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


Chaotic Time Series Prediction with residual Analysis Method Using Hybrid Elman–NARX Neural Networks, Muhammad Ardalani-Farsa (2010)
Orthogonal Least Squares Methods and their Application to Non-Linear System Identification, S. Chen, S. A. Billings, W. Luo (1989)
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:


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