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on Econometric Time Series |
| By: | Boris David; Gilles Zumbach |
| Abstract: | Risk evaluation is a forecast, and its validity must be backtested. Probability distribution forecasts are used in this work and allow for more powerful validations compared to point forecasts. Our aim is to use bivariate copulas in order to characterize the in-sample copulas and to validate out-of-sample a bivariate forecast. For both set-ups, probability integral transforms (PIT) and Rosenblatt transforms are used to map the problem into an independent copula. For this simple copula, statistical tests can be applied to validate the choice of the in-sample copula or the validity of the bivariate forecast. The salient results are that a Student copula describes well the dependencies between financial time series (regardless of the correlation), and that the bivariate forecasts provided by a risk methodology based on historical innovations performs correctly out-of-sample. A prerequisite is to remove the heteroskedasticity in order to have stationary time series, in this work a long-memory ARCH volatility model is used. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.03896&r= |
| By: | Jushan Bai; Jiangtao Duan; Xu Han |
| Abstract: | A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but a change in the variance of its factors. This effectively transforms a structural change problem of high dimension into a problem of low dimension. This paper considers the likelihood ratio (LR) test for a variance change in the estimated factors. The LR test implicitly explores a special feature of the estimated factors: the pre-break and post-break variances can be a singular matrix under the alternative hypothesis, making the LR test diverging faster and thus more powerful than Wald-type tests. The better power property of the LR test is also confirmed by simulations. We also consider mean changes and multiple breaks. We apply the procedure to the factor modelling and structural change of the US employment using monthly industry-level-data. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.08052&r= |
| By: | Gregor Boehl, Felix Strobel |
| Abstract: | We propose a set of tools for the efficient and robust Bayesian estimation of medium- and large-scale DSGE models while accounting for the effective lower bound on nominal interest rates. We combine a novel nonlinear recursive filter with a computationally efficient piece-wise linear solution method and a state-of-the-art MCMC sampler. The filter allows for fast likelihood approximations, in particular of models with large state spaces. Using artificial data, we demonstrate that our methods accurately capture the true model parameters even with very long lower bound episodes. We apply our approach to analyze post-2008 US business cycle properties. |
| Keywords: | Effective Lower Bound, Bayesian Estimation, Great Recession, Business Cycles |
| JEL: | C11 C63 E31 E32 E44 |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2022_356&r= |
| By: | Gregor Boehl |
| Abstract: | This paper develops an adaptive differential evolution Markov chain Monte Carlo (ADEMC) sampler. The sampler satisfies five requirements that make it suitable especially for the estimation of models with high-dimensional posterior distributions and which are computationally expensive to evaluate: (i) A large number of chains (the "ensemble") where the number of chains scales inversely (nearly one-to-one) with the number of necessary ensemble iterations until convergence, (ii) fast burn-in and convergence (thereby superseding the need for numerical optimization), (iii) good performance for bimodal distributions, (iv) an endogenous proposal density generated from the state of the full ensemble, which (v) respects the bounds of prior distribution. Consequently, ADEMC is straightforward to parallelize. I use the sampler to estimate a heterogeneous agent New Keynesian (HANK) model including the micro parameters linked to the stationary distribution of the model. |
| Keywords: | Bayesian Estimation, Monte Carlo Methods, DSGE Models, Heterogeneous Agents |
| JEL: | C11 C13 C15 E10 |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2022_355&r= |