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on Econometric Time Series |
| By: | Helmut Lütkepohl; Mika Meitz; Aleksei NetŠunajev; Pentti Saikkonen |
| Abstract: | Tests for identification through heteroskedasticity in structural vector autoregressive analysis are developed for models with two volatility states where the time point of volatility change is known. The tests are Wald type tests for which only the unrestricted model including the covariance matrices of the two volatility states have to be estimated. The residuals of the model are assumed to be from the class of elliptical distributions which includes Gaussian models. The asymptotic null distributions of the test statistics are derived and simulations are used to explore their small sample properties. Two empirical examples illustrate the usefulness of the tests. |
| Keywords: | Heteroskedasticity, structural identi cation, vector autoregressive process |
| JEL: | C32 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1764&r=ets |
| By: | Lütkepohl, Helmut (DIW Berlin and Freie Universität Berlin); Staszewska-Bystrova, Anna (Faculty of Economics and Sociology, University of Lodz); Winker, Peter (University of Giessen) |
| Abstract: | Methods for constructing joint confidence bands for impulse response functions which are commonly used in vector autoregressive analysis are reviewed. While considering separate intervals for each horizon individually still seems to be the most common approach, a substantial number of methods have been proposed for making joint inferences about the complete impulse response paths up to a given horizon. A structured presentation of these methods is provided. Furthermore, existing evidence on the small-sample performance of the methods is gathered. The collected information can help practitioners to decide on a suitable confidence band for a structural VAR analysis. |
| Keywords: | Impulse responses, vector autoregressive model, joint confidence bands |
| JEL: | C32 |
| Date: | 2018–09–30 |
| URL: | http://d.repec.org/n?u=RePEc:ann:wpaper:4/2018&r=ets |
| By: | Audrone Virbickaite (Universitat de les Illes Balears); Hedibert F. Lopes (Insper Institute of Education and Research) |
| Abstract: | This paper proposes a novel Bayesian semi-parametric Stochastic Volatility model with Markov switching regimes for modeling the dynamics of the financial returns. The distribution of the error term of the returns is modeled as an infinite mixture of Normals, meanwhile the intercept of the volatility equation is allowed to switch between two regimes. The proposed model is estimated using a novel sequential Monte Carlo method called Particle Learning that is especially well suited for state-space models. The model is tested on simulated data and, using real financial times series, compared to a model without the Markov switching regimes. The results show that including a Markov switching specification provides higher predictive power for the entire distribution, as well as in the tails of the distribution. Finally, the estimate of the persistence parameter decreases significantly, a finding consistent with previous empirical studies. |
| Keywords: | Bayes Factor; Dirichlet Process Mixture; Particle Learning; Sequential Monte Carlo. |
| JEL: | C58 C11 C14 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:ubi:deawps:89&r=ets |
| By: | Bingduo Yang (School of Finance, Jiangxi University of Finance and Economics, Nanchang, China); Xiaohui Liu (School of Finance, Jiangxi University of Finance and Economics, Nanchang, China); Liang Peng (Department of Risk Management and Insurance, Georgia State University); Zongwu Cai (Department of Economics, University of Kansas) |
| Abstract: | Testing for predictability of asset returns has been a long history in economics and finance. Recently, based on a simple predictive regression, Kostakis, Magdalinos and Stamatogiannis (2015, Review of Financial Studies) derived a Wald type test based on the context of the extended instrumental variable (IVX) methodology for testing predictability of stock returns and Demetrescu (2014) showed that the local power of the standard IVX-based test could be improved in some cases when a lagged predicted variable is added to the predictive regression on purpose, which poses a general important question on whether a lagged predicted variable should be included in the model or not. This paper proposes novel robust procedures for testing both the existence of a lagged predicted variable and the predictability of asset returns in a predictive regression regardless of regressors being stationary or nearly integrated or unit root and the AR model for regressors with or without intercept. A simulation study confirms the good finite sample performance of the proposed tests before applying the proposed tests to some real datasets in finance to illustrate their practical usefulness. |
