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on Econometric Time Series |
| By: | Luca Vincenzo Ballestra; Enzo D'Innocenzo; Christian Tezza |
| Abstract: | We introduce a novel GARCH model that integrates two sources of uncertainty to better capture the rich, multi-component dynamics often observed in the volatility of financial assets. This model provides a quasi closed-form representation of the characteristic function for future log-returns, from which semi-analytical formulas for option pricing can be derived. A theoretical analysis is conducted to establish sufficient conditions for strict stationarity and geometric ergodicity, while also obtaining the continuous-time diffusion limit of the model. Empirical evaluations, conducted both in-sample and out-of-sample using S\&P500 time series data, show that our model outperforms widely used single-factor models in predicting returns and option prices. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.14585 |
| By: | Christopher D. Walker |
| Abstract: | Conditional moment equality models are regularly encountered in empirical economics, yet they are difficult to estimate. These models map a conditional distribution of data to a structural parameter via the restriction that a conditional mean equals zero. Using this observation, I introduce a Bayesian inference framework in which an unknown conditional distribution is replaced with a nonparametric posterior, and structural parameter inference is then performed using an implied posterior. The method has the same flexibility as frequentist semiparametric estimators and does not require converting conditional moments to unconditional moments. Importantly, I prove a semiparametric Bernstein-von Mises theorem, providing conditions under which, in large samples, the posterior for the structural parameter is approximately normal, centered at an efficient estimator, and has variance equal to the Chamberlain (1987) semiparametric efficiency bound. As byproducts, I show that Bayesian uncertainty quantification methods are asymptotically optimal frequentist confidence sets and derive low-level sufficient conditions for Gaussian process priors. The latter sheds light on a key prior stability condition and relates to the numerical aspects of the paper in which these priors are used to predict the welfare effects of price changes. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.16017 |
| By: | Sylvia Kaufmann (Study Center Gerzensee); Markus Pape (Ruhr-University Bochum) |
| Abstract: | We use the geometric representation of factor models to represent the factor loading structure by sets corresponding to unit-specific non-zero loadings. We formulate global and local identification conditions based on set conditions. We propose two algorithms to efficiently evaluate Sato (1992)’s counting rule. We demonstrate the efficiency and the performance of the algorithms with a simulation study. An application to exchange rate returns illustrates the approach. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:szg:worpap:2406 |
| By: | Yong Li (Renmin University of China); Zhou Wu (Zhejiang University); Jun Yu (University of Macau); Tao Zeng (Zhejiang University) |
| Abstract: | This note gives a rigorous justification to Akaike information criterion (AIC) and Takeuchi information criterion (TIC). The existing literature has shown that, when the candidate model is a good approximation of the true data generating process (DGP), AIC is an asymptotic unbiased estimator of the expected Kullback-Leibler divergence between the DGP and the plug-in predictive distribution. When the candidate model is misspecified, TIC can be regraded as a robust version of AIC with its justification following a similar line of argument. However, the justifications in current literature are predominantly confined to the iid scenario. In this note, we establish the asymptotic unbiasedness of AIC and TIC under certain regular conditions. These conditions are applicable in various scenarios, encompassing weakly dependent data. |
| JEL: | C11 C52 C25 C22 C32 |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:boa:wpaper:202420 |