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on Econometric Time Series |
| By: | Jiti Gao; Peter M. Robinson |
| Abstract: | A semiparametric model is proposed in which a parametric filtering of a non-stationary time series, incorporating fractionally differencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Unit root tests with standard asymptotics are thereby justified. Estimation of the trend function is also considered. We include a Monte Carlo study of finite-sample performance. |
| Keywords: | fractional time series; fixed design nonparametric regression; non-stationary time series; unit root tests. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2013-15&r=ets |
| By: | Jiti Gao; Peter C.B. Phillips |
| Abstract: | This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coefficient components. The model accommodates a cointegrating structure and allows for endo-geneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixture of stationary and non-stationary data and is well suited to a variety of models that are commonly used in applied econometric work. Nonparametric and semiparametric estimation methods are proposed to estimate the varying coefficient functions. The analytical findings reveal some important differences, including convergence rates, that can arise in the conduct of semiparametric regression with nonstationary data. The results include some new asymptotic theory for nonlinear functionals of nonstationary and stationary time series that are of wider interest and applicability and subsume much earlier research on such systems. The finite sample properties of the proposed econometric methods are analyzed in simulations. An empirical illustration examines nonlinear dependencies in aggregate consumption function behavior in the US over the period 1960 - 2009. |
| Keywords: | fractional Aggregate consumption, Asymptotic theory, cointegration, density, local time, nonlinear functional, nonparametric estimation, semiparametric, time series, varying coefficient model. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2013-16&r=ets |
| By: | Biqing Cai; Jiti Gao |
| Abstract: | This paper discusses nonparametric series estimation of integrable cointegration models using Hermite functions. We establish the uniform consistency and asymptotic normality of the series estimator. The Monte Carlo simulation results show that the performance of the estimator is numerically satisfactory. We then apply the estimator to estimate the stock return predictive function. The out-of-sample evaluation results suggest that dividend yield has nonlinear predictive power for stock returns while book-to-market ratio and earning-price ratio have little predictive power. |
| Keywords: | Cointegration, Hermite Functions, Return Predictability, Series Estimator, Unit Root |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2013-17&r=ets |
| By: | Yuanhua Feng (University of Paderborn) |
| Abstract: | This paper introduces a spatial framework for high-frequency returns and a faster double-conditional smoothing algorithm to carry out bivariate kernel estimation of the volatility surface. A spatial multiplicative component GARCH with random effects is proposed to deal with multiplicative random effects found from the data. It is shown that the probabilistic properties of the stochastic part and the asymptotic properties of the kernel volatility surface estimator are all strongly affected by the multiplicative random effects. Data example shows that the volatility surface before, during and after the 2008 financial crisis forms a volatility saddle. |
| Keywords: | Spatial multiplicative component GARCH, high-frequency returns, double-conditional smoothing, multiplicative random effect, volatility arch, volatility saddle. |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:wpaper:65&r=ets |
| By: | Christoph Hanck; Robert Czudaj |
| Abstract: | This paper argues that typical applications of panel unit root tests should take possible nonstationarity in the volatility process of the innovations of the panel time series into account. Nonstationarity volatility arises for instance when there are structural breaks in the innovation variances. A prominent example is the reduction in GDP growth variances enjoyed by many industrialized countries, known as the “Great Moderation”. It also proposes a new testing approach for panel unit roots that is, unlike many previously suggested tests, robust to such volatility processes. The panel test is based on Simes‘ (1986) classical multiple test, which combines evidence from time series unit root tests of the series in the panel. As time series unit root tests, we employ recently proposed tests of Cavaliere and Taylor (2008b). The panel test is robust to general patterns of cross-sectional dependence and yet is straightforward to implement, only requiring valid p-values of time series unit root tests, and no resampling. Monte Carlo experiments show that other panel unit root tests suffer from sometimes severe size distortions in the presence of nonstationary volatility, and that this defect can be remedied using the test proposed here. We use the methods developed here to test for unit roots in OECD panels of gross domestic products and inflation rates, yielding inference robust to the “Great Moderation”. We find little evidence of trend stationarity, and mixed evidence regarding inflation stationarity. |
