# Modeling Volatility Characteristics of Epileptic EEGs using GARCH Models
## 6 Results
### Half-life and Confidence Intervals
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Seizure Channels**} & \multicolumn{2}{c}{**Non-seizure Channels**} \\ \hline  & **RAST3** & **RAST4** & **RMST4** & **Half Life** \\ \hline \multirow{4}{*}{**Segment**} & **HL** & **HL** & **HL** & **Median** \\  & **95\% CI** & **95\% CI** & **95\% CI** & **Min** \\  & **Overlapping** & **Overlapping** & **Overlapping** & **Max** \\  & **Interval Count** & **Interval Count** & **Interval Count** & **Max** \\ \hline \multirow{4}{*}{**7**} & 5.5 & 1.71 & & 7.42 \\  & (4.76,6.48) & (1.50,1.98) & N/A & 2.65 \\  & 28 & 0 & & 187.9 \\  & 1.47 & 1.55 & 6.46 & 6.45 \\
8 & (1.21,1.84) & (1.34,1.82) & (4.19,13.20) & 5.68 \\  & 0 & 0 & 45 & 92.53 \\  & 1.41 & 1.34 & 6.49 & 13.26 \\
9 & (1.16,1.75) & (1.16,1.56) & (4.3,12.53) & 4.59 \\  & 0 & 0 & 36 & 94.41 \\ \hline \multicolumn{4}{c}{**(B)** Awake data.} \\ \hline  & \multicolumn{2}{c}{**Seizure Channels**} & \multicolumn{2}{c}{**Non-seizure Channels**} \\ \hline  & **RAST3** & **RAST4** & **RMST4** & **Half Life** \\ \hline \multirow{4}{*}{**Segment**} & **HL** & **HL** & **HL** & **Median** \\  & **95\% CI** & **95\% CI** & **95\% CI** & **95\% CI** & **Min** \\  & **Overlapping** & **Overlapping** & **Overlapping** & **Max** \\  & **Interval Count** & **Interval Count** & **Interval Count** & **Max** \\ \hline \multirow{4}{*}{**1**} & 8.43 & 14.86 & 6.26 & 26.15 \\  & (6.78,11.08) & (11.16,22.06) & (5.12,8) & 9.94 \\  & 0 & 16 & 0 & 64.51 \\  & 7.93 & 13.28 & 14.38 & 29.67 \\
2 & (6.12,11.16) & (9.03,24.61) & (9.9,25.82) & 1.19 \\  & 0 & 17 & 18 & 57.56 \\  & 7.38 & 15.51 & 7.84 & 29.51 \\
3 & (6.08,9.32) & (11.87,22.25) & (6.58,9.65) & 6.36 \\  & 0 & 11 & 0 & 55.36 \\  & 10.13 & 6.44 & 13.05 & 26.31 \\
4 & (8.31,12.92) & (5.24,8.31) & (10.51,17.12) & 10.65 \\  & 3 & 0 & 4 & 47.97 \\  & 18.57 & 16.33 & 22.54 & 30.11 \\
5 & (15.27,23.62) & (12.16,24.66) & (17.85,30.51) & 7.08 \\  & 14 & 16 & 24 & 82.57 \\  & 10.31 & 13.41 & 13.39 & 28 \\
6 & (8.40,13.27) & (9.80,20.97) & (10.63,18.01) & 7.14 \\  & 0 & 5 & 1 & 79.1 \\  & 13.7 & 29.43 & 41.87 & 29.67 \\
7 & (11.77,16.35) & (21.47,46.53) & (30.66,65.77) & 11 \\  & 1 & 50 & 53 & 63.35 \\  & 28.15 & 25.51 & 32.9 & 28.22 \\
8 & (21.79,39.64) & (17.63,45.67) & (23.75,53.22) & 1.21 \\  & 48 & 50 & 53 & 64.22 \\  & 12.05 & 12.26 & 22.84 & 25.75 \\
9 & (9.69,15.87) & (9.41,17.43) & (17.85,31.58) & 8.99 \\  & 2 & 6 & 36 & 729.5 \\  & 12.13 & 10.73 & 20.78 & 26.01 \\
10 & (10.29,14.74) & (8.71,13.9) & (16.28,28.6) & 7.98 \\  & 2 & 2 & 35 & 67.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._For the sleep and sleep to awake data, the half-life estimates are higher than the pre-seizure and awake data for all channels (Table 2c,d). The half-life CIs for RAST3 and RAST4 overlap a greater number of non-seizure CIs in both datasets; however, in the sleep to awake data, both channels overlap approximately half of the non-seizure CIs. The half-life values appear to be highest in the sleep data relative to the other three datasets. For the non-seizure channels, the median half-life is higher for all segments in both datasets, with the exception of the last segment of the sleep to awake data (Table 2d). This particular segment is the second segment of awake data in the sleep to awake segment and has a median half-life of 14.58, which is similar to the values for the segments of the awake data. Similar behavior is seen for RMST4, which has similar half-life values to the awake data, but not in RAST3 and RAST4, which both have half-life values greater than the median.