Flexible Time-Varying Betas in a Novel Mixture Innovation Factor Model with Latent Threshold
Abstract
1. Introduction
2. Literature Review
3. Data and Methodology
3.1. Data
3.2. Methodology
4. Empirical Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Statistic | DURBL | MANUF | ENRGY | HITEC | MKT | SMB | HML | RMW | CMA |
---|---|---|---|---|---|---|---|---|---|
Mean | 0.624 | 0.610 | 0.537 | 0.711 | 0.568 | 0.230 | 0.251 | 0.249 | 0.256 |
S.D. | 6.726 | 4.955 | 5.901 | 6.394 | 4.468 | 3.026 | 2.867 | 2.167 | 1.988 |
Min | −32.710 | −27.930 | −34.730 | −26.530 | −23.240 | −14.890 | −13.960 | −18.480 | −6.860 |
Max | 42.620 | 17.500 | 32.330 | 20.320 | 16.100 | 18.080 | 12.580 | 13.380 | 9.560 |
Skewness | 0.602 | −0.504 | 0.005 | −0.241 | −0.507 | 0.334 | 0.013 | −0.327 | 0.316 |
Kurtosis | 5.975 | 2.506 | 4.032 | 1.290 | 1.878 | 2.947 | 2.358 | 12.238 | 1.603 |
Jarque–Bera (JB) | 1077.237 * | 212.099 * | 472.145 * | 55.471 * | 132.675 * | 265.584 * | 161.942 * | 4349.274 * | 86.602 * |
Q(1) | 8.152 * | 1.676 | 0.717 | 2.408 | 2.652 | 2.947 * | 21.859 * | 15.273 * | 9.901 * |
Q(6) | 23.302 * | 7.253 | 4.158 | 4.806 | 7.417 | 10.664 * | 30.461 * | 20.396 * | 19.610 * |
ARCH(1) | 14.192 * | 10.178 * | 83.967 * | 55.253 * | 18.336 * | 58.167 * | 40.465 * | 122.214 * | 69.473 * |
Variable | Mean | Median | S.D. | Min | Max | 5th Percentile | 95th Percentile |
---|---|---|---|---|---|---|---|
Panel A: TTVP-SV Model | |||||||
Intercept | −0.338 | −0.381 | 0.093 | −0.436 | −0.037 | −0.431 | −0.153 |
MKT | 1.165 | 1.162 | 0.010 | 1.153 | 1.180 | 1.154 | 1.180 |
SMB | 0.224 | 0.378 | 0.192 | 0.000 | 0.415 | 0.002 | 0.414 |
HML | 0.287 | 0.267 | 0.073 | 0.162 | 0.421 | 0.171 | 0.416 |
RMW | 0.157 | 0.097 | 0.110 | 0.047 | 0.356 | 0.050 | 0.350 |
CMA | 0.094 | 0.057 | 0.098 | −0.023 | 0.269 | −0.018 | 0.266 |
Panel B: Rolling Model | |||||||
Intercept | −0.443 | −0.506 | 0.288 | −0.978 | 0.208 | −0.827 | 0.105 |
MKT | 1.221 | 1.181 | 0.182 | 0.954 | 1.623 | 0.991 | 1.583 |
SMB | 0.303 | 0.256 | 0.246 | −0.149 | 0.838 | −0.106 | 0.762 |
HML | 0.376 | 0.406 | 0.333 | −0.408 | 1.030 | −0.277 | 0.887 |
RMW | 0.264 | 0.198 | 0.424 | −0.382 | 1.150 | −0.287 | 1.034 |
CMA | 0.117 | 0.071 | 0.300 | −0.575 | 0.632 | −0.340 | 0.583 |
Panel C: Static Model | |||||||
Intercept | −0.340 | 0.150 | −0.586 | −0.094 | |||
MKT | 1.267 | 0.037 | 1.207 | 1.327 | |||
SMB | 0.214 | 0.052 | 0.128 | 0.300 | |||
HML | 0.377 | 0.069 | 0.263 | 0.491 | |||
