A standard approach for analyses of survival data is the Cox proportional hazards model. It assumes that covariate effects are constant over time, i.e. that the hazards are proportional. With longer follow-up times, t...A standard approach for analyses of survival data is the Cox proportional hazards model. It assumes that covariate effects are constant over time, i.e. that the hazards are proportional. With longer follow-up times, though, the effect of a variable often gets weaker and the proportional hazards (PH) assumption is violated. In the last years, several approaches have been proposed to detect and model such time-varying effects. However, comparison and evaluation of the various approaches is difficult. A suitable measure is needed that quantifies the difference between time-varying effects and enables judgement about which method is best, i.e. which estimate is closest to the true effect. In this paper we adapt a measure proposed for the area between smoothed curves of exposure to time-varying effects. This measure is based on the weighted area between curves of time-varying effects relative to the area under a reference function that represents the true effect. We introduce several weighting schemes and demonstrate the application and performance of this new measure in a real-life data set and a simulation study.展开更多
The most appropriate heteroskedastic models for predicting volatility of daily stocks prices of 10 major Nigerian banks are proposed. The banks are Access, United Bank for Africa (UBA), Guaranty Trust, Skye, Diamond, ...The most appropriate heteroskedastic models for predicting volatility of daily stocks prices of 10 major Nigerian banks are proposed. The banks are Access, United Bank for Africa (UBA), Guaranty Trust, Skye, Diamond, Fidelity, Sterling,?Union, ETI and Zenith banks;and these are examined from 2004 to 2014.?The models employed are Autoregressive Conditional Heteroscedastic (ARCH(1)), Generalized Autoregressive Conditional Heteroscedastic (GARCH(1, 1)),?Exponential Generalized Autoregressive Conditional Heteroscedastic?(EGARCH(1, 1))?and Glosten, Jagananthan and Runkle-Generalized Autoregressive Conditional Heteroscedastic?(GJR-GARCH(1, 1)). The results show that all the?bank returns are highly leptokurtic, significantly skewed and thus non-normal across the four periods except for Fidelity bank during financial crises;findings similar to those of other global markets. Also noticed is the strong evidence for the presence of heteroscedasticity, and that volatility persistence during crisis?is?higher than before the crisis across the 10 banks, with that of UBA taking the lead, about 11 times higher during the crisis. The same with persistence?levels in volatility, which were relatively higher during financial crises across the ten banks compared to before the crises.?Findings further indicate that Asymmetric GARCH models outperformed the symmetric GARCH models, especially during the financial crises and post the crises. Thus with these findings, one could generally conclude that Nigerian banks’?returns are volatility persistent during and after the crises, and are characterized by leverage effects of negative and positive shocks during these periods.展开更多
文摘A standard approach for analyses of survival data is the Cox proportional hazards model. It assumes that covariate effects are constant over time, i.e. that the hazards are proportional. With longer follow-up times, though, the effect of a variable often gets weaker and the proportional hazards (PH) assumption is violated. In the last years, several approaches have been proposed to detect and model such time-varying effects. However, comparison and evaluation of the various approaches is difficult. A suitable measure is needed that quantifies the difference between time-varying effects and enables judgement about which method is best, i.e. which estimate is closest to the true effect. In this paper we adapt a measure proposed for the area between smoothed curves of exposure to time-varying effects. This measure is based on the weighted area between curves of time-varying effects relative to the area under a reference function that represents the true effect. We introduce several weighting schemes and demonstrate the application and performance of this new measure in a real-life data set and a simulation study.
文摘The most appropriate heteroskedastic models for predicting volatility of daily stocks prices of 10 major Nigerian banks are proposed. The banks are Access, United Bank for Africa (UBA), Guaranty Trust, Skye, Diamond, Fidelity, Sterling,?Union, ETI and Zenith banks;and these are examined from 2004 to 2014.?The models employed are Autoregressive Conditional Heteroscedastic (ARCH(1)), Generalized Autoregressive Conditional Heteroscedastic (GARCH(1, 1)),?Exponential Generalized Autoregressive Conditional Heteroscedastic?(EGARCH(1, 1))?and Glosten, Jagananthan and Runkle-Generalized Autoregressive Conditional Heteroscedastic?(GJR-GARCH(1, 1)). The results show that all the?bank returns are highly leptokurtic, significantly skewed and thus non-normal across the four periods except for Fidelity bank during financial crises;findings similar to those of other global markets. Also noticed is the strong evidence for the presence of heteroscedasticity, and that volatility persistence during crisis?is?higher than before the crisis across the 10 banks, with that of UBA taking the lead, about 11 times higher during the crisis. The same with persistence?levels in volatility, which were relatively higher during financial crises across the ten banks compared to before the crises.?Findings further indicate that Asymmetric GARCH models outperformed the symmetric GARCH models, especially during the financial crises and post the crises. Thus with these findings, one could generally conclude that Nigerian banks’?returns are volatility persistent during and after the crises, and are characterized by leverage effects of negative and positive shocks during these periods.