| Keywords: | Autoregressive Errors; Empirical Likelihood; Predictive Regression; Weighted Score. |
| JEL: | C12 C22 |
| Date: | 2018–09 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:201808&r=ets |
| By: | Manabu Asai (Faculty of Economics, Soka University, Japan.); Chia-Lin Chang (Department of Applied Economics & Department of Finance National Chung Hsing University, Taiwan.); Michael McAleer (Department of Quantitative Finance National Tsing Hua University, Taiwan and Econometric Institute Erasmus School of Economics Erasmus University Rotterdam, The Netherlands and Department of Quantitative Economics Complutense University of Madrid, Spain And Institute of Advanced Sciences Yokohama National University, Japan.); Laurent Pauwels (Discipline of Business Analytics, University of Sydney Business School, Australia.) |
| Abstract: | In this paper, we derive the statistical properties of a two step approach to estimating multivariate GARCH rotated BEKK (RBEKK) models. By the definition of rotated BEKK, we estimate the unconditional covariance matrix in the first step in order to rotate observed variables to have the identity matrix for its sample covariance matrix. In the second step, we estimate the remaining parameters via maximizing the quasi-likelihood function. For this two step quasi-maximum likelihood (2sQML) estimator, we show consistency and asymptotic normality under weak conditions. While second-order moments are needed for consistency of the estimated unconditional covariance matrix, the existence of finite sixthorder moments are required for convergence of the second-order derivatives of the quasilog-likelihood function. We also show the relationship of the asymptotic distributions of the 2sQML estimator for the RBEKK model and the variance targeting (VT) QML estimator for the VT-BEKK model. Monte Carlo experiments show that the bias of the 2sQML estimator is negligible, and that the appropriateness of the diagonal specification depends on the closeness to either of the Diagonal BEKK and the Diagonal RBEKK models. |
| Keywords: | BEKK, Rotated BEKK, Diagonal BEKK, Variance targeting, Multivariate GARCH, Consistency, Asymptotic normality. |
| JEL: | C13 C32 |
| Date: | 2018–10 |
| URL: | http://d.repec.org/n?u=RePEc:ucm:doicae:1827&r=ets |
| By: | M. Bohdalov\'a; M. Kalina; O. N\'an\'asiov\'a |
| Abstract: | The intention of this paper is to discuss the mathematical model of causality introduced by C.W.J. Granger in 1969. The Granger's model of causality has become well-known and often used in various econometric models describing causal systems, e.g., between commodity prices and exchange rates. Our paper presents a new mathematical model of causality between two measured objects. We have slightly modified the well-known Kolmogorovian probability model. In particular, we use the horizontal sum of set $\sigma$-algebras instead of their direct product. |
| Date: | 2018–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1810.01654&r=ets |
| By: | Ashley, Richard (Virginia Tech); Tsang, Kwok Ping (Virginia Tech); Verbrugge, Randal (Federal Reserve Bank of Cleveland) |
| Abstract: | The historical analysis of FOMC behavior using estimated simple policy rules requires the specification of either an estimated natural rate of unemployment or an output gap. But in the 1970s, neither output gap nor natural rate estimates appear to guide FOMC deliberations. This paper uses the data to identify the particular implicit unemployment rate gap (if any) that is consistent with FOMC behavior. While its ability appears to have improved over time, our results indicate that, both before the Volcker period and through the Bernanke period, the FOMC distinguished persistent movements in the unemployment rate from other movements; implicitly such movements were treated as an intermediate target, one that departs substantially from conventional estimates of the natural rate. We further investigate historical FOMC responses to inflation fluctuations. In this regard, FOMC behavior changed in the Volcker-Greenspan-Bernanke period: its response to the inflation rate became much stronger, and it focused more intensely on very persistent movements in this variable. Our results shed light on the “Great Inflation” experience of the 1970s, and are consistent with the view that political pressures effectively limited the FOMC response to the buildup of inflation. They also suggest new directions for DSGE modeling. |
| Keywords: | Taylor rule; Great Inflation; intermediate target; natural rate; persistence; dependence; |
| JEL: | C22 C32 E52 |
| Date: | 2018–10–12 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwp:1814&r=ets |