351. Cointegration in frequency domain
- Author
-
Daniel Levy, Rimini Center for Economic Analysis (RCEA), Emory University [Atlanta, GA], and Bar-Ilan University [Israël]
- Subjects
common stochastic trend ,cointegration: frequency domain anlysis ,JEL: C - Mathematical and Quantitative Methods/C.C4 - Econometric and Statistical Methods: Special Topics/C.C4.C40 - General ,Common Stochastic Trend, Cointegration, Frequency Domain Anlysis, Cross-Spectrum, Zero-Frequency ,[SHS]Humanities and Social Sciences ,Common Stochastic Trend ,Econometrics ,Zero frequency ,Gain ,Mathematics ,Cointegration ,C18 ,Applied Mathematics ,Mathematical analysis ,jel:C50 ,JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C10 - General ,[SHS.ECO]Humanities and Social Sciences/Economics and Finance ,jel:C14 ,Zero-Frequency ,Frequency domain ,Statistics, Probability and Uncertainty ,Coherence ,C22 ,Long Run ,Statistics and Probability ,Stationary process ,Bivariate analysis ,jel:O40 ,Spectrum ,ddc:330 ,Long-Run ,Applied mathematics ,Coherence (signal processing) ,Time domain ,cross-spectrum ,C32 ,Cross-spectrum ,JEL: C - Mathematical and Quantitative Methods/C.C3 - Multiple or Simultaneous Equation Models • Multiple Variables/C.C3.C32 - Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models • Diffusion Processes • State Space Models ,Short-Run ,JEL: C - Mathematical and Quantitative Methods/C.C2 - Single Equation Models • Single Variables/C.C2.C22 - Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models • Diffusion Processes ,jel:E30 ,jel:C32 ,Statistics::Computation ,Spectral Analysis ,C40 ,Phase ,Frequency Domain Anlysis ,zero-frequency ,Cross-Spectrum ,Common Stochastic Trend, Cointegration, Integration, Frequency Domain Anlysis, Cross-Spectrum, Zero-Frequency, Coherence, Squared Coherence, Phase, Gain, Cross-Spectral Properties, Bivariate Cointegrated System, Long Run Comovement ,C01 - Abstract
International audience; Existence of a cointegration relationship between two time series in the time domain imposes restrictions on the series zero‐frequency behaviour in terms of their squared coherence, phase and gain, in the frequency domain. I derive these restrictions by studying cross‐spectral properties of a cointegrated bivariate system. Specifically, I demonstrate that if two difference stationary series, X(t) and Y(t), are cointegrated with a cointegrating vector [1 b] and thus share a common stochastic trend, then at the zero frequency, the squared coherence of (1 ‐ L)X(t) and (1 ‐ L)Y(t) will equal one, their phase will equal zero, and their gain will equal |b|.
- Published
- 2002
- Full Text
- View/download PDF