Forecasting Stock Market Volatility: A Combination Approach
Table 5
Out-of-sample forecasting performance over business cycles.
WTI
BRT
VIX
WTI + VIX
BRT + VIX
CC ()
CC ()
Out-of-sample forecasting results for 1998–2018
Recession period
2.648
0.596
20.781
21.056
21.208
19.854
19.883
Expansion period
0.825
0.116
12.124
13.553
13.112
11.896
11.783
Out-of-sample forecasting results for 2003–2018
Recession period
0.597
0.572
26.792
26.786
25.937
24.809
24.695
Expansion period
1.572
0.191
8.778
9.659
9.215
8.945
8.803
Out-of-sample forecasting results for 2008–2018
Recession period
3.151
2.071
12.409
13.352
12.711
12.806
12.468
Expansion period
1.773
0.425
6.482
9.787
9.872
7.531
6.917
Out-of-sample forecasting results for 2013–2018
Recession period
5.141
0.725
32.515
36.125
35.894
35.003
33.055
Expansion period
1.461
0.555
7.719
11.011
10.874
8.367
7.840
Note. This table reports the out-of-sample performance from statistical perspectives over business cycles based on the recursive window. The forecasting results for the predictive regression models in (3), (4), and (5) for monthly stock volatility are shown. Statistical performance is defined as out-of-sample R-square ().
