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on Econometric Time Series |
| By: | Min Seong Kim (Department of Economics, Ryerson University, Toronto, Canada); Yixiao Sun (Department of Economics, UC San Diego); Jingjing Yang (University of Nevada, Reno, NV) |
| Abstract: | This paper develops robust testing procedures for nonparametric kernel methods in the presence of temporal dependence of unknown forms. Based on the ?fixed-bandwidth asymptotic variance and the pre-asymptotic variance, we propose a heteroskedasticity and autocorrelation robust (HAR) variance estimator that achieves double robustness ? it is asymptotically valid regardless of whether the temporal dependence is present or not, and whether the kernel smoothing bandwidth is held constant or allowed to decay with the sample size. Using the HAR variance estimator, we construct the studentized test statistic and examine its asymptotic properties under both the fi?xed-smoothing and increasing-smoothing asymptotics. The ?fixed-smoothing approximation and the associated convenient t-approximation achieve extra robustness ? it is asymptotically valid regardless of whether the truncation lag parameter governing the covariance weighting grows at the same rate as or a slower rate than the sample size. Finally, we suggest a simulation-based calibration approach to choose smoothing parameters that optimize testing oriented criteria. Simulation shows that the proposed procedures work very well in ?finite samples. |
| Keywords: | heteroskedasticity and autocorrelation robust variance, calibration, fi?xed-smoothing asymptotics, ?fixed-bandwidth asymptotics, kernel density estimator, local polynomial estimator, t-approximation, testing-optimal smoothing-parameters choice, temporal dependence |
| JEL: | C12 C14 C22 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:rye:wpaper:wp049&r=all |
| By: | Yingyao Hu (Johns Hopkins); Matthew Shum (Caltech); Matthew Shum (Compass-Lexecon); Ruli Xiao (Indiana University) |
| Abstract: | We present a method for estimating Markov dynamic models with unobserved state variables which can be serially correlated over time. We focus on the case where all the model variables have discrete support. Our estimator is simple to compute because it is noniterative, and involves only elementary matrix manipulations. Our estimation method is nonparametric, in that no parametric assumptions on the distributions of the unobserved state variables or the laws of motions of the state variables are required. Monte Carlo simulations show that the estimator performs well in practice, and we illustrate its use with a dataset of doctors' prescription of pharmaceutical drugs |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:inu:caeprp:2015017&r=all |
| By: | Ricardo Quineche (Banco Central de la Reserva del Perú); Gabriel Rodríguez (Departamento de Economía de la PUC del Perú) |
| Abstract: | We analyze the choice of the truncation lag for unit root tests as the ADF(GLS) and the M(GLS) tests proposed by Elliott et al. (1996) and Ng and Perron (2001) and extended to the context of structural change by Perron and RodrÌguez (2003). We consider the models that allows for a change in slope and a change in the intercept and slope at unknown break date, respectively. Using Monte-Carlo experiments, the truncation lag selected according to several methods as the AIC, BIC, M(AIC), MBIC is analyzed. We also include and analyze the performance of the hybrid version suggested by Perron and Qu (2007) which uses OLS instead of GLS detrended data when constructing the information criteria. All these methods are compared to the sequential t-sig method based on testing for the signiÖcance of coe¢ cients on additional lags in the ADF autoregression. Results show that the MGLS tests present explosive values associated with large values of the lag selected which happens more often when AIC, AIC(OLS) and t-sig are used to select the lag length. The values are so negative that imply an over rejection of the null hypothesis of a unit root. On the opposite side, lag length selected using M(AIC), M(AICOLS), M(BIC), M(BICOLS) methods lead to very small values of the M-tests implying very conservative results, that is, no rejection of the null hypothesis. These opposite power problems are not observed in the case of the ADF(GLS) test for which it is highly recommended. JEL Classification-JEL: C22, C52 |
| Keywords: | Unit Root Tests, Structural Change, Truncation Lag, GLS Detrending, Information Criteria, Sequential General to SpeciÖc t-sig Method. |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:pcp:pucwps:wp00404&r=all |
| By: | Schober, Dominik; Woll, Oliver |
