Demand for Money: A Study in Testing Time Series for Long Memory and Nonlinearity

This paper draws attention to the limitations of the standard unit root/cointegration approach to economic and financial modelling, and to some of the alternatives based on the idea of fractional integration, long memory models, and the random field regression approach to nonlinearity. Following brief explanations of fractional integration and random field regression, and the methods of applying them, selected techniques are applied to a demand for money dataset. Comparisons of the results from this illustrative case study are presented, and conclusions are drawn that should aid practitioners in applied time-series econometrics.

Exploring Long Memory and Nonlinearity in Irish Real Exchange Rates using Tests based on Semiparametric Estimation

Deciding whether a time series that appears nonstationary is in fact fractionally integrated or subject to structural change is a difficult task. However, various tests have recently been introduced for distinguishing long memory from level shifts and nonlinearity. In this paper, three testing approaches based on the properties of semiparametric estimators of the fractional differencing parameter, d, are described and applied to the (log) Ireland-United Kingdom and Ireland-Germany real exchange rates. The two exchange rates behave quite differently over time and the new tests give different results for each; but overall the results provide fairly strong support for the possibility of nonlinearity rather than long memory.Fractional integration, long memory, nonlinearity, real exchange rates, struc- tural change

Testing For Nonlinearity Using Redundancies: Quantitative and Qualitative Aspects

A method for testing nonlinearity in time series is described based on information-theoretic functionals -- redundancies, linear and nonlinear forms of which allow either qualitative, or, after incorporating the surrogate data technique, quantitative evaluation of dynamical properties of scrutinized data. An interplay of quantitative and qualitative testing on both the linear and nonlinear levels is analyzed and robustness of this combined approach against spurious nonlinearity detection is demonstrated. Evaluation of redundancies and redundancy-based statistics as functions of time lag and embedding dimension can further enhance insight into dynamics of a system under study.Comment: 32 pages + 1 table in separate postscript files, 12 figures in 12 encapsulated postscript files, all in uuencoded, compressed tar file. Also available by anon. ftp to santafe.edu, in directory pub/Users/mp/qq. To be published in Physica D., [email protected]

Smooth transition autoregressive models - A survey of recent developments

This paper surveys recent developments related to the smooth transition autoregressive [STAR] time series model and several of its variants. We put emphasis on new methods for testing for STAR nonlinearity, model evaluation, and forecasting. Several useful extensions of the basic STAR model, which concern multiple regimes, time-varying nonlinear properties, and models for vector time series, are also reviewed

Episodic Nonlinearity in Leading Global Currencies

We perform non-linearity tests using daily data for leading currencies that include the Australian dollar, British pound, Brazilian real, Canadian dollar, euro, Japanese yen, Mexican peso, and the Swiss franc to resolve the issue of whether these currencies are driven by fundamentals or exogenous shocks to the global economy. In particular, we use a new method of testing for linear and nonlinear lead/lag relationships between time series, introduced by Brooks and Hinich (1999), based on the concepts of cross-correlation and cross-bicorrelation. Our evidence points to a relatively rare episodic nonlinearity within and across foreign exchange rates. We also test the validity of specifying ARCH-type error structures for foreign exchange rates. In doing so, we estimate Bollerslevs (1986) general- ized ARCH (GARCH) model and Nelsons (1988) exponential GARCH (EGARCH) model,using a variety of error densities [including the normal, the Student-t distribution, and the Generalized Error Distribution (GED)] and a comprehensive set of diagnostic checks. We apply the Brooks and Hinich (1999) nonlinearity test to the standardized residuals of the optimal GARCH/EGARCH model for each exchange rate series and show that the nonlinearity in the exchange rates is not due to ARCH-type e¤ects. This result has important implications for the interpretation of the recent voluminous literature which attempts to model fi nancial asset returns using this family of models.Global nancial markets; Currencies; Episodic nonlinearity; Conditional heteroskedasticity.

Testing for nonlinearity in time series without the Fourier transform

2005-2006 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Testing the assumptions of linear prediction analysis in normal vowels

This paper develops an improved surrogate data test to show experimental evidence, for all the simple vowels of US English, for both male and female speakers, that Gaussian linear prediction analysis, a ubiquitous technique in current speech technologies, cannot be used to extract all the dynamical structure of real speech time series. The test provides robust evidence undermining the validity of these linear techniques, supporting the assumptions of either dynamical nonlinearity and/or non-Gaussianity common to more recent, complex, efforts at dynamical modelling speech time series. However, an additional finding is that the classical assumptions cannot be ruled out entirely, and plausible evidence is given to explain the success of the linear Gaussian theory as a weak approximation to the true, nonlinear/non-Gaussian dynamics. This supports the use of appropriate hybrid linear/nonlinear/non-Gaussian modelling. With a calibrated calculation of statistic and particular choice of experimental protocol, some of the known systematic problems of the method of surrogate data testing are circumvented to obtain results to support the conclusions to a high level of significance

The Use of Trimming to Improve the Performance of Tests for Nonlinear Serial Dependence with Application to the Australian National Electricity Market

In this article, we build on the results reported in Wild, Hinich and Foster (2008) for the National Electricity Market (NEM) of Australia by testing for episodic nonlinearity in the dynamics governing weekly cycles in spot price time series data. We apply the portmanteau correlation, bicorrelation and tricorrelation tests introduced in Hinich (1996) and the Engle (1982) ARCH LM test to the time series of half hourly spot prices from 7/12/1998 to 29/02/2008. We use trimming to improve the finite sample performance of the various test statistics mentioned above given the presence of significant skewness and leptokurtosis in the source datasets which may adversely affect the convergence properties of the test statistics in finite samples. With trimming, we still find the presence of significant third and fourth order (non-linear) serial dependence in the weekly spot price data, pointing to the presence of ‘deep’ nonlinear structure in this data.