| Keywords: | Panel unit root test; nonstationary volatility; cross-sectional dependence; GDP stationarity; inflation stationarity |
| JEL: | C12 C23 E31 O40 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:rwi:repape:0434&r=ets |
| By: | In Choi (Department of Economics, Sogang University, Seoul) |
| Abstract: | This paper surveys the literature on panel cointegration. It starts by dis- cussing cointegrating panel regressions for both cross-sectionally independent and correlated panels. It then introduces three groups of tests for panel coin-tegration : residual-based tests for the null of noncointegration, residual-based tests for the null of cointegration, and tests based on vector autoregression. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:sgo:wpaper:1208&r=ets |
| By: | Peter C. B. Phillips (Yale University, University of Auckland, University of Southampton & Singapore Management University); Shu-Ping Shi (The Australian National University); Jun Yu (Singapore Management University) |
| Abstract: | Recent work on econometric detection mechanisms has shown the effectiveness of recursive procedures in identifying and dating financial bubbles. These procedures are useful as warning alerts in surveillance strategies conducted by central banks and fiscal regulators with real time data. Use of these methods over long historical periods presents a more serious econometric challenge due to the complexity of the nonlinear structure and break mechanisms that are inherent in multiple bubble phenomena within the same sample period. To meet this challenge the present paper develops a new recursive flexible window method that is better suited for practical implementation with long historical time series. The method is a generalized version of the sup ADF test of Phillips, Wu and Yu (2011, PWY) and delivers a consistent date-stamping strategy for the origination and termination of multiple bubbles. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. An empirical application of the methodology is conducted on S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach successfully identi.es the well-known historical episodes of exuberance and collapse over this period, whereas the strategy of PWY and a related CUSUM dating procedure locate far fewer episodes in the same sample range. |
| Keywords: | Date-stamping strategy; Flexible window; Generalized sup ADF test; Multiple bubbles, Rational bubble; Periodically collapsing bubbles; Sup ADF test; |
| JEL: | C15 C22 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:04-2013&r=ets |
| By: | Peter C. B. Phillips (Yale University, University of Auckland, University of Southampton & Singapore Management University); Shu-Ping Shi (The Australian National University); Jun Yu (Singapore Management University) |
| Abstract: | This paper provides the limit theory of real time dating algorithms for bubble detection that were suggested in Phillips, Wu and Yu (2011, PWY) and Phillips, Shi and Yu (2013b, PSY). Bubbles are modeled using mildly explosive bubble episodes that are embedded within longer periods where the data evolves as a stochastic trend, thereby capturing normal market behavior as well as exuberance and collapse. Both the PWY and PSY estimates rely on recursive right tailed unit root tests (each with a different recursive algorithm) that may be used in real time to locate the origination and collapse dates of bubbles. Under certain explicit conditions, the moving window detector of PSY is shown to be a consistent dating algorithm even in the presence of multiple bubbles. The other algorithms are consistent detectors for bubbles early in the sample and, under stronger conditions, for subsequent bubbles in some cases. These asymptotic results and accompanying simulations guide the practical implementation of the procedures. They indicate that the PSY moving window detector is more reliable than the PWY strategy, sequential application of the PWY procedure and the CUSUM procedure. |
| Keywords: | Bubble duration, Consistency, Dating algorithm, Limit theory, Multiple bubbles, Real time detector. |
| JEL: | C15 C22 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:05-2013&r=ets |
| By: | Giorgio Calzolari (University of Florence); Laura Magazzini (Department of Economics (University of Verona)) |
| Keywords: | panel data, dynamic model, GMM estimation, test of overidentifying restrictions |
| JEL: | C23 C12 |
| Date: | 2013–08 |
| URL: | http://d.repec.org/n?u=RePEc:ver:wpaper:14/2013&r=ets |