Monthly excess stock market returns against conditional variances, implied variance and volatility innovations with uncertainty
| Model | c(c1) | d(d1) | e(e1) | c2 | d2 | e2 | Adj. R2 (%) |
|---|---|---|---|---|---|---|---|
| Panel A: Rolling window model | |||||||
| (1) | 0.0127*** (7.3580) | −2.4713*** (−12.1310) | −4.5140*** (−5.8518) | 23.919 | |||
| (1)-E | 0.0141*** (6.8807) | −3.3810*** (−2.8929) | −13.1511*** (−7.0153) | 0.0017 (0.4118) | 0.6644 (0.5879) | 9.6562*** (5.5191) | 33.200 |
| (1)-V | 0.0122*** (6.3176) | −2.7114*** (−5.6440) | −7.9211*** (−4.0476) | 0.0036 (0.9818) | 0.1817 (0.4548) | 2.7468** (2.3258) | 28.109 |
| Model | Adj. | ||||||
|---|---|---|---|---|---|---|---|
| Panel A: Rolling window model | |||||||
| (1) | 0.0127*** (7.3580) | −2.4713*** (−12.1310) | −4.5140*** (−5.8518) | 23.919 | |||
| (1)-E | 0.0141*** (6.8807) | −3.3810*** (−2.8929) | −13.1511*** (−7.0153) | 0.0017 (0.4118) | 0.6644 (0.5879) | 9.6562*** (5.5191) | 33.200 |
| (1)-V | 0.0122*** (6.3176) | −2.7114*** (−5.6440) | −7.9211*** (−4.0476) | 0.0036 (0.9818) | 0.1817 (0.4548) | 2.7468** (2.3258) | 28.109 |
| Panel B: MIDAS | |||||||
|---|---|---|---|---|---|---|---|
| (2) | 0.0137*** (8.8590) | −3.3620*** (−11.1890) | −5.7707*** (−4.3743) | 25.579 | |||
| (2)-E | 0.0100*** (3.5257) | −4.4473** (−2.1610) | −10.8156*** (−3.4397) | 0.0074 (1.4790) | 1.2914 (0.6825) | 6.5161** (2.2780) | 30.525 |
| (2)-V | 0.0070** (2.4858) | −2.1715* (−1.8547) | −7.5626*** (−4.9310) | 0.0098** (2.5979) | −0.5778 (−0.8695) | 4.5875*** (3.5795) | 30.185 |
| Panel B: MIDAS | |||||||
|---|---|---|---|---|---|---|---|
| (2) | 0.0137*** (8.8590) | −3.3620*** (−11.1890) | −5.7707*** (−4.3743) | 25.579 | |||
| (2)-E | 0.0100*** (3.5257) | −4.4473** (−2.1610) | −10.8156*** (−3.4397) | 0.0074 (1.4790) | 1.2914 (0.6825) | 6.5161** (2.2780) | 30.525 |
| (2)-V | 0.0070** (2.4858) | −2.1715* (−1.8547) | −7.5626*** (−4.9310) | 0.0098** (2.5979) | −0.5778 (−0.8695) | 4.5875*** (3.5795) | 30.185 |
| Panel C: GARCH(1,1) | |||||||
|---|---|---|---|---|---|---|---|
| (3) | 0.0112*** (6.1250) | −2.2474*** (−6.9994) | −4.0364*** (−6.3578) | 21.463 | |||
| (3)-E | 0.0069* (1.8890) | −1.4596 (−0.4567) | −8.9600** (−2.0007) | 0.0076* (1.6687) | −1.1033 (−0.3623) | 5.5141 (1.2932) | 26.246 |
| (3)-V | 0.0046** (2.2378) | 0.4845 (0.8697) | −5.5790*** (−5.9684) | 0.0098** (2.3244) | −2.9811*** (−5.9331) | 2.5081*** (2.8718) | 25.507 |
| Panel C: GARCH(1,1) | |||||||
|---|---|---|---|---|---|---|---|
| (3) | 0.0112*** (6.1250) | −2.2474*** (−6.9994) | −4.0364*** (−6.3578) | 21.463 | |||
