Table 3.
Estimation results
| Aggregate | Oil & Gas | Materials | Industrials | Consumer Goods | Health Care | Consumer Services | Telecommunications | Utilities | Financials | Technology | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| β0 | 6.066⁎⁎ | − 5.527 | 16.376⁎⁎ | − 2.407 | 15.737⁎⁎ | 50.920⁎⁎⁎ | 20.833⁎⁎ | − 2.485 | 10.583⁎⁎⁎ | − 2.990 | 23.345⁎⁎⁎ |
| − 1.651 | − 2.11 | − 1.043 | (− 1.904) | − 1.149 | − 2.037 | − 3.218 | − 2.172 | − 0.263 | (− 4.344) | − 1.005 | |
| β1 | 0.426⁎ | 0.888⁎⁎ | 0.109 | 0.650⁎ | 0.088 | − 1.199⁎ | − 0.032 | − 0.029 | 0.028 | 0.517⁎ | − 0.322 |
| − 0.304 | − 1.369 | − 2.213 | − 0.304 | − 1.619 | (− 0.228) | (− 1.576) | (− 0.131) | − 0.109 | − 0.106 | (− 1.271) | |
| δ0 | − 6.388⁎⁎ | 38.440⁎⁎ | − 17.203⁎⁎ | 10.915⁎⁎ | − 16.039⁎⁎ | − 50.959⁎⁎⁎ | − 22.062⁎⁎ | 1.988 | − 17.780⁎⁎⁎ | 11.621 | − 21.505⁎⁎⁎ |
| (− 1.622) | − 2.174 | (− 1.874) | − 2.212 | (− 1.748) | (− 1.988) | (− 3.009) | − 2.171 | (− 0.215) | − 4.369 | (− 1.039) | |
| δ1 | 0.933⁎⁎ | − 0.551 | 0.998⁎⁎⁎ | 0.437 | 1.118⁎⁎⁎ | 1.870⁎⁎⁎ | 1.138 | 0.927⁎ | 1.413⁎⁎⁎ | 0.677 | 1.299⁎⁎⁎ |
| − 1.835 | (− 1.633) | − 0.946 | − 2.684 | − 1.161 | − 2.432 | − 3.418 | − 1.016 | − 1.438 | − 2.698 | − 0.526 | |
| α1 | 0.341⁎ | 0.488⁎⁎ | 0.309 | 0.403⁎⁎ | − 0.177 | − 0.027 | 0.075 | 0.577 | − 0.060⁎⁎ | 0.015 | 0.248 |
| − 0.825 | − 1.334 | − 1.741 | − 0.825 | (− 2.091) | (− 0.736) | − 0.171 | − 0.621 | (−1.100) | − 1.722 | − 0.058 | |
| α2 | − 0.462⁎⁎ | − 0.511⁎⁎ | − 0.584⁎⁎ | − 0.337⁎ | − 0.483⁎ | − 0.070 | 0.011 | − 0.434⁎⁎ | 0.005 | − 0.219⁎ | − 0.811⁎⁎ |
| (− 1.455) | (− 1.766) | (− 1.667) | (− 1.962) | (− 1.384) | (− 1.395) | − 1.186 | (− 0.171) | − 1.941 | (− 0.375) | (− 1.259) | |
| Γ | 3.914⁎⁎⁎ | 3.277⁎⁎ | 2.950⁎⁎⁎ | 3.368⁎⁎ | 3.487⁎⁎⁎ | 35.775⁎⁎⁎ | 4.354⁎⁎⁎ | 3.057⁎⁎ | 5.851⁎⁎⁎ | 4.242⁎⁎ | 1.884⁎⁎⁎ |
| − 2.998 | − 2.998 | − 1.754 | − 3.828 | − 2.226 | − 4.123 | − 4.257 | − 3.95 | − 1.934 | − 4.831 | − 2.277 | |
| Ψ | 5.555⁎⁎⁎ | 4.734⁎⁎⁎ | 5.977⁎⁎⁎ | 5.373⁎⁎⁎ | 5.968⁎⁎⁎ | 5.670⁎⁎⁎ | 5.382⁎⁎⁎ | 5.910⁎⁎⁎ | 5.684⁎⁎⁎ | 5.539⁎⁎⁎ | 6.159⁎⁎⁎ |
| − 100.891 | − 103.877 | − 120.973 | − 47.227 | − 93.006 | − 81.434 | − 307.775 | − 116.207 | − 95.155 | − 89.256 | − 93.965 | |
| Adj-R2 | 0.833 | 0.785 | 0.901 | 0.844 | 0.849 | 0.949 | 0.9 | 0.81 | 0.885 | 0.843 | 0.88 |
| BIC | 6.167 | 8.542 | 5.305 | 6.561 | 5.825 | 4.472 | 5.184 | 5.422 | 3.481 | 6.545 | 5.94 |
| Q(8) | 11.759 | 10.197 | 11.119 | 12.142 | 12.87 | 8.274 | 15.346⁎ | 14.212⁎ | 17.607⁎⁎ | 10.115 | 12.876 |
| Linearity test | 2.410⁎ | 2.583⁎⁎ | 2.739⁎⁎ | 3.072⁎⁎ | 3.033⁎⁎ | 2.248⁎ | 3.083⁎⁎ | 3.067⁎⁎ | 2.486⁎⁎ | 2.603⁎⁎ | 4.276⁎⁎⁎ |
| EJ test | 3.027⁎ | 3.688⁎⁎ | 2.462⁎ | 3.176⁎⁎ | 3.666⁎⁎ | 3.774⁎⁎ | 3.390⁎⁎ | 3.738⁎⁎ | 3.247⁎ | 3.467⁎⁎ | 3.241⁎⁎ |
In parenthesis, the table records median approximate coefficients and t-statistics from Eq. (8). The Schwarz knowledge criteria are abbreviated as B.I.C. The Ljung-Box test for serial correlation up to lag eight is known as Q(8). The F-statistic known as the linearity test compares the null hypothesis of linearity to a non-linear model’s alternative. The Escribano-Jorda test determines if an exponential transformation function in a non-linear specification is sufficient. The symbols ***, **, and * represent statistical significance at the 1%, 5%, and 10% rate, respectively