Selected Problems in the Analysis of Nonstationary & Nonlinear Time Series (original) (raw)

Information-theoretic analysis of serial dependence and cointegration

1998

This paper is devoted to presenting wider characterizations of memory and cointegration in time series, in terms of information-theoretic statistics such as the entropy and the mutual information between pairs of variables. We suggest a nonparametric and nonlinear methodology for data analysis and for testing the hypotheses of long memory and the existence of a cointegrating relationship in a nonlinear context. This new framework represents a natural extension of the linear-memory concepts based on correlations. Finally, we show that our testing devices seem promising for exploratory analysis with nonlinearly cointegrated time series. . We are grateful to Ignacio Pena and to Z. Ding for kindly providing the foreign exchange rate and the stock-return series, respectively, and to Matt Kennel for helping with the software. Any remaining errors or inconsistencies are entirely of our responsibility. that of a (linear) cointegrating relationship, in which the equilibrium error z t = y t − ax t is different from zero but fluctuates around this value much more frequently than each of the individual series (i.e., z t is mean-reverting), and the size of these fluctuations is much smaller.

Econometrics: Non-linear Cointegration

Encyclopedia of Complexity and Systems Science, 2009

Cointegration is an econometric property relating time series variables. If two or more series are themselves nonstationary, but a linear combination of them is stationary, then the series are said to be cointegrated.

Nonstationarity Modeling of Economic and Financial Time Series

World Academy of Science, Engineering and Technology, International Journal of Social, Behavioral, Educational, Economic, Business and Industrial Engineering, 2017

Traditional techniques for analyzing time series are based on the notion of stationarity of phenomena under study, but in reality most economic and financial series do not verify this hypothesis, which implies the implementation of specific tools for the detection of such behavior. In this paper, we study nonstationary nonseasonal time series tests in a non-exhaustive manner. We formalize the problem of nonstationary processes with numerical simulations and take stock of their statistical characteristics. The theoretical aspects of some of the most common unit root tests will be discussed. We detail the specification of the tests, showing the advantages and disadvantages of each. The empirical study focuses on the application of these tests to the exchange rate (USD/TND) and the Consumer Price Index (CPI) in Tunisia, in order to compare the Power of these tests with the characteristics of the series.

Nonlinear cointegration in financial time series

Mathematical and Statistical Methods for Actuarial Sciences and Finance, 2010

In this paper, the concept of linear cointegration as introduced by Engle and Granger [5] is merged into the local paradigm. Adopting a local approach enables the achievement of a local error correction model characterised by dynamic parameters. Another important result obtained using the local paradigm is that the mechanism that leads the dynamic system back to a steady state is no longer a constant: it is a function not defined a priori but estimated point by point.

Modern approaches for nonlinear data analysis of economic and financial time series

2014

This thesis centers on introducing modern non-linear approaches for data analysis in economics and finance with special attention on business cycles and financial crisis. It is now well stated in the statistical and economic literature that major economic variables display non-linear behaviour over the different phases of the business cycle. As such, nonlinear approaches/models are required to capture the features of the data generating mechanism of inherently asymmetric realizations, since linear models are incapable of generating such behavior. In this respect, the thesis provides an interdisciplinary and open-minded approach to analyzing economic and financial systems in a novel way. The thesis presents approaches that are robust to extreme values, non-stationarity, applicable to both short and long data length, transparent and adaptive to any financial/economic time series. The thesis provides step-by-step procedures in analyzing economic/financial indicators by incorporating concepts based on surrogate data method, wavelets, phase space embedding, 'delay vector variance' (DVV) method and recurrence plots. The thesis also centers on transparent ways of identifying, dating turning points, evaluating impact of economic and financial crisis. In particular, the thesis also provides a procedure on how to anticipate future crisis and the possible impact of such crisis. The thesis shows that the incorporation of these techniques in learning the structure and interactions within and between economic and financial variables will be very useful in policy-making, since it facilitates the selection of appropriate processing methods, suggested by the data itself. In addition, a novel procedure to test for linearity and unit root in a nonlinear framework is proposed by introducing a new model-the MT-STAR model-which has similar properties of the ESTAR model but reduces the effects of the identification problem and can also account for asymmetry in the adjustment mechanism towards equilibrium. The asymptotic distributions of the proposed unit root test is non-standard and is derived. The power of the test is evaluated through a simulation study and some empirical illustrations on real exchange rates show its accuracy. Finally, the thesis defines a multivariate Self-Exciting Threshold Autoregressive with eXogenous input (MSETARX) models and present an estimation procedure for the parameters. The modeling procedure for the MSETARX models and problems of estimation are briefly considered.

