modeling this is the only way. If you use some other kind of non stationary interpolation (neural networks) then not necessarily.
Non-stationery signal for financial as behavior human condition, i suggest if the use condition model stationer or make non-stationer become stationer assumption is not relevant to follow the signal. Prediction may be have standard toleration or variation from source signal condition.
I agree with Ramesh Babu and with Dimitris Roualis. It depends on the forecasting algorithm selected. If the forecasting algorithm is based on Box-Jenkins methodology, than it is necessary that the time series to be stationary. This is because the predicted model must be of ARIMA type. The advantage is the possibility to predict the long range tendency of the time series. If the forecasting algorithm is based on neural networks than it is not necessar that the time series to be stationary. The transformation of a not stationary time series into a stationary time series is very simple requiring only a finite number of iterations (two or three) and consits in computing finite differences.
After 20 years of doing it, I must admit that this is domain dependent - different econometric and financial series would require different priors. It may be worth thinking about your objective function (forecasting accuracy or else) and remembering that most series are resulting from a very complex network of game-like system dynamics, where different regimes (modes) can be triggered by different price or factor levels.
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