| Abstract: | Cycles play an important role when analyzing market phenomena. In many markets, both overlaying (weekly, seasonal or business cycles) and time-varying cycles (e.g. asymmetric lengths of peak and off peak or variation of business cycle length) exist simultaneously. Identification of these market cycles is crucial and no standard detection procedure exists to disentangle them. We introduce and investigate an adaptation of an endogenous structural break test for detecting at the same time simultaneously overlaying as well as time-varying cycles. This is useful for growth or business cycle analysis as well as for analysis of complex strategic behavior and short-term dynamics. |
| Keywords: | structural breaks,cluster analysis,filter,rolling regression,change points,model selection,cycles,economic dynamics |
| JEL: | C22 C24 C29 O47 L50 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:zewdip:15067&r=all |
| By: | Guillermo Carlomagno; Antoni Espasa |
| Abstract: | This paper deals with macro variables which have a large number of components and our aim is to model and forecasts all of them. We adopt a basic statistical procedure for discovering common trends among a large set of series and propose some extensions to take into account data irregularities and small samples issues. The forecasting strategy consists on estimating single-equation models for all the components, including the restrictions derived from the existence of common trends. An application to the disaggregated US CPI shows the usefulness of the procedure in real data problems. |
| Keywords: | Cointegration , Pairwise testing , Disaggregation , Forecast model selection , Outliers treatment , Inflation |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws1518&r=all |
| By: | Zhu, Ke |
| Abstract: | This paper proposes some novel Hausman tests to examine the error distribution in conditionally heteroskedastic models. Unlike the existing tests, all Hausman tests are easy-to-implement with the limiting null distribution of $\chi^{2}$, and moreover, they are consistent and able to detect the local alternative of order n−1=2. The scope of the Hausman test covers all Generalized error distributions and Student’s t distributions. The performance of each Hausman test is assessed by simulated and real data sets. |
| Keywords: | Conditionally heteroskedastic model; Consistent test; GARCH model; Goodness-of-fit test; Hausman test; Nonlinear time series. |
| JEL: | C1 C12 |
| Date: | 2015–09–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:66991&r=all |
| By: | Rasmus Søndergaard Pedersen (Department of Economics, University of Copenhagen) |
| Abstract: | We consider inference and testing in extended constant conditional correlation GARCH models in the case where the true parameter vector is a boundary point of the parameter space. This is of particular importance when testing for volatility spillovers in the model. The large-sample properties of the QMLE are derived together with the limiting distributions of the related LR, Wald, and LM statistics. Due to the boundary problem, these large-sample properties become nonstandard. The size and power properties of the tests are investigated in a simulation study. As an empirical illustration we test for (no) volatility spillovers between foreign exchange rates. |
| Keywords: | ECCC-GARCH, QML, boundary, spillovers |
| JEL: | C32 C51 C58 |
| Date: | 2015–09–04 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1510&r=all |
| By: | Kim Christensen (Aarhus University and CREATES); Mark Podolskij (Aarhus University and CREATES); Nopporn Thamrongrat (Heidelberg University); Bezirgen Veliyev (Aarhus University and CREATES) |
| Abstract: | In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in many central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by subsampling, an approach that computes rescaled copies of the original statistic based on local stretches of high-frequency data, and then it studies the sampling variation of these. We show that our estimator is consistent both in frictionless markets and models with additive microstructure noise. We derive a rate of convergence for it and are also able to determine an optimal rate for its tuning parameters (e.g., the number of subsamples). Subsampling does not require an extra set of estimators to do inference, which renders it trivial to implement. As a variance-covariance matrix estimator, it has the attractive feature that it is positive semi-definite by construction. Moreover, the subsampler is to some extent automatic, as it does not exploit explicit knowledge about the structure of the asymptotic covariance. It therefore tends to adapt to the problem at hand and be robust against misspecification of the noise process. As such, this paper facilitates assessment of the sampling errors inherent in high-frequency estimation of volatility. We highlight the finite sample properties of the subsampler in a Monte Carlo study, while some initial empirical work demonstrates its use to draw feasible inference about volatility in financial markets. |
