NARX network for multi step prediction, possible to use "extrapolation time vectors"?

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Staffan on 30 Mar 2016
Edited: Greg Heath on 15 May 2016
I just watched the inspiring video about development of forecast models: http://se.mathworks.com/videos/developing-forecast-models-from-time-series-data-in-matlab-part-1-93067.html
- A NARX network with three input variables: power consumption (target vector), time (input vector no. 1) and day (input vector no. 2)
- After training the network in open and closed loop a multi-step prediction is completed using a vector with time (06:00 - 12:00), a vector with the same length detailing the day and empty vector for the corresponding power consumption values. I'm not quite sure how (and if) this specific setup with a "extrapolation time and day vectors" could be used, I would be very greatful for some help here..
- For clarification: In the dataset the time vector will repeat every 24 h (00:00 00:01 ... 23:59 00:00 00:01 ... and so forth). The day vector will also repeat itself every week (1 = Monday, 2 = Tuesday) (this should be compared with the time vector in the two parenthesis ago: 1 1 ... 1 2 2 ... and so forth). With the day and time vectors I'm hoping it would be possible to determine if any weekly reoccurring trends are present, e.g. if the power demand if generally both higher later in the evening on Friday evenings compared to Tuesday evenings.
Generally I would think that knowledge of what day the prediction is valid for and even more importantly the power consumption in the morning (between 00:00 and 12:00, see above) would enhance the accuracy of the prediction (predicted values 12:00 - 24:00, see above). (example: if e.g. higher than expected values were obtained between 00:00 - 12:00 it might be possible that the power consumption is higher than expected at 12:00 - 24:00)
All suggestions are most welcome
Sincerely
Staffan

Greg Heath on 15 May 2016
Edited: Greg Heath on 15 May 2016
It is good to conjecture. However, there are calculations that will put more meat on the bone:
1. Transform all variables to zero-mean/unit-variance
e.g., help/doc ZSCORE
2. Simultaneous plots of all inputs and targets
3. Autocorrelation plots of targets with significant values highlighted
4. Crosscorrelation plots of targets and inputs with significant values highlighted
5. Plots of SOME targets vs SOME inputs
6. Combining all three models (Timedelaynet, Narnet and Narxnet) for post target prediction:
For example, using Narnet on BOTH input and target can yield post target predictions of both input and output.
The predicted input can then be used with Timedelaynet and Narxnet to obtain more predictions of the output.
If the original data is error-free and stationary, success will depend, primarily, on the accumulation of errors because effective combinations of lags and hidden nodes can be obtained via trial and error.
NOTE: IN CONTRADICTION TO PREVIOUS POSTS, POST-TARGET NARXNET PREDICTIONS CANNOT BE ADEQUATELY APPROXIMATED WHEN EMPTY CELLS ARE SUBSTITUTED FOR THE POST-TARGET INPUT!
Hope this helps.
Greg