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on Econometric Time Series |
| By: | Alain Hecq; Jan P. A. M. Jacobs; Michalis P. Stamatogiannis |
| Abstract: | Before being considered definitive, data currently produced by statistical agencies undergo a recurrent revision process resulting in different releases of the same phenomenon. The collection of all these vintages is referred to as a real-time data set. Economists and econometricians have realized the importance of this type of information for economic modeling and forecasting. This paper focuses on testing non-stationary data for forecastability, i.e., whether revisions reduce noise or are news. To deal with historical revisions which affect the whole vintage of time series due to redefinitions, methodological innovations etc., we employ the recently developed impulse indicator saturation approach, which involves potentially adding an indicator dummy for each observation to the model. We illustrate our procedures with the U.S. Real Gross National Product series from ALFRED and find that revisions to this series neither reduce noise nor can be considered as news. |
| Keywords: | Data revision, Non-Stationary Data, News-Noise Tests, Structural Breaks, |
| JEL: | C32 C82 E01 |
| Date: | 2016–01–18 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2016s-01&r=ets |
| By: | Zadrozny, Peter A. |
| Abstract: | Chen and Zadrozny (1998) developed the linear extended Yule-Walker (XYW) method for determining the parameters of a vector autoregressive (VAR) model with available covariances of mixed-frequency observations on the variables of the model. If the parameters are determined uniquely for available population covariances, then, the VAR model is identified. The present paper extends the original XYW method to an extended XYW method for determining all ARMA parameters of a vector autoregressive moving-average (VARMA) model with available covariances of single- or mixed-frequency observations on the variables of the model. The paper proves that under conditions of stationarity, regularity, miniphaseness, controllability, observability, and diagonalizability on the parameters of the model, the parameters are determined uniquely with available population covariances of single- or mixed-frequency observations on the variables of the model, so that the VARMA model is identified with the single- or mixed-frequency covariances. |
| Keywords: | block-Vandermonde eigenvectors of block-companion state-transition,matrix of state-space representation,matrix spectral factorization |
| JEL: | C32 C80 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cfswop:526&r=ets |
| By: | Haas, Markus; Liu, Ji-Chun |
| Abstract: | We consider a multivariate Markov-switching GARCH model which allows for regime-specific volatility dynamics, leverage effects, and correlation structures. Stationarity conditions are derived, and consistency of the maximum likelihood estimator (MLE) is established under the assumption of Gaussian innovations. A Lagrange Multiplier (LM) test for correct specification of the correlation dynamics is devised, and a simple recursion for computing multi-step-ahead conditional covariance matrices is provided. The theory is illustrated with an application to global stock market and real estate equity returns. The empirical analysis highlights the importance of the conditional distribution in Markov-switching time series models. Specifications with Student's t innovations dominate their Gaussian counterparts both in- and out-of-sample. The dominating specification appears to be a two-regime Student's t process with correlations which are higher in the turbulent (high-volatility) regime. |
| JEL: | C32 C51 C58 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc15:112855&r=ets |
| By: | Kruse, Yves Robinson; Kaufmann, Hendrik |
| Abstract: | This paper provides a comprehensive Monte Carlo comparison of different finite-sample biascorrection methods for autoregressive processes. We consider situations where the process is either mildly explosive or has a unit root. The case of highly persistent stationary is also studied. We compare the empirical performance of the plain OLS estimator with an OLS and a Cauchy estimator based on recursive demeaning, as well as an estimator based on second differencing. In addition, we consider three different approaches for bias-correction for the OLS estimator: (i) bootstrap, (ii) jackknife and (iii) indirect inference. The estimators are evaluated in terms of bias and root mean squared errors (RMSE) in a variety of practically relevant settings. Our findings suggest that the indirect inference method clearly performs best in terms of RMSE for all considered orders of integration. If bias-correction abilities are solely considered, the jackknife works best for stationary and unit root processes. For the explosive case, the bootstrap and the indirect inference can be recommended. As an empirical application, we study Asian stock market overvaluation during bubbles and emphasize the importance of bias-correction for explosive series. |
| JEL: | C13 C22 G12 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc15:112897&r=ets |
| By: | Hanck, Christoph; Demetrescu, Matei; Kruse, Robinson |
| Abstract: | The fixed-b asymptotic framework provides refinements in the use of heteroskedasticity and autocorrelation consistent variance estimators. We show however that the fixed-b limiting distributions of t-statistics are not pivotal when the variance of the underlying data generating process changes over time. To regain pivotal fixed-b inference under such time heteroskedasticity, we discuss three alternative approaches. We employ (1) the wild bootstrap (Cavaliere and Taylor, 2008, ET), (2) resort to time transformations (Cavaliere and Taylor, 2008, JTSA) and (3) suggest to pick suitable the asymptotics according to the outcome of a heteroskedasticity test, since small-b asymptotics deliver standard limiting distributions irrespective of the so-called variance profile of the series. We quantify the degree of size distortions from using the standard fixed-b approach and compare the effectiveness of the corrections via simulations. We also provide an empirical application to excess returns. |
| JEL: | C12 C32 C15 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc15:112916&r=ets |
| By: | Conrad, Christian; Schienle, Melanie |