| (3)-E | 0.0069* (1.8890) | −1.4596 (−0.4567) | −8.9600** (−2.0007) | 0.0076* (1.6687) | −1.1033 (−0.3623) | 5.5141 (1.2932) | 26.246 |
| (3)-V | 0.0046** (2.2378) | 0.4845 (0.8697) | −5.5790*** (−5.9684) | 0.0098** (2.3244) | −2.9811*** (−5.9331) | 2.5081*** (2.8718) | 25.507 |
| Panel D: GJR-GARCH(1,1) | |||||||
|---|---|---|---|---|---|---|---|
| (4) | 0.0111*** (4.7355) | −2.4344*** (−3.5514) | −6.3264*** (−3.7760) | 26.805 | |||
| (4)-E | 0.0072** (2.2234) | −2.5108 (−1.0646) | −16.2551*** (−3.5881) | 0.0081* (1.7952) | −0.3699 (−0.1575) | 10.9728** (2.4313) | 33.315 |
| (4)-V | 0.0016 (0.6390) | 2.4062*** (3.1317) | −5.9096*** (−4.5766) | 0.0131*** (3.1319) | −5.5449*** (−6.8486) | −1.0096 (−1.1106) | 29.415 |
| Panel D: GJR-GARCH(1,1) | |||||||
|---|---|---|---|---|---|---|---|
| (4) | 0.0111*** (4.7355) | −2.4344*** (−3.5514) | −6.3264*** (−3.7760) | 26.805 | |||
| (4)-E | 0.0072** (2.2234) | −2.5108 (−1.0646) | −16.2551*** (−3.5881) | 0.0081 | −0.3699 (−0.1575) | 10.9728** (2.4313) | 33.315 |
| (4)-V | 0.0016 (0.6390) | 2.4062*** (3.1317) | −5.9096*** (−4.5766) | 0.0131*** (3.1319) | −5.5449*** (−6.8486) | −1.0096 (−1.1106) | 29.415 |
| Panel E: Implied variance | |||||||
|---|---|---|---|---|---|---|---|
| (5) | 0.0059** (1.9835) | −0.0136 (−0.1229) | −0.1855** (−2.5653) | 0.821 | |||
| (5)-E | −0.0042 (−1.3380) | 0.4625*** (4.6442) | 0.2939* (1.9550) | 0.0142** (2.1479) | −0.5506*** (−3.4403) | −0.4644*** (−2.6341) | 4.075 |
| (5)-V | −0.0033 (−1.1283) | 0.5035*** (4.3046) | 0.6882*** (3.1617) | 0.0134** (2.0459) | −0.4561*** (−2.9663) | −1.2897*** (−4.6225) | 11.665 |
| Panel E: Implied variance | |||||||
|---|---|---|---|---|---|---|---|
| (5) | 0.0059** (1.9835) | −0.0136 (−0.1229) | −0.1855** (−2.5653) | 0.821 | |||
| (5)-E | −0.0042 (−1.3380) | 0.4625*** (4.6442) | 0.2939* (1.9550) | 0.0142** (2.1479) | −0.5506*** (−3.4403) | −0.4644*** (−2.6341) | 4.075 |
| (5)-V | −0.0033 (−1.1283) | 0.5035*** (4.3046) | 0.6882*** (3.1617) | 0.0134** (2.0459) | −0.4561*** (−2.9663) | −1.2897*** (−4.6225) | 11.665 |
Note(s): The table reports estimates from the regressions of monthly excess stock market returns against conditional variances, implied variance and volatility innovations. Models (1) to (5) are estimates from the regressions without a dummy variable of uncertainty. Models (1)-E to (5)-E ((1)-V to (5)-V) are estimates from the regressions with a dummy variable of FEPU (FVOV). Newey and West (1987) corrected t-statistics are reported in parentheses. *, ** and *** represent significance at the 10, 5 and 1% levels, respectively
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