I have historic error of time series. I want to analyze error series to improve forecast series. Are there any methods to do this?

  • $\begingroup$ More information would be very helpful. What are you forecasting? what is the error distribution? $\endgroup$ – Sean Owen Nov 25 '14 at 23:18
  • $\begingroup$ @SeanOwen I am forecasting wind-speed at a particular location, The error series is obeying normal distribution. please intimate me if you need any other information. $\endgroup$ – dimbul Nov 26 '14 at 4:53

NARMAX Methodology and Residual analysis both address this issue. Search for the following articles:(Error = Residual = Noise)

  1. Chaotic Time Series Prediction with residual Analysis Method Using Hybrid Elman–NARX Neural Networks, Muhammad Ardalani-Farsa (2010)

  2. Orthogonal Least Squares Methods and their Application to Non-Linear System Identification, S. Chen, S. A. Billings, W. Luo (1989)

  3. Any article working on NARMAX, NARMA and Residual Analysis. Remember in NARX and NAR there is no error estimation and analysis.

Notice in general you can follow this steps:

  1. Estimate a time series and calculate Error or Residuals using any .

  2. Consider errors or residuals as a new time series. Try to estimate Error-Time-Series. Now you can add this estimations to your initial model.

  3. You can do this residual analysis as many times as you need. In practice 2 or 3 times suffices. Remember in practice, residual time series are noisy and SNR in this time series is so small. So you should use some Noise-Robust methods for residual analysis.


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