| Abstract: | We develop a misspecification test for the multiplicative two-component GARCH-MIDAS model suggested in Engle et al. (2013). In the GARCH-MIDAS model a short-term unit variance GARCH component fluctuates around a smoothly timevarying long-term component which is driven by the dynamics of a macroeconomic explanatory variable. We suggest a Lagrange Multiplier statistic for testing the null hypothesis that the macroeconomic variable has no explanatory power. Hence, under the null hypothesis the long-term component is constant and the GARCHMIDAS reduces to the simple GARCH model. We provide asymptotic theory for our test statistic and investigate its finite sample properties by Monte Carlo simulation. Our test statistic can be considered as an extension of the Lundbergh and Ter svirta (2002) ARCH nested in GARCH test for evaluating GARCH models. We illustrate the usefulness of our procedure by an empirical application to S&P 500 return data. |
| JEL: | C58 C52 G17 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc15:112919&r=ets |
| By: | Krüger, Fabian; Clark, Todd E.; Ravazzolo, Francesco |
| Abstract: | This paper shows entropic tilting to be a flexible and powerful tool for combining medium-term forecasts from BVARs with short-term forecasts from other sources (nowcasts from either surveys or other models). Tilting systematically improves the accuracy of both point and density forecasts, and tilting the BVAR forecasts based on nowcast means and variances yields slightly greater gains in density accuracy than does just tilting based on the nowcast means. Hence entropic tilting can offer -- more so for persistent variables than not-persistent variables -- some benefits for accurately estimating the uncertainty of multi-step forecasts that incorporate nowcast information. |
| JEL: | E17 C11 C53 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc15:113077&r=ets |
| By: | Herwartz, Helmut |
| Abstract: | GARCH specifications have been widely applied in financial literature and practice. For purposes of (Quasi) ML (QML) estimation innovations to GARCH processes are assumed identically and independently distributed (iid) with mean zero and unit variance. In this note GARCH innovations entering daily S\&P 500 quotes are diagnosed to lack independence and to signal ex-ante the directions of stock price changes. |
| JEL: | C22 G14 C01 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc15:113109&r=ets |
| By: | Schreiber, Sven; Breitung, Jörg |
| Abstract: | We extend the frequency-specific Granger-causality test of Breitung and Candelon (2006) to a more general null hypothesis that allows non-causality at unknown frequencies within an interval, instead of having to prespecify a single frequency. This setup corresponds better to most hypotheses that are typically analyzed in applied research and is easy to implement. We also discuss a test approach that departs from strict non-causality, given the impossibility of (non-trivial) non-causality over a continuum of frequencies. In an empirical application dealing with the dynamics of US temperatures and CO2 emissions we find that emissions cause temperature changes only at very low frequencies with more than 30 years of oscillation. |
| JEL: | C32 Q54 C53 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc15:113111&r=ets |
| By: | Marczak, Martyna; Proietti, Tommaso |
| Abstract: | Structural change affects the estimation of economic signals, like the underlying growth rate or the seasonally adjusted series. An important issue, which has attracted a great deal of attention also in the seasonal adjustment literature, is its detection by an expert procedure. The general to specific approach to the detection of structural change, currently implemented in Autometrics via indicator saturation, has proven to be both practical and effective in the context of stationary dynamic regression models and unit-root autoregressions. By focusing on impulse- and step-indicator saturation, we investigate via Monte Carlo simulations how this approach performs for detecting additive outliers and level shifts in the analysis of nonstationary seasonal time series. The reference model is the basic structural model, featuring a local linear trend, possibly integrated of order two, stochastic seasonality and a stationary component. Further, we apply both kinds of indicator saturation to detect additive outliers and level shifts in the industrial production series in five European countries. |
| JEL: | C22 C51 C53 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc15:113137&r=ets |
| By: | Mutschler, Willi |
| Abstract: | This note shows how to derive unconditional moments, cumulants and polyspectra of order higher than two for the pruned state-space of nonlinear DSGE models. Useful Matrix tools and computational aspects are also discussed. |
| JEL: | C10 C51 E10 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc15:113138&r=ets |
| By: | Demetrescu, Matei; Kruse, Robinson |
| Abstract: | Normality testing is an evergreen topic in statistics and econometrics and other disciplines. The paper focuses on testing economic time series for normality in a robust way, taking specific data features such as serial dependence and time-varying volatility into account. Here, we suggest tests based on raw moments of probability integral transform of standardized time series. The use of raw moments is advantageous as they are quite sensitive to deviations from the null other than asymmetry and excess kurtosis. To standardize the series, nonparametric estimators of the (time-varying) variance may be used, but the mean as a function of time has to be estimated parametrically. Short-run dynamics is taken into account using the Heteroskedasticity and Autocorrelation Robust [HAR] approach of Kiefer and Vogelsang (2005, ET). The effect of estimation uncertainty arising from estimated standardization is accounted for by providing a necessary modification. In a simulation study, we compare the suggested tests to a benchmark test by Bai and Ng (2005, JBES). The results show that the new tests are performing well in terms of size (which is mainly due to the adopted fixed-b framework for long-run covariance estimation), but also in terms of power. An empirical application to G7 industrial production growth rates sheds further light on the empirical usefulness and limitations of the proposed test. |
| JEL: | C22 C46 C52 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc15:113221&r=ets |