Variance Ratio Testing for Fractional Cointegration in Presence of Trends and Trend Breaks

Dechert, Andreas (2012): Variance Ratio Testing for Fractional Cointegration in Presence of Trends and Trend Breaks.

Abstract

Modeling fractional cointegration relationships has become a major topic in applied time series analysis as it steps back from the traditional rigid I(1)/I(0) methodology. Hence, the number of proposed tests and approaches has grown over the last decade. The aim of this paper is to study the nonparametric variance ratio approach suggested by Nielsen for the case of fractional cointegration in presence of linear trend and trend breaks. The consideration of trend breaks is very important in order to avoid spurious fractional integration, so this possibility should be regarded by practitioners. This paper proposes to calculate p-values by means of gamma distributions and gives response regressions parameters for the asymptotic moments of them. In Monte Carlo simulations this work compares the power of the approach against a Johansen type rank test suggested, which is robust against trend breaks but not fractional (co-)integration. As the approach also obtains an estimator for the cointegration space, the paper compares it with OLS estimates in simulations. As an empirical example the validity of the market expectation hypothesis is tested for monthly Treasury bill rates ranging from 1958-2011, which might have a trend break around September 1979 due to change of American monetary policy.

• Item Type: MPRA Paper
• Language: English
• Keywords: fractional integration; fractional cointegration; long memory; variance ratio; nonparametric; trend breaks; market expectation hypothesis
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E43 - Interest Rates: Determination, Term Structure, and Effects; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General

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