My data are non stationary seasonal data. I need to know is there any forecasting models can handle non stationary data. and I also want to know STL( Seasonal Trend LOESS) and ETS can handle non stationary data.
Thank you.
You can easily work with seasonal ARIMA models. In these models, the difference and the seasonal difference operators take care for the lack of stationarity and the two (regular and seasonal) moving average operators partially compensate the effect of the differences. If there is still non-stationarity, it is possible to use models with time-dependent coefficients but it is probably non useful in your case. I can provide references.
Guy Mélard right now i am trying on Seasonal ARIMA model. Do i have to put same p,d,q values to the non seasonal and seasonal? Screen capture attach with this.
Not at all. First look at the data plot. If there are level changes, use d = 1, otherwise 0. I suppose you have a seasonality so D = 1. Look at the plot of the residuals. If there are no more level changes and deterministic seasonality, you can move to the next step. Look at the autocorrelation and partial autocorrelation. A cut in the correlogram indicates the need for moving averages (MA). A cut in the partial correlogram indicates the need of autoregressions (AR). By changing p (for regular AR), q (for regular MA), P (for seasonal AR), and Q (for seasonal MA), once at the time, you will have a good model in a few steps. Each time, check the residual correlogram and partial correlogram for pikes above 2 or 2.5 the standard error. Don't be too strict. Indeed, looking at a large number of lags is doing multiple statistical tests. It is quite normal that 5% of the pikes are out of the interval +/- 2 standard errors. Sometimes, especially when d + D 1 or Q > 1. It is better not to have large p and q together (because there is the risk of common roots in the AR and MA operators). Note that often p = P = 0 and q = Q = 1 will do the job. I can check if I have an example in English but my book is in French.