| Keywords: | bipower variation, high-frequency data, microstructure noise, positive semi-definite estimation, pre-averaging, stochastic volatility, subsampling. |
| JEL: | C10 C80 |
| Date: | 2015–08–30 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-45&r=all |
| By: | Trenkler, Carsten; Weber, Enzo |
| Abstract: | This paper analyses identification for multivariate unobserved components models in which the innovations to trend and cycle are correlated. We address order and rank criteria as well as potential non-uniqueness of the reduced-form VARMA model. Identification is shown for lag lengths larger than one in case of a diagonal vector autoregressive cycle. We also discuss UC models with common features and with cycles that allow for dynamic spillovers. |
| Keywords: | Unobserved components models , Identification , VARMA |
| JEL: | C32 E32 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:mnh:wpaper:39656&r=all |
| By: | Fady Barsoum (Department of Economics, University of Konstanz, Germany) |
| Abstract: | This paper compares the forecasting performance of the unrestricted mixed-frequency VAR (MF-VAR) model to the more commonly used VAR (LF-VAR) model sampled a common low-frequency. The literature so far has successfully documented the forecast gains that can be obtained from using high-frequency variables in forecasting a lower frequency variable in a univariate mixed-frequency setting. These forecast gains are usually attributed to the ability of the mixed-frequency models to nowcast. More recently, Ghysels (2014) provides an approach that allows the usage of mixed-frequency variables in a VAR framework. In this paper we assess the forecasting and nowcasting performance of the MF-VAR of Ghysels (2014), however, we do not impose any restrictions on the parameters of the models. Although the unrestricted version is more flexible, it suffers from parameter proliferation and is therefore only suitable when the difference between the low- and high-frequency variables is small (i.e. quarterly and monthly frequencies). Unlike previous work, our interest is not only limited to evaluating the out-of-sample performance in terms of point forecasts but also density forecasts. Thus, we suggest a parametric bootstrap approach as well as a Bayesian approach to compute density forecasts. Moreover, we show how the nowcasts can be obtained using both direct and iterative forecasting methods. We use both Monte Carlo simulation experiments and an empirical study for the US to compare the forecasting performance of both the MF-VAR model and the LF-VAR model. The results highlight the point and density forecasts gains that can be achieved by the MF-VAR model. |
| Keywords: | Mixed-frequency, Bayesian estimation, Bootstrapping, Density forecasts, Nowcasting |
| JEL: | C32 C53 E37 |
| Date: | 2015–09–25 |
| URL: | http://d.repec.org/n?u=RePEc:knz:dpteco:1519&r=all |
| By: | Yacine Aït-Sahalia; Dacheng Xiu |
| Abstract: | We develop the necessary methodology to conduct principal component analysis at high frequency. We construct estimators of realized eigenvalues, eigenvectors, and principal components and provide the asymptotic distribution of these estimators. Empirically, we study the high frequency covariance structure of the constituents of the S&P 100 Index using as little as one week of high frequency data at a time. The explanatory power of the high frequency principal components varies over time. During the recent financial crisis, the first principal component becomes increasingly dominant, explaining up to 60% of the variation on its own, while the second principal component drives the common variation of financial sector stocks. |
| JEL: | C22 C58 G01 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:21584&r=all |
| By: | Michel Fliess; C\'edric Join |
| Abstract: | Recent advances in the understanding of time series permit to clarify seasonalities and cycles, which might be rather obscure in today's literature. A theorem due to P. Cartier and Y. Perrin, which was published only recently, in 1995, and several time scales yield, perhaps for the first time, a clear-cut definition of seasonalities and cycles. Their detection and their extraction, moreover, become easy to implement. Several computer experiments with concrete data from various fields are presented and discussed. The conclusion suggests the application of this approach to the debatable Kondriatev waves. |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1510.00237&r=all |