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on Econometric Time Series |
| By: | Matei Demetrescu (University of Bonn); Robinson Kruse (Leibniz University Hannover and CREATES) |
| Abstract: | This article extends the analysis of local power of unit root tests in a nonlinear direction by considering local nonlinear alternatives and tests built specically against stationary nonlinear models. In particular, we focus on the popular test proposed by Kapetanios et al. (2003, Journal of Econometrics 112, 359-379) in comparison to the linear Dickey-Fuller test. To this end, we consider different adjustment schemes for deterministic terms. We provide asymptotic results which imply that the error variance has a severe impact on the behavior of the tests in the nonlinear case; the reason for such behavior is the interplay of nonstationarity and nonlinearity. In particular, we show that nonlinearity of the data generating process can be asymptotically negligible when the error variance is moderate or large (compared to the "amount of nonlinearity"), rendering the linear test more powerful than the nonlinear one. Should however the error variance be small, the nonlinear test has better power against local alternatives. We illustrate this in an asymptotic framework of what we call persistent nonlinearity. The theoretical findings of this article explain previous results in the literature obtained by simulation. Furthermore, our own simulation results suggest that the user-specied adjustment scheme for deterministic components (e.g. OLS, GLS, or recursive adjustment) has a much higher impact on the power of unit root tests than accounting for nonlinearity, at least under local (linear or nonlinear) alternatives. |
| Keywords: | Nonlinear models, Stochastic trend, Near integration, Persistent nonlinearity, Local power |
| JEL: | C12 C22 |
| Date: | 2012–01–04 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-01&r=ets |
| By: | M. FRÖMMEL; R. KRUSE |
| Abstract: | We analyze the time series properties of the S&P500 dividend-price ratio in the light of long memory, structural breaks and rational bubbles. We find an increase in the long memory parameter in the early 1990s by applying a recently proposed test by Sibbertsen and Kruse (2009). An application of the unit root test against long memory by Demetrescu et al. (2008) suggests that the pre-break data can be characterized by long memory, while the post-break sample contains a unit root. These results reconcile two empirical findings which were seen as contradictory so far: on the one hand they confirm the existence of fractional integration in the S&P500 log dividend-price ratio and on the other hand they are consistent with the existence of a rational bubble. The result of a changing memory parameter in the dividend-price ratio has an important implication for the literature on return predictability: the shift from a stationary dividend-price ratio to a unit root process in 1991 is likely to have caused the well-documented failure of conventional return prediction models since the 1990s. |
| Keywords: | Rational bubbles, dividend-price ratio, fractional integration, changing persistence. |
| JEL: | C12 C22 G12 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:rug:rugwps:11/722&r=ets |
| By: | Mario Cerrato; Christian de Peretti; Rolf Larsson; Nicholas Sarantis |
| Abstract: | We propose a nonlinear heterogeneous panel unit root test for testing the null hypothesis of unit-roots processes against the alternative that allows a proportion of units to be generated by globally stationary ESTAR processes and a remaining non-zero proportion to be generated by unit root processes. The proposed test is simple to implement and accommodates cross sectional dependence. We show that the distribution of the test statistic is free of nuisance parameters as (N, T) −∞. Monte Carlo simulation shows that our test holds correct size and under the hypothesis that data are generated by globally stationary ESTAR processes has a better power than the recent test proposed in Pesaran [2007]. Various applications are provided |
| Keywords: | Nonlinear panel unit root tests, cross sectional dependence. |
| JEL: | C12 C15 C22 C23 F31 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:gla:glaewp:2011_08&r=ets |
| By: | Peter Martey Addo (Centre d'Economie de la Sorbonne); Monica Billio (Ca' Foscari University of Venice - Department of Economics); Dominique Guegan (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | In ESTAR models it is usually quite difficult to obtain parameter estimates, as it is discussed in the literature. The problem of properly distinguishing the transition function in relation to extreme parameter combinations often leads to getting strongly biased estimators. This paper proposes a new procedure to test for the unit root in a nonlinear framework, and contributes to the existing literature in three separate directions. First, we propose a new alternative model – the MT-STAR model – which has similar properties as the ESTAR model but reduces the effects of the identification problem and can also account for cases where the adjustment mechanism towards equilibrium is not symmetric. Second, we develop a testing procedure to detect the presence of a nonlinear stationary process by establishing the limiting non-standard asymptotic distributions of the proposed test-statistics. Finally, we perform Monte Carlo simulations to assess the small sample performance of the test and then to highlight its power gain over existing tests for a unit root. We proposed two applications. |
