Transitivity Property of the Cointegration Relationship and the Engle–Granger Test
https://doi.org/10.1134/S2304487X2002008X
Abstract
To consider the system of two or more cointegration equations with the same variables, it appears necessary to reveal whether the cointegration relationship has the standard properties of reflexivity, symmetry, and transitivity. In this work, the transitivity property of the cointegration relationship is analyzed. The theoretical substantiation for the transitivity of cointegration is presented. The computational experiment with the use of the Engle–Granger test to check the transitivity property of the cointegration relationship is carried out. It has shown that statistical tests do not necessarily confirm the theoretical calculations: the Engle–Granger test rejects the null hypothesis for the (Z; Y) and (Y; X) pairs in favor of cointegration, but does not necessarily reject it for the (Z; X) pair. A possible interpretation of this result has been proposed: low power and high probability of type II error of the Dickey–Fuller test underlying the Engle–Granger test. A new methodology for identifying cointegrated asset pairs has been proposed: to test the regression residuals obtained with the Engle–Granger test for stationarity using the KPSS test and combine the results of these tests. The results of the backtests of the proposed methodology on the Moscow Exchange 2017 data are presented. According to the results of the backtests, the average annual return on the proposed methodology for identifying cointegrated pairs of shares was 19.67 %. Compared to identifying cointegrated pairs of shares using the Engle–Granger test, the average annual return increased by 7.05 %.
References
1. Vidyamurthy G. Pairs trading: quantitative methods and analysis. Wiley, 2004.
2. Watsham T., Parramore K. Quantitative Methods in Finance. Cengage Learning EMEA, 1996.
3. Ferre M. The Johansen Test and the Transitivity Property. Economics Bulletin, 2004, vol. 3 (27), pp. 1–7.
4. Engle R., Granger C. Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 1987, vol. 55, no. 2, pp. 251–276.
5. Magnus Y. R., Katyshev P. K., Peresetski A. A. Ekonometrika. Nachalnyj kurs: uchebnik [Econometrics. Basic course: textbook]. Moscow: Delo, 2004 (in Russian).
6. Shreider Y. A. Ravenstvo, skhodstvo, poryadok [Equality, similarity, order]. Moscow: Nauka, 1951 (in Russian).
7. Kocenda E. Elements of time series econometrics: an applied approach. Karolinum press, 2015.
8. Stock J. Cointegration, Long-Run Comovements, and Long-Horizon Forecasting. Advances in Economics and Econometrics: Theory and Applications, 1997, vol. 3, pp. 34–60.
9. Kwiatkowski D., Phillips P., Schmidt P., Shin Y. Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 1992, vol. 54 (1–3), pp. 159–178.
10. Blyumin S., Kuznetsova X. Svojstvo simmetrichnosti otnosheniya kointegracii i test Englarendzhera [The symmetry property of the cointegration relation and Engle–Granger test]. News of Higher Educational Institutions of the Chernozem Region, 2019, vol. 2 (56), pp. 76–85 (in Russian).
11. Kuznetsova X. Svojstvo simmetrichnosti otnosheniya kointegracii [The symmetry property of the cointegration relation]. Available at: https://habr.com/ru/post/457794/ (accessed 29. 08. 2019)
12. Kuznetsova X. Analiz effektivnosti torgovli kointegrirovannymi parami na fondovyh rynkah [Analysis of the trade effectiveness of cointegrated pairs in stock markets]. Matematicheskoe i programmnoe obespechenie informacionnyh, tekhnicheskih i ekonomicheskih sistem: materialy konferencii [Software of information, technical and economic systems: conference proceedings]. Tomsk, 2017, pp. 180–188 (in Russian).
13. Kuznetsova X. Torgovaya strategiya dlya torgovli kointegrirovannymi parami akcij [Trading strategy for trading cointegrated stock pairs]. Available at: https://habr.com/post/344674/ (accessed 29. 08. 2019)
Review
For citations:
Kuznetsova X. Transitivity Property of the Cointegration Relationship and the Engle–Granger Test. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2020;9(2):184-188. (In Russ.) https://doi.org/10.1134/S2304487X2002008X
Views:
205
Email this article 