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Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

Testing for long memory in the presence of non-linear deterministic trends with Chebyshev... Abstract This paper examines the interaction between non-linear deterministic trends and long run dependence by means of employing Chebyshev time polynomials and assuming that the detrended series displays long memory with the pole or singularity in the spectrum occurring at one or more possibly non-zero frequencies. The combination of the non-linear structure with the long memory framework produces a model which is linear in parameters and therefore it permits the estimation of the deterministic terms by standard OLS-GLS methods. Moreover, the orthogonality property of Chebyshev’s polynomials makes them especially attractive to approximate non-linear structures of data. We present a procedure which allows us to test (possibly fractional) orders of integration at various frequencies in the presence of the Chebyshev trends with no effect on the standard limit distribution of the method. Several Monte Carlo experiments are conducted and the results indicate that the method performs well. An empirical application, using data of real exchange rates is also carried out at the end of the article. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Studies in Nonlinear Dynamics & Econometrics de Gruyter

Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1081-1826
eISSN
1558-3708
DOI
10.1515/snde-2014-0005
Publisher site
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Abstract

Abstract This paper examines the interaction between non-linear deterministic trends and long run dependence by means of employing Chebyshev time polynomials and assuming that the detrended series displays long memory with the pole or singularity in the spectrum occurring at one or more possibly non-zero frequencies. The combination of the non-linear structure with the long memory framework produces a model which is linear in parameters and therefore it permits the estimation of the deterministic terms by standard OLS-GLS methods. Moreover, the orthogonality property of Chebyshev’s polynomials makes them especially attractive to approximate non-linear structures of data. We present a procedure which allows us to test (possibly fractional) orders of integration at various frequencies in the presence of the Chebyshev trends with no effect on the standard limit distribution of the method. Several Monte Carlo experiments are conducted and the results indicate that the method performs well. An empirical application, using data of real exchange rates is also carried out at the end of the article.

Journal

Studies in Nonlinear Dynamics & Econometrics – de Gruyter

Published: Feb 1, 2016

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    Chung
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    Hosking
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    Koenker
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    Giraitis
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    Andel
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    Gray
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    Bierens
  • de When Long Memory Meets the Filter Comparative Study Data
    Grassi
  • The Use of Model as an Approximation to ARMA Processes in the Context of Fractional Integration and Modelling
    Gil
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    Lothian
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    Robinson
  • Long Memory and Aggregation in Macroeconomic Time Series
    Chambers
  • Long Memory and Persistence in Aggregate Output of
    Diebold
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    Magnus
  • An Exponential Model in the Spectrum of a Scalar Time Series
    Bloomfield
  • Non - linearities and Fractional Integration in the US Unemployment Rate of and
    Caporale
  • Multiple Trend Breaks and the Unit - root Hypothesis of and
    Lumsdaine
  • Testing of Seasonal Fractional Integration in the UK and Japanese Consumption and Income of
    Gil
  • a Generalized Fractionally Integrated Autoregressive Moving - Average Process
    Chung
  • Seasonal Periodic Long Memory Model for Monthly River Flows Environmental Modelling and Software
    Ooms
  • Time Series Forecasting using Fractional Differencing of
    Sutcliffe
  • Efficient Tests of Nonstationary Hypotheses of the
    Robinson
  • Testing of Unit Roots and Other Nonstationary Hypotheses in Macroeconomic Time Series of
    Gil
  • Numerical Recipes The Art of Scientific University
    Press
  • Testing for a Unit Root in the Presence of a Maintained Trend in Modelling edited by Dordrecht
    Ouliaris
  • Noise in the Distribution of
    Wolf
  • An Introduction to Long Memory Time Series and Fractional Differencing of
    Granger
  • Purchasing Power Parity Over Two Centuries : Strengthening the Case for Real Exchange Rate Stability reply to Cuddington of and
    Lothian
  • Testing of Unit Roots and Other Nonstationary Hypotheses in Macroeconomic Time Series of
    Gil
  • Long Range Forecasting of IBM Product Revenues using a Seasonal Fractionally Differenced ARMA Model of
    Ray
  • Generalized Fractionally Differencing Approach in Long Memory Modelling
    Giraitis
  • Time Varying Cointegration
    Bierens
  • Occasional Structural Breaks and Long Memory with an Application to the Absolute Stock Returns of Empirical
    Granger
  • factor Gegenbauer ARMA Process for Network Computers Communications
    Sadek
  • Modelling Long Run Behavior with the Fractional ARIMA Model of
    Sowell
  • Minimum Unit Root Test with Two Structural Breaks of and
    Lee
  • The Great Crash the Oil Price Shock and the Unit Root Hypothesis
    Perron
  • Non - linearities and Fractional Integration in the US Unemployment Rate of and
    Caporale
  • The Determination of the Order of an Autoregression of the Series
    Hannan
  • Nonlinearities in Real Exchange Rate Determination : Do African Exchange Rates Follow a Random Walk
    Cuestas
  • factor Gegenbauer ARMA Process for Network Computers Communications
    Sadek
  • Formulas and Theorems for the Special Functions of Mathematical Physics
    Magnus
  • Modelling African Inflation Rates : Nonlinear Deterministic Terms and Long - range Dependence
    Caporale
  • Estimating a Generalized Long Memory Process of
    Chung
  • Testing for a Unit Root in the Presence of a Maintained Trend in Modelling edited by Dordrecht
    Ouliaris
  • Real Exchange Rates May have Nonlinear Trends of
    Cushman
  • a Testing Against General Autoregressive and Moving Average Error Models when the Regressors Include Lagged Dependent Variables
    Godfrey
  • On the Inherent Origin of Noise of
    Kaulakys
  • Special Functions New York
    Rainville
  • On the Inherent Origin of Noise of
    Kaulakys
  • On the Interpretation of Noise in
    Marinari
  • On Generalized Fractional Processes Correction
    Gray
  • Long Memory Time Series Models
    Andel
  • Efficient Wald Tests for Fractional Unit Root
    Lobato
  • Testing of Seasonal Fractional Integration in the UK and Japanese Consumption and Income of
    Gil
  • An Application of the Seasonal Fractionally Differenced Model to the Monetary Aggregate of the
    Porter
  • Purchasing Parity in Central and Eastern European Countries An Analysis of Unit Roots
    Cuestas
  • Parametric Bootstrap Test for Cycles of
    Dalla
  • Ocker On Unified Model Selection for Stationary and Nonstationary Short - and Long - memory Autoregressive Processes
    Beran
  • Estimation of Noise Transactions of Theory
    Ninness
  • The Great Crash the Oil Price Shock and the Unit Root Hypothesis
    Perron
  • The Determination of the Order of an Autoregression of the Series
    Hannan