# Modeling Volatility Characteristics of Epileptic EEGs using GARCH Models
## 6 Results
### GARCH Models
\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** & \\  & **95\% CI** & **95\% CI** & **95\% CI** & **Median** \\  & **Overlapping** & **Overlapping** & **Overlapping** & **Min** \\  & **Interval Count** & **Interval Count** & **Interval Count** & **Max** \\ \hline \multirow{4}{*}{**5**} & 18.57 & 16.33 & 22.54 & 41.25 \\  & (14.58,22.55) & (10.77,21.88) & (16.63,28.45) & 8.21 \\  & 23 & 22 & 37 & 151.69 \\  & 10.31 & 13.41 & 13.39 & 37.05 \\  & (7.99,12.62) & (8.53,18.20) & (9.93,16.85) & 8.69 \\  & 6 & 14 & 11 & 127.36 \\  & 13.70 & 29.42 & 41.87 & 40.41 \\  & (11.47,15.93) & (18.56,40.29) & (26.61,57.13) & 16.16 \\  & 6 & 55 & 56 & 91.14 \\  & 28.15 & 25.51 & 32.90 & 38.86 \\  & (19.96,36.34) & (14.18,36.84) & (20.28,45.51) & 1.26 \\  & 56 & 56 & 60 & 94.01 \\  & 12.05 & 12.26 & 22.84 & 32.98 \\
9 & (9.23,14.97) & (8.59,15.93) & (16.49,29.19) & 12.27 \\  & 7 & 13 & 43 & 93.52 \\  & 12.13 & 10.73 & 20.78 & 34.07 \\
10 & (9.97,14.29) & (8.26,13.20) & (15.07,26.49) & 9.67 \\  & 10 & 7 & 41 & 98.84 \\ \hline \multicolumn{4}{c}{**(C) Sleep 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** & \\  & **95\% CI** & **95\% CI** & **95\% CI** & **Median** \\  & **Overlapping** & **Overlapping** & **Overlapping** & **Max** \\ \hline \multirow{4}{*}{**1**} & 8.47 & 10.00 & 37.68 & 29.9 \\  & (5.74,11.21) & (7.10,12.90) & (12.44,62.93) & 2.82 \\  & 22 & 23 & 49 & 308.76 \\  & 17.07 & 29.08 & 23.14 & 30.64 \\
2 & (12.91,21.22) & (12.12,46.04) & (8.68,37.61) & 6.32 \\  & 29 & 43 & 49 & 134 \\  & 6.32 & 8.27 & 6.23 & 21.72 \\
3 & (5.11,7.54) & (5.20,11.35) & (3.87,8.59) & 0.77 \\  & 24 & 25 & 27 & 126.04 \\  & 12.14 & 181.4 & 36.23 & 9.26 \\
4 & (8.40,15.88) & (80.7,282.1) & (13.53,58.92) & 5.42 \\  & 38 & 12 & 27 & 342.14 \\  & 8.41 & 8.68 & 6.33 & 18.84 \\
5 & (6.59,10.24) & (4.51,12.85) & (3.94,8.72) & 6.18 \\  & 36 & 41 & 33 & 178.51 \\  & 18.86 & 22.62 & 10.51 & 20.32 \\
6 & (13.29,24.44) & (5.77,39.47) & (6.7,14.33) & 4.56 \\  & 41 & 59 & 40 & 136.41 \\  & 15.83 & 72.72 & 6.43 & 11.35 \\
7 & (10.98,20.68) & (24.29,121.2) & (2.43,10.44) & 3.63 \\  & 28 & 27 & 39 & 188.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._For the seizure data, the estimates across the six segments for the seizure channels for RAST3 show the most variation. RAST3 ranges from 0.4449 to 0.7485 for the GARCH coefficient, while the estimates for the ARCH coefficient only range from 0.1145 to 0.1516; the sum of the coefficients has a maximum of 0.8763 in the third segment, while the other sums are relatively similar. The unconditional volatility has a range of 79.1 to 96.5. The variation of the estimates for RAST4 and RMST4 do not show as large of differences as RAST3. The coefficients for RAST4 are similar across all segments; however, the unconditional volatility ranges from 62.4 to 80.9. RMST4 shows similar estimates across the first five segments, with noticeable differences in the sixth segment for the GARCH estimate. All three channels show jumps in unconditional volatility from the fifth to the sixth segment. The estimates across the nine segments of the awake data do not show as much variation. Segments 5 and 7 for RAST3 and segment 5 for RAST4 have higher GARCH coefficients and higher coefficient sums than the estimates for the other segments. The unconditional variation is similar across all segments for all three channels. For the sleep to awake data, the estimates are similar across the segments with the exception of the unconditional volatility for segment 9 (first awake only segment) of RAST3 and RAST4. All three channels have their minimum unconditional volatility in the last segment.