Conclusions and Future Directions
The autoregressive model was able to consistently determine the presence and onset time of signals buried in correlated noise, and was able to predict future values of the noise from its previous values well enough to extract signals buried in the noise to a satisfactory degree.
Three extensions could be made on the foundation of current result:
1. Although our program worked quite well with synthesized correlated noise, it would be of practical interest to find correlated noise in nature and apply the autoregressive model to that noise. For instance, in the paper this project was based on, the author applied it to seismic noise[2].
2.A more complex non-stationary AR Model may be adopted to extract a signal from non-stationary noise.
3. Use the autocorrelation matrix ( also know as Yule-Walker method) to determine AR coefficients more efficiently with larger data sets.
References:
[1] G. P. Nason, “Stationary and non-stationary time series,” Stat. Volcanol. Publ. IAVCEI, vol. 1, pp. 000–000, 2006.
[2] M. M. A. Razak, “Detection and extraction of weak signals buried in noise,” Am. J. Phys., vol. 77, no. 11, pp. 1061–1065, Nov. 2009.
[3] H. Akaike, “Statistical predictor identification,” Ann. Inst. Stat. Math., vol. 22, no. 1, pp. 203–217, 1970.