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on Econometric Time Series |
| By: | Allin Cottrell (Wake Forest University); Riccardo (Jack) Lucchetti (Universita' Politecnica delle Marche, Dipartimento di Scienze Economiche Sociali); Matteo Pelagatti (Universita' di Milano - Bicocca) |
| Abstract: | We clarify a point regarding the appropriate measure(s) of the variance of smoothed disturbances in the context of linear state-space models. This involves explaining how two different concepts, which are sometimes given the same name in the literature, relate to each other. We also describe the behavior of several common software packages is in this regard. |
| Keywords: | State-space models, Disturbance smoother, Auxiliary residuals. |
| JEL: | C32 C63 |
| Date: | 2016–07–29 |
| URL: | http://d.repec.org/n?u=&r=ets |
| By: | Robert F. Engle; Olivier Ledoit; Michael Wolf |
| Abstract: | Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroskedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present paper aims to marry these two strands of literature in order to deliver improved estimation of large dynamic covariance matrices. |
| Keywords: | Composite likelihood, dynamic conditional correlations, GARCH, Markowitz portfolio selection, nonlinear shrinkage. |
| JEL: | C13 C58 G11 |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=&r=ets |
| By: | Sergey Ivashchenko (Saint Petersburg Institute for Economics and Mathematics (Russian Academy of Sciences), National Research University Higher School of Economics,Russia); Rangan Gupta (Department of Economics, University of Pretoria, Pretoria) |
| Abstract: | A medium-scale nonlinear dynamic stochastic general equilibrium (DSGE) model was estimated (54 variables, 29 state variables, 7 observed variables). The model includes an observed variable for stock market returns. The root-mean square error (RMSE) of the in-sample and out-of-sample forecasts was calculated. The nonlinear DSGE model with measurement errors outperforms AR (1), VAR (1) and the linearised DSGE in terms of the quality of the out-of-sample forecasts. The nonlinear DSGE model without measurement errors is of a quality equal to that of the linearised DSGE model |
| Keywords: | nonlinear DSGE; Quadratic Kalman Filter; out-of-sample |
| JEL: | E32 E37 E44 E47 |
| Date: | 2016–08 |
| URL: | http://d.repec.org/n?u=&r=ets |
| By: | Jungjun Choi (School of Economics, Sogang University, Seoul); In Choi (School of Economics, Sogang University, Seoul) |
| Abstract: | This paper studies maximum likelihood estimation of autoregressive models of order 1 with a near unit root and Cauchy errors. Autoregressive models with an intercept and with an intercept and a linear time trend are also considered. The maximum likelihood estimator (MLE) for the autoregressive coeffcient is n^(3/2)-consistent with n denoting the sample size and has a mixture-normal dis- tribution in the limit. The MLE for the scale parameter of Cauchy distribution is n^(1/2)-consistent and its limiting distribution is normal. The MLEs of the intercept and the linear time trend are n^(1/2)- and n^(3/2)-consistent, respectively. It is also shown that the t-statistic for a unit root based on the MLE has a standard normal distribution in the limit. In addition, finite sample properties of the MLE are compared with those of the least square estimator (LSE). It is found that the MLE is more effcient than the LSE when the errors have a Cauchy distribution or a distribution which is a mixture of Cauchy and normal distributions. It is also shown that empirical power of the MLE-based t-test for a unit root is much higher than that of the Dickey-Fuller t-test. |
| Keywords: | autoregressive model, near unit root, Cauchy distribution, maxi- mum likelihood estimator, infi?nite variance |
| Date: | 2016–07 |
| URL: | http://d.repec.org/n?u=&r=ets |