# Time-Series Analysis

We dove into several different existing research methods for time evolution series in order to explore for ourselves the pros and cons of each method, and what we were able to take away from our results at an undergraduate research level.

### Threshold Analysis

Our first analysis method was a simple threshold test. We tested the data from all 18 channels of each patient’s EEG data against a threshold value. In EEG analysis, activity above a certain threshold activity is thought to be correlated with certain brain conditions. The specific conditions that can be extrapolated from these findings are beyond the scope of this project and are best left up to medical professionals.

For the purposes of this experiment, we worked with 300 data points from every patient. For the control patients, we used data points 1 – 300. These points contained nonzero data, so we felt that they were acceptable for this experiment. For the experimental patients, the first several hundred data points were often zero. Consequently, we used data points 251 – 550 to look at nonzero data. We hypothesize that the experimental patient data was collected in a different method than the control patients, accounting for the shift in data. Our chosen threshold was zero, which was an arbitrary choice given that our data was not normalized. The rationale for this choice is that we are merely exploring this method of time series analysis, not trying to analyze any trends in the data.

### Autocorrelation Analysis

We ran each channel of each patient through an autocorrelation filter (described earlier in this paper) to test how well each channel clustered over time. Each of our graphs demonstrates all 18 channels of a given patient over time. The function for autocorrelation is defined earlier in this paper. If a value is autocorrelated with itself, so if the lag value is zero, then the autocorrelation function with output 1, since every data point should be 100% correlated with itself.

### Wavelet Analysis

We devised a version of the algorithm used by Blanco et. al. in their work in the early 2000s. For the purposes of this experiment, we worked with 100 data points from every patient. For the control patients, we used data points 1 – 100. For the experimental patients, we used data points 251 – 350 to look at nonzero data. We hypothesize that the experimental patient data was collected in a different method than the control patients, accounting for the shift in data.