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on Econometric Time Series |
| By: | Jiti Gao; Dag Tjøstheim; Jiying Yin |
| Abstract: | This paper considers a general model specification between a parametric co-integrating model and a nonparametric co-integrating model in a multivariate regression model, which involves a univariate integrated time series regressor and a vector of stationary time series regressors. A new and simple test is proposed and the resulting asymptotic theory is established. The test statistic is constructed based on a natural distance function between a nonparametric estimate and a smoothed parametric counterpart. The asymptotic distribution of the test statistic under the parametric specification is proportional to that of a local-time random variable with a known distribution. In addition, the finite sample performance of the proposed test is evaluated through using both simulated and real data examples. |
| Keywords: | Cointegration, nonparametric kernel estimation, parametric model specification, time series. |
| JEL: | C12 C14 C22 |
| Date: | 2012–08–24 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2012-18&r=ets |
| By: | Degui Li; Oliver Linton; Zudi Lu |
| Abstract: | We consider approximating a multivariate regression function by an affine combination of one-dimensional conditional component regression functions. The weight parameters involved in the approximation are estimated by least squares on the first-stage nonparametric kernel estimates. We establish asymptotic normality for the estimated weights and the regression function in two cases: the number of the covariates is finite, and the number of the covariates is diverging. As the observations are assumed to be stationary and near epoch dependent, the approach in this paper is applicable to estimation and forecasting issues in time series analysis. Furthermore, the methods and results are augmented by a simulation study and illustrated by application in the analysis of the Australian annual mean temperature anomaly series. We also apply our methods to high frequency volatility forecasting, where we obtain superior results to parametric methods. |
| Keywords: | Asymptotic normality, model averaging, Nadaraya-Watson kernel estimation, near epoch dependence, semiparametric method |
| JEL: | C14 C22 |
| Date: | 2012–08–04 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2012-17&r=ets |
| By: | Götz Thomas B.; Hecq Alain; Urbain Jean-Pierre (METEOR) |
| Abstract: | We combine the issues of dealing with variables sampled at mixed frequencies and the use ofreal-time data. In particular, the repeated observations forecasting (ROF) analysis of Stark andCroushore (2002) is extended to an autoregressive distributed lag setting in which the regressorsmay be sampled at higher frequencies than the regressand. For the US GDP quarterly growth rate, wecompare the forecasting performances of an AR model with several mixed-frequency models amongwhich the MIDAS approach. The additional dimension provided by different vintages allows us tocompute several forecasts for a given calendar date and use them to construct forecast densities.Scoring rules are employed to test for their equality and to construct combinations of them. Giventhe change of the implied weights over time, we propose time-varying ROF-based weights usingvintage data which present an alternative to traditional weighting schemes. |
| Keywords: | macroeconomics ; |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2012021&r=ets |
| By: | Frank Schorfheide; Dongho Song |
| Abstract: | This paper develops a vector autoregression (VAR) for macroeconomic time series which are observed at mixed frequencies – quarterly and monthly. The mixed-frequency VAR is cast in state-space form and estimated with Bayesian methods under a Minnesota-style prior. Using a real-time data set, we generate and evaluate forecasts from the mixed-frequency VAR and compare them to forecasts from a VAR that is estimated based on data time-aggregated to quarterly frequency. We document how information that becomes available within the quarter improves the forecasts in real time. |
| Keywords: | Bayesian statistical decision theory ; Forecasting ; Vector autoregression |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedmwp:701&r=ets |
| By: | Zhipeng Liao (Dept. of Economics, UCLA); Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | Model selection and associated issues of post-model selection inference present well known challenges in empirical econometric research. These modeling issues are manifest in all applied work but they are particularly acute in multivariate time series settings such as cointegrated systems where multiple interconnected decisions can materially affect the form of the model and its interpretation. In cointegrated system modeling, empirical estimation typically proceeds in a stepwise manner that involves the determination of cointegrating rank and autoregressive lag order in a reduced rank vector autoregression followed by estimation and inference. This paper proposes an automated approach to cointegrated system modeling that uses adaptive shrinkage techniques to estimate vector error correction models with unknown cointegrating rank structure and unknown transient lag dynamic order. These methods enable simultaneous order estimation of the cointegrating rank and autoregressive order in conjunction with oracle-like efficient estimation of the cointegrating matrix and transient dynamics. As such they offer considerable advantages to the practitioner as an automated approach to the estimation of cointegrated systems. The paper develops the new methods, derives their limit theory, reports simulations and presents an empirical illustration with macroeconomic aggregates. |
| Keywords: | Adaptive shrinkage, Automation, Cointegrating rank, Lasso regression, Oracle efficiency, Transient dynamics, Vector error correction |
| JEL: | C22 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1873&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Zhipeng Liao (Dept. of Economics, UCLA) |
| Abstract: | This paper overviews recent developments in series estimation of stochastic processes and some of their applications in econometrics. Underlying this approach is the idea that a stochastic process may under certain conditions be represented in terms of a set of orthonormal basis functions, giving a series representation that involves deterministic functions. Several applications of this series approximation method are discussed. The first shows how a continuous function can be approximated by a linear combination of Brownian motions (BMs), which is useful in the study of the spurious regressions. The second application utilizes the series representation of BM to investigate the effect of the presence of deterministic trends in a regression on traditional unit-root tests. The third uses basis functions in the series approximation as instrumental variables (IVs) to perform efficient estimation of the parameters in cointegrated systems. The fourth application proposes alternative estimators of long-run variances in some econometric models with dependent data, thereby providing autocorrelation robust inference methods in these models. We review some work related to these applications and some ongoing research involving series approximation methods. |
| Keywords: | Cointegrated system, HAC estimation; Instrumental variables, Lasso regression, Karhunen-Loeve representation, Long-run variance, Reproducing kernel Hilbert space, Oracle effciency, Orthonormal system, Trend basis |
| JEL: | C22 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1871&r=ets |
| By: | Ioannis Kasparis (Dept. of Economics, University of Cyprus); Peter C.B. Phillips (Cowles Foundation, Yale University); Tassos Magdalinos (Dept. of Economics, University of Southampton) |
| Abstract: | In regressions involving integrable functions we examine the limit properties of IV estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I(0) or nearly integrated (NI) processes. We show that this kind of nonlinearity in the regression function can significantly affect the relevance of the instruments. In particular, such instruments become weak when the signal of the regressor is strong, as it is in the NI case. Instruments based on integrable functions of lagged NI regressors display long range dependence and so remain relevant even at long lags, continuing to contribute to variance reduction in IV estimation. However, simulations show that OLS is generally superior to IV estimation in terms of MSE, even in the presence of endogeneity. Estimation precision is also reduced when the regressor is nonstationary. |
| Keywords: | Instrumental variables, Integrable function, Integrated process, Invariance principle, Local time, Mixed normality, Stationarity, Nonlinear cointegration, Unit roots, Weak Instruments |
| JEL: | C22 C32 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1872&r=ets |
| By: | Jerzy P. Rydlewski; Ma{\l}gorzata Snarska |
| Abstract: | Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for geometric ergodicity of a general class of nonparametric stochastic volatility models with skewness driven by hidden Markov Chain with switching. |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1209.1544&r=ets |