It's a very initial version of my analyzing time series data from scripts, as well as using MatLab. It's only a school work, but I felt interested in modeling these EEG signal data acquired during a patient's seizure due to epilepsy, which looks like a chaos at the first sight.
And yes, by looking at the autocorrelation and partial autocorrelation estimates, the data are highly autocorrelated, but with many lags (around 20), even conditional on the 1st lag.
It would be appropriate to conduct an analysis by applying an ARIMA (p,d,q) function on such a time series with very large p and q, but I would try a different approach to see how it works. Here, I came up with an idea of using Fourier Transformation.
First, I split the entire 25,000 records into odd and even records. The odd records were used to form the model and the even ones were for cross-validation. Second, a fast Fourier transformation function was employed to model the odd records, transferring them from the time domain to a frequency domain, and the low-amplitude frequencies were removed by assuming those signals belong to some physiological activities, such as heart beats, breath, etc. Third, an inverse Fourier transformation was used to generate model-based records, and these generated records were compared with the odd records to obtain the residuals. As seen from the residual plot, the residuals were small. In addition, the autocorrelation of the residuals was also checked, and they seemed not autocorrelated very much.
The model specific records (green) were generated based on fast Fourier transformation. These records were compared to the original odd records (blue) to obtain residuals (in the right).
The left: Autocorrelation of model residuals on odd records. The right: Plot of model-generated records against even records left for cross-validation.
A further step to validate the model was to compare the model-generated records with the even records left for cross-validation. Again, the residuals were plotted and checked autocorrelation.
The residuals obtained from cross-validation (the left) were compared with the residuals obtained from the odd records (the right). Both were small and not autocorrelated.
The method helped me try a different approach in terms of modeling time series data. Given more time and put in a more realistic framework, I would have thought more on how to brush up the method, understand the similarity and difference between time series functions and Fourier transformation in terms of modeling time series data, as well as interpret and utilize the model parameters from the Fourier transformation in order to apply the method into more generalized reality.