Linear Cointegration of Nonlinear Time Series with an Application to Interest Rate Dynamics

Studies in Nonlinear Dynamics & Econometrics, 2000

We derive a de nition of linear cointegration for nonlinear stochastic processes using a martingale representation theorem. The result shows that stationary linear cointegrations can exhibit nonlinear dynamics, in contrast with the normal assumption of linearity. We propose a sequential nonparametric method to test rst for cointegration and second for nonlinear dynamics in the cointegrated system. We apply this method to weekly US interest rates constructed using a multirate lter rather than averaging. The Treasury Bill, Commercial Paper and Federal Funds rates are cointegrated, with two cointegrating vectors. Both cointegrations behave nonlinearly. Consequently, linear models will not fully replicate the dynamics of monetary policy transmission.

Nonlinear Econometric Modeling in Time Series

RePEc: Research Papers in Economics, 2006

Modeling in Time Series presents some recent developments in that area of research. This volume is the eleventh in a series entitled International Symposia in Economic Theory and Econometrics under the general editorship of William Barnett. Many of the prior volumes in this series have included investigations of nonlinearity and complex dynamics in economic theory and in structural econometric modeling. This is the first one to focus on the more recent literature on nonlinear time series. Specific topics covered with respect to nonlinearity include cointegration tests, risk-related asymmetries, structural breaks and outliers, Bayesian analysis with a threshold, consistency and asymptotic normality, asymptotic inference, and error-correction models. This proceedings volume includes the most important papers presented at a conference held at the University of Aarhus in Aarhus, Denmark, December 14-16, 1995. This volume constitutes the proceedings volume of the Sixth Meeting of the European Conference Series in Quantitative Economics and Econometrics, (EC) 2 .

Nonlinear cointegration and nonlinear error correction

RePEc: Research Papers in Economics, 1996

In this paper we propose a record counting cointegration (RCC) test which is robust to nonlinearities and certain types of structural breaks. The RCC test is based on the synchronicity property of the jumps (or new records) of cointegrated series, counting the number of jumps that simultaneously occur in both series. We obtain the rate of convergence of the RCC statistics under the null and alternative hypothesis. The distribution of RCC under the null of a unit root depends on the short run dependence of the cointegrated series. We propose a small sample correction and show by Monte Carlo simulation techniques their excellent small sample behaviour. Finally we apply our new cointegration test statistic to several financial and macroeconomic time series that have some structural breaks and nonlinearities. 1. INTRODUCTION Granger (1981) introduced the concept of cointegration and with the contribution of Engle and Granger (1987) and Johansen (1991) this concept has achieved immense popularity among econometricians and applied economists. Only a few recent papers have been dedicated to the simultaneous consideration of nonstationarity and nonlinearity, even though many people agree that those are likely characteristics of many macroeconomic and financial economic relationships. Granger (1995) discussed the concepts of long-range dependence in mean and extended memory which generalize the linear concept of integration, I(1), to a nonlinear framework. On the other hand, there are interesting empirical macroeconomic applications where nonlinearity has been found in a nonstationary context and therefore, there is a need to justify those results econometrically. Most unit root tests, like Dickey and Fuller (1979) or Phillips and Perron (1988), are not robust to outliers, Franses and Haldrup (1994), nor to structural breaks Perron (1990), nor to nonlinear transformations Granger and Hallman (1991) and Aparicio, Escribano and Garcia (2006b). Therefore, tests for non-cointegration based on the augmented Dickey and Fuller (ADF) test applied to the residuals of the cointegrating relationship, Engle and Granger (1987), have size distortions and losses in power. Aparicio, Escribano and Garcia (2004,2006b) analyzed the asymptotic properties of a new range unit root (RUR) test and provide evidence of their nice behavior by Monte Carlo simulation of nonlinearities and structural breaks and by some empirical applications.

Nonlinearities and Nonstationarities in Stock Returns

Journal of Business & Economic Statistics, 1998

This article addresses the question of whether recent findings of nonlinearities in high-frequency financial time series have been contaminated by possible shifts in the distribution of the data. It applies a recursive version of the Brock-Dechert-Scheinkman statistic to daily data on two stock-market indexes between January 1980 and December 1990. It is shown that October 1987 is highly influential in the characterization of the stock-market dynamics and appears to correspond to a shift in the distribution of stock returns. Sampling experiments show that simple linear processes with shifts in variance can replicate the behavior of the tests, but autoregressive conditional heteroscedastic filters are unable to do so.