| Keywords: | Nonlinearity, smooth transition, unit root testing, Monte Carlo simulations. |
| JEL: | C12 C22 C58 |
| Date: | 2011–12 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:11083&r=ets |
| By: | Anindya Banerjee; Josep Lluis Carrion-i-Silvestre |
| Abstract: | Panel cointegration, structural break, common factors, cross-section dependence |
| Keywords: | Panel cointegration, structural break, common factors, cross-section dependence |
| JEL: | C12 C22 |
| Date: | 2011–12 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:11-25&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Shu-Ping Shi (Australian National University); Jun Yu (Singapore Management University) |
| Abstract: | Identifying and dating explosive bubbles when there is periodically collapsing behavior over time has been a major concern in the economics literature and is of great importance for practitioners. The complexity of the nonlinear structure inherent in multiple bubble phenomena within the same sample period makes econometric analysis particularly difficult. The present paper develops new recursive procedures for practical implementation and surveillance strategies that may be employed by central banks and fiscal regulators. We show how the testing procedure and dating algorithm of Phillips, Wu and Yu (2011, PWY) are affected by multiple bubbles and may fail to be consistent. The present paper proposes a generalized version of the sup ADF test of PWY to address this difficulty, derives its asymptotic distribution, introduces a new date-stamping strategy for the origination and termination of multiple bubbles, and proves consistency of this dating procedure. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. Empirical applications are conducted to S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach identifies many key historical episodes of exuberance and collapse over this period, whereas the strategy of PWY and the CUSUM procedure locate far fewer episodes in the same sample range. |
| Keywords: | Date-stamping strategy, Generalized sup ADF test, Multiple bubbles, Rational bubble, Periodically collapsing bubbles, Sup ADF test |
| JEL: | C15 C22 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1843&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Ji Hyung Lee (Dept. of Economics, Yale University) |
| Abstract: | Limit theory is developed for nonstationary vector autoregression (VAR) with mixed roots in the vicinity of unity involving persistent and explosive components. Statistical tests for common roots are examined and model selection approaches for discriminating roots are explored. The results are useful in empirical testing for multiple manifestations of nonstationarity -- in particular for distinguishing mildly explosive roots from roots that are local to unity and for testing commonality in persistence. |
| Keywords: | Common roots, Local to unity, Mildly explosive, Mixed roots, Model selection, Persistence, Tests of common roots |
| JEL: | C22 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1845&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University); Shu-Ping Shi (Australian National University); Jun Yu (Singapore Management University) |
| Abstract: | Right-tailed unit root tests have proved promising for detecting exuberance in economic and financial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model specification used in parameter estimation. This paper aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focussing on the sup ADF test of Phillips, Wu and Yu (2011), which implements a right-tailed ADF test repeatedly on a sequence of forward sample recursions. We analyze and compare the limit theory of the sup ADF test under different hypotheses and model specifications. The size and power properties of the test under various scenarios are examined in simulations and some recommendations for empirical practice are given. Empirical applications to the Nasdaq and to Australian and New Zealand housing data illustrate these specification issues and reveal their practical importance in testing. |
| Keywords: | Unit root test, Mildly explosive process, Recursive regression, Size and power |
| JEL: | C15 C22 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1842&r=ets |
| By: | Jozef Barunik; Tomaso Aste; Tiziana Di Matteo; Ruipeng Liu |
| Abstract: | In this paper, we use the generalized Hurst exponent approach to study the multi- scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multiscaling. We observe a puzzling phenomenon where an apparent increase in multifractality is measured in time series generated from shuffled returns, where all time-correlations are destroyed, while the return distributions are conserved. This effect is robust and it is reproduced in several real financial data including stock market indices, exchange rates and interest rates. In order to understand the origin of this effect we investigate different simulated time series by means of the Markov switching multifractal (MSM) model, autoregressive fractionally integrated moving average (ARFIMA) processes with stable innovations, fractional Brownian motion and Levy flights. Overall we conclude that the multifractality observed in financial time series is mainly a consequence of the characteristic fat-tailed distribution of the returns and time-correlations have the effect to decrease the measured multifractality. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.1535&r=ets |