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Testing for no cointegration in vector autoregressions with estimated degree of fractional integration

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  • Demetrescu, Matei
  • Kusin, Vladimir
  • Salish, Nazarii

Abstract

Confirming the existence of long-run relations between persistent variables is an important empirical goal. Fractional (co)integration allows for flexible modelling of such variables. The persistence of many fractional VAR processes is characterized by the integration parameter d and, under cointegration, by the persistence of the equilibrium deviations, where both are typically unknown in practice. To deal with unknown persistence of equilibrium deviations, we linearize here the involved fractional difference filter. When d is known, this results in test statistics possessing standard (normal or χ2) asymptotic distributions. For unknown d, conditions are provided, under which plugging in consistent estimators of d does not affect the standard asymptotics; the key insight is that letting the number of lags increase as the sample size goes to infinity accounts for the estimation error of d. The proposed approach is illustrated in Monte Carlo experiments and a fractional cointegration analysis of short-term U.S. T-bills.

Suggested Citation

  • Demetrescu, Matei & Kusin, Vladimir & Salish, Nazarii, 2022. "Testing for no cointegration in vector autoregressions with estimated degree of fractional integration," Economic Modelling, Elsevier, vol. 108(C).
    • Handle: RePEc:eee:ecmode:v:108:y:2022:i:c:s0264999321002832
    DOI: 10.1016/j.econmod.2021.105694
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    References listed on IDEAS

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    More about this item

    Keywords

    Fractional VAR model; Persistence; Strong and weak cointegration; Weak exogeneity; Simultaneity; Nonparametric estimator; Long autoregression;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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