RMW | 0.254 | 0.072 | 0.136 | 0.373 | |||
CMA | 0.147 | 0.106 | −0.027 | 0.320 |
Variable | Mean | Median | S.D. | Min | Max | 5th Percentile | 95th Percentile |
---|---|---|---|---|---|---|---|
Panel A: TTVP-SV Model | |||||||
Intercept | −0.086 | −0.083 | 0.033 | −0.135 | −0.001 | −0.133 | −0.025 |
MKT | 1.067 | 1.067 | 0.000 | 1.066 | 1.067 | 1.066 | 1.067 |
SMB | 0.102 | 0.102 | 0.001 | 0.101 | 0.104 | 0.101 | 0.104 |
HML | 0.085 | 0.085 | 0.001 | 0.084 | 0.086 | 0.085 | 0.086 |
RMW | 0.240 | 0.240 | 0.003 | 0.235 | 0.245 | 0.236 | 0.245 |
CMA | 0.053 | 0.075 | 0.036 | 0.002 | 0.108 | 0.006 | 0.107 |
Panel B: Rolling Model | |||||||
Intercept | −0.118 | −0.095 | 0.148 | −0.471 | 0.120 | −0.369 | 0.078 |
MKT | 1.105 | 1.091 | 0.058 | 0.980 | 1.265 | 1.022 | 1.200 |
SMB | 0.103 | 0.115 | 0.062 | −0.024 | 0.258 | 0.001 | 0.198 |
HML | 0.014 | 0.018 | 0.106 | −0.253 | 0.263 | −0.204 | 0.161 |
RMW | 0.222 | 0.281 | 0.230 | −0.337 | 0.606 | −0.225 | 0.478 |
CMA | 0.116 | 0.127 | 0.134 | −0.175 | 0.406 | −0.105 | 0.336 |
Panel C: Static Model | |||||||
Intercept | −0.164 | 0.061 | −0.265 | −0.063 | |||
MKT | 1.084 | 0.015 | 1.059 | 1.108 | |||
SMB | 0.110 | 0.021 | 0.074 | 0.145 | |||
HML | 0.088 | 0.028 | 0.041 | 0.134 | |||
RMW | 0.320 | 0.030 | 0.271 | 0.369 | |||
CMA | 0.126 | 0.043 | 0.055 | 0.197 |
Variable | Mean | Median | S.D. | Min | Max | 5th Percentile | 95th Percentile |
---|---|---|---|---|---|---|---|
Panel A: TTVP-SV Model | |||||||
Intercept | −0.087 | −0.117 | 0.129 | −0.302 | 0.099 | −0.292 | 0.094 |
MKT | 0.963 | 0.954 | 0.017 | 0.951 | 1.007 | 0.952 | 1.003 |
SMB | −0.118 | −0.181 | 0.143 | −0.255 | 0.335 | −0.250 | 0.261 |
HML | 0.096 | 0.026 | 0.172 | −0.018 | 0.547 | −0.011 | 0.527 |
RMW | −0.086 | −0.103 | 0.184 | −0.404 | 0.195 | −0.400 | 0.192 |
CMA | 0.415 | 0.168 | 0.403 | −0.084 | 1.261 | −0.047 | 1.256 |
Panel B: Rolling Model | |||||||
Intercept | 0.022 | 0.131 | 0.529 | −1.181 | 1.010 | −0.823 | 0.815 |
MKT | 0.967 | 0.973 | 0.135 | 0.680 | 1.348 | 0.739 | 1.153 |
SMB | −0.161 | −0.196 | 0.218 | −0.577 | 0.518 | −0.487 | 0.172 |
HML | 0.031 | −0.063 | 0.261 | −0.362 | 0.733 | −0.279 | 0.563 |
RMW | 0.042 | 0.052 | 0.545 | −0.991 | 0.921 | −0.910 | 0.773 |
CMA | 0.304 | 0.145 | 0.605 | −0.689 | 1.748 | −0.510 | 1.675 |
Panel C: Static Model | |||||||
Intercept | −0.224 | 0.168 | −0.499 | 0.052 | |||
MKT | 1.008 | 0.041 | 0.941 | 1.075 | |||
SMB | −0.063 | 0.058 | −0.159 | 0.033 | |||
HML | 0.230 | 0.078 | 0.102 | 0.357 | |||
