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on Econometric Time Series |
| By: | Chao Wang (Discipline of Business Analytics, The University of Sydney); Qian Chen (HSBC Business School, Peking University); Richard Gerlach (Discipline of Business Analytics, The University of Sydney) |
| Abstract: | The realized GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized variance or daily returns, is employed in the realized GARCH framework. Further, sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with inherent micro-structure noise and inefficiency. An adaptive Bayesian Markov Chain Monte Carlo method is developed and employed for estimation and forecasting, whose properties are assessed and compared with maximum likelihood, via a simulation study. Compared to a range of well-known parametric GARCH, GARCH with two-sided Weibull distribution and realized GARCH models, tail risk forecasting results across 7 market index return series and 2 individual assets clearly favor the realized GARCH models incorporating two-sided Weibull distribution, especially models employing the sub-sampled realized variance and sub-sampled realized range, over a six year period that includes the global financial crisis. |
| Date: | 2017–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1707.03715&r=ets |
| By: | Sun, Yixiao; Hwang., Jungbin |
| Abstract: | This paper proposes new, simple, and more accurate statistical tests in a cointegrated system that allows for endogenous regressors and serially dependent errors. The approach involves first transforming the time series using orthonormal basis functions in L²[0,1], which has energy concentrated at low frequencies, and then running an augmented regression based on the transformed data and constructing the test statistics in the usual way. The approach is essentially the same as the trend instrumental variable approach of Phillips (2014), but we hold the number of orthonormal basis functions fixed in order to develop the standard F and t asymptotic theory. The tests are extremely simple to implement, as they can be carried out in exactly the same way as if the transformed regression is a classical linear normal regression. In particular, critical values are from the standard F or t distribution. The proposed F and t tests are robust in that they are asymptotically valid regardless of whether the number of basis functions is held fixed or allowed to grow with the sample size. The F and t tests have more accurate size in finite samples than existing tests such as the asymptotic chi-squared and normal tests based on the fully modified OLS estimator of Phillips and Hansen (1990) and can be made as powerful as the latter test. |
| Keywords: | Social and Behavioral Sciences, Cointegration, F test, Alternative Asymptotics, Nonparametric Series Method, t test, Transformed and Augmented OLS |
| Date: | 2017–07–10 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:qt83b4q8pk&r=ets |
| By: | Fabian Goessling; Martina Danielova Zaharieva |
| Abstract: | We propose a new and highly exible Bayesian sampling algorithm for non-linear state space models under non-parametric distributions. The estimation framework combines a particle filtering and smoothing algorithm for the latent process with a Dirichlet process mixture model for the error term of the observable variables. In particular, we overcome the problem of constraining the models by transformations or the need for conjugate distributions. We use the Chinese restaurant representation of the Dirichlet process mixture, which allows for a parsimonious and generally applicable sampling algorithm. Thus, our estimation algorithm combines a pseudo marginal Metropolis Hastings scheme with a marginalized hierarchical semi-parametric model. We test our approach for several nested model specifications using simulated data and provide density forecasts. Furthermore, we carry out a real data example using S&P 500 returns. |
| Keywords: | Bayesian Nonparametrics, Particle Filtering, Stochastic Volatility, MCMC, Forecasting |
| Date: | 2017–07 |
| URL: | http://d.repec.org/n?u=RePEc:cqe:wpaper:6417&r=ets |
| By: | Hiroyuki Kasahara (Vancouver School of Economics, University of British Columbia); Katsumi Shimotsu (Faculty of Economics, The University of Tokyo) |
| Abstract: | Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically popular Markov regime switching models. In particular, the asymptotic distribution of the MLE has been unknown for models in which the regime-specific density depends on both the current and the lagged regimes, which include the seminal model of Hamilton (1989) and the switching ARCH model of Hamilton and Susmel (1994). This paper shows the asymptotic normality of the MLE and the consistency of the asymptotic covariance matrix estimate of these models. |
| Date: | 2017–05 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2017cf1049&r=ets |