Dear all,
i am trying to forecast a time series(named 'OSVEXT').
the attached file contains the following tests: ACF, PACF, Box-Ljung test, KPSS test, ARIMA (auto.arima using R-package 'forecast')
fast overview: it's stationary; based on ACF & Ljung test it's a white noise!!
NOTE: all info and tests in the attached file was conducted using R.
many thanks;
1) If a process is really white noise then it is not forecastable by definition (because its values at different times are statistically independent).
2) By far not all processes in the world are forecastable. Many real processes depend not only on their own previous values (autocorrelation), but on other processes and phenomena. And so they are forecatable only as a part of bigger system (and as a part of bigger mathematical model that describes the whole system).
3) If linear prediction models (like ARIMA) do not work, you may try to find non-linear autocorrelation. For example, you may try to produce a 3D-plot of points [x(t),x(t-1),x(t-2)], where x(t) is the value of the process of interest at time t. If you manage to see a "structure" in the 3D plot (instead of homogeneous "white noise" picture), then you will get a clue to building a corresponding non-linear autoregression model. Alas, as our space has only 3 dimensions and our brain effectively analyses only 3-dimentional objects, it is not possible to construct deeper autoregression models using this approach. Another limitation is that the data sample has to be quite long in order to form any stable non-trivial pattern on the 3D plot.
Sometimes by separately forecasting different percentiles of the data, you can find a "system behind the madness" and even may be able to get reasonable forecasts. I did not look at your data though; so IDK if these statements apply in your case.
Alex, given we can predict different percentiles of the data separately, how can we predict which percentile the next point will fall into (and, hence, which prediction model to choose to predict the next point of the process)?
We can use quantile regression. There's been quite a bit of research lately (2-3 years) on using quantile regression in forecasting. AIC can be used to find the best model. Theil's U can be used as well, we'll just have to jacknife (resample) the forecast.
White noise is serially uncorrelated random variable, you may also add an iid assumption. No, it cannot be forecast, although with enough data mining you might find an in-sample fit but it will essentially be meaningless
In real problems the white noise that you find will not be the statistical white noise.
recommend the addition to predict the average (ARIMA) also predict volatility (variance) (GARCH), the Eviews software, is an excellent tool.
Dear all,
thank you for your notes.
it was really a tough task. I did reformulate the original version of the addressed forecasting problem.
the new formulation and suggested forecasting solution have been published here:
http://ieeexplore.ieee.org/document/7850020/
looking forward to your comment.
Best,
Amer.
I am shocked by the expression that " perfectly predictable ", and I am very eager to know the method to reach this end.
Amer Bakhach can you email me your paper given through this link.
http://ieeexplore.ieee.org/document/7850020/
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