Time-Series Analysis

Discussion of Results

Threshold analysis allows us to filter out outliers in the data. In the control patients, this showed us that the channels fall into one of three categories: non-positive values that are filtered out of the results, increasing at what appears to be a logarithmic rate before decreasing at what appears to be an exponential rate, or increasing what appears to be a logarithmic rate before reaching a stable value that the channel maintains as time continues. In the experimental patients, this showed us loose sinusoidal trends in the data. Autocorrelation allows us to see variability, or lack thereof, in the data over time. In our example, we could see that as lag increased, autocorrelation decreased in the control patients, indicating more randomness in the data. We were also able to see sinusoidal behavior in the autocorrelation functions for the experimental patients, indicating sinusoidal behavior of the data over time. In the wavelet analysis, we can determine at what degrees of scale each data set was best analyzed at via the wavelet transformation.

Considerations for Future Work

There are several future directions that this type of work can go. Many research labs around the world are exploring the pros and cons of the three types of analysis that we outlined in this paper, threshold analysis, autocorrelation analysis, and wavelet analysis. New forms of analysis are also being developed. Notably, the lab run by Wang and Veluolu has critiqued Fourier transforms, wavelet transforms, and clustering (specifically the autoregressive model) as not being effective or efficient techniques for analysis with modern technology. Wang and Velvolu cite several perceived limitations of current analysis techniques when dealing with analyzing modern EEGs (Wang and Veluvolu, 2017). They in turn have proposed the use of modern evolutionary algorithms to better address time analysis of EEG signals.