RMW | 0.209 | 0.081 | 0.076 | 0.342 | |||
CMA | 0.365 | 0.118 | 0.170 | 0.559 |
Variable | Mean | Median | S.D. | Min | Max | 5th Percentile | 95th Percentile |
---|---|---|---|---|---|---|---|
Panel A: TTVP-SV Model | |||||||
Intercept | 0.227 | 0.247 | 0.057 | 0.105 | 0.318 | 0.151 | 0.315 |
MKT | 1.054 | 1.053 | 0.002 | 1.051 | 1.056 | 1.051 | 1.056 |
SMB | 0.075 | 0.084 | 0.021 | 0.025 | 0.088 | 0.026 | 0.087 |
HML | −0.234 | −0.278 | 0.119 | −0.362 | −0.010 | −0.359 | −0.028 |
RMW | −0.149 | −0.163 | 0.219 | −0.646 | 0.181 | −0.619 | 0.179 |
CMA | −0.466 | −0.462 | 0.054 | −0.561 | −0.387 | −0.556 | −0.392 |
Panel B: Rolling Model | |||||||
Intercept | 0.326 | 0.178 | 0.390 | −0.150 | 1.452 | −0.104 | 1.181 |
MKT | 1.043 | 1.032 | 0.124 | 0.835 | 1.376 | 0.873 | 1.266 |
SMB | 0.125 | 0.107 | 0.127 | −0.222 | 0.398 | −0.035 | 0.379 |
HML | −0.290 | −0.263 | 0.306 | −0.860 | 0.318 | −0.768 | 0.202 |
RMW | −0.131 | −0.246 | 0.320 | −0.718 | 0.573 | −0.508 | 0.493 |
CMA | −0.398 | −0.419 | 0.407 | −1.357 | 0.365 | −1.088 | 0.242 |
Panel C: Static Model | |||||||
Intercept | −0.224 | 0.168 | −0.499 | 0.052 | |||
MKT | 1.008 | 0.041 | 0.941 | 1.075 | |||
SMB | −0.063 | 0.058 | −0.159 | 0.033 | |||
HML | 0.230 | 0.078 | 0.102 | 0.357 | |||
RMW | 0.209 | 0.081 | 0.076 | 0.342 | |||
CMA | 0.365 | 0.118 | 0.170 | 0.559 |
Model | DURBL | MANUF | ENRGY | HITEC |
---|---|---|---|---|
TTVP-SV | 3.670 | 1.531 | 3.796 | 2.403 |
TTVP | 3.525 | 1.520 | 3.696 | 2.372 |
Rolling | 3.708 | 1.544 | 4.163 | 2.484 |
Static | 3.747 | 1.533 | 4.195 | 2.575 |
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Balcilar, M.; Demirer, R.; Bekun, F.V. Flexible Time-Varying Betas in a Novel Mixture Innovation Factor Model with Latent Threshold. Mathematics 2021, 9, 915. https://doi.org/10.3390/math9080915
Balcilar M, Demirer R, Bekun FV. Flexible Time-Varying Betas in a Novel Mixture Innovation Factor Model with Latent Threshold. Mathematics. 2021; 9(8):915. https://doi.org/10.3390/math9080915
Chicago/Turabian StyleBalcilar, Mehmet, Riza Demirer, and Festus V. Bekun. 2021. "Flexible Time-Varying Betas in a Novel Mixture Innovation Factor Model with Latent Threshold" Mathematics 9, no. 8: 915. https://doi.org/10.3390/math9080915
APA StyleBalcilar, M., Demirer, R., & Bekun, F. V. (2021). Flexible Time-Varying Betas in a Novel Mixture Innovation Factor Model with Latent Threshold. Mathematics, 9(8), 915. https://doi.org/10.3390/math9080915