Unit Root Dynamics in Financial Time Series: A Comparative Study of Parametric and Non-Parametric Testing Frameworks
DOI:
https://doi.org/10.54536/ajase.v5i2.7557Keywords:
Financial Time Series, Parametric Non-Parametric Methods, Stationarity Persistence, Time Series Econometrics, Unit Root TestingAbstract
The study explores unit heterogeneity implication in financial time series analysis and investment decision guide, using some parametric and non-parametric tests that includes Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and Kwiatkowski-Phillips-Schmidt-Shin (KPSS), i.e one parametric unit root test (ADF) against two non-parametric unit root test (PP and KPSS). The study selects 5 US financial and macroeconomic variables spanning from January 2020 to December 2023 (monthly series) that includes US Dollar Index, S&P 500 Index, NASDAQ, Bond Yield, and Consumer Price Index for all urban consumers. The findings underscore the heterogeneous nature of unit roots in financial time series, with differences in persistence, integration order, and mean-reverting properties across variables, which reinforces the need for a multi-test approach combining parametric and non-parametric techniques to achieve robust stationarity inference.
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Akinbobola, T. O. (2012). The dynamics of real exchange rate in Nigeria: A cointegration approach. Journal of Applied Finance and Banking, 2(1), 181–201.
Bai, J., & Ng, S. (2004). A PANIC attack on unit roots and cointegration. Econometrica, 72(4), 1127–1177. https://doi.org/10.1111/j.1468-0262.2004.00538.x
Baillie, R. T., Bollerslev, T., & Mikkelsen, H. O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74(1), 3–30. https://doi.org/10.1016/S0304-4076(95)01749-6
Bakker, B. B. (2024). Reconciling random walks and predictability: A dual-component model of exchange rate dynamics (IMF Working Paper No. 2024/252). International Monetary Fund. https://doi.org/10.5089/9798400295034.001
Bariviera, A. F. (2017). The inefficiency of Bitcoin revisited: A dynamic approach. Economics Letters, 161, 1–4. https://doi.org/10.1016/j.econlet.2017.09.013
Baum, C. F., Barkoulas, J. T., & Caglayan, M. (1999). Long memory or structural breaks: Can either explain nonstationary real exchange rates under the current float? Journal of International Financial Markets, Institutions and Money, 9(4), 359–376. https://doi.org/10.1016/S1042-4431(99)00015-7
Campbell, J. Y., & Shiller, R. J. (1987). Cointegration and tests of present value models. Journal of Political Economy, 95(5), 1062–1088. https://doi.org/10.1086/261502
Caner, M., & Kilian, L. (2001). Size distortions of tests of the null hypothesis of stationarity: Evidence and implications for the PPP debate. Journal of International Money and Finance, 20(5), 639–657. https://doi.org/10.1016/S0261-5606(01)00004-X
Chang, T., Nieh, C. C., & Wei, C. C. (2010). Unit root heterogeneity in the international equity markets. Applied Economics Letters, 17(7), 669–673. https://doi.org/10.1080/13504850802270772
Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366), 427–431. https://doi.org/10.2307/2286348
Diebold, F. X., & Li, C. (2006). Forecasting the term structure of government bond yields. Journal of Econometrics, 130(2), 337–364. https://doi.org/10.1016/j.jeconom.2005.03.005
Doganlar, M., & Ozmen, M. (2000). Purchasing power parity and real exchange rates in case of developing countries. Istanbul Stock Exchange Review, 4(16), 91–102.
Enders, W., & Granger, C. W. J. (1998). Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics, 16(3), 304–311. https://doi.org/10.1080/07350015.1998.10524769
Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276. https://doi.org/10.2307/1913236
Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25(2), 383–417. https://doi.org/10.2307/2325486
Granger, C. W. J., & Newbold, P. (1974). Spurious regressions in econometrics. Journal of Econometrics, 2(2), 111–120. https://doi.org/10.1016/0304-4076(74)90034-7
Guo, Z. (2023). Research on the augmented Dickey–Fuller test for predicting stock prices and returns. Advances in Economics, Management and Political Sciences, 44, 101–106. https://doi.org/10.54254/2754-1169/44/20232198
Hall, A. D., Anderson, H. M., & Granger, C. W. J. (1992). A cointegration analysis of Treasury bill yields. Review of Economics and Statistics, 74(1), 116–126. https://doi.org/10.2307/2109558
Harris, R., & Sollis, R. (2003). Applied time series modelling and forecasting. John Wiley & Sons.
Ibrahim, W., & Aminu, S. B. (2002). Tests of the random walk hypothesis in selected West African stock markets. The Nigerian Journal of Economic and Social Studies, 44(2), 125–138.
Johansen, S. (1995). Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press.
Kapetanios, G., Shin, Y., & Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics, 112(2), 359–379. https://doi.org/10.1016/S0304-4076(02)00202-6
Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics, 54(1–3), 159–178. https://doi.org/10.1016/0304-4076(92)90104-Y
Lo, A. W., & MacKinlay, A. C. (1988). Stock market prices do not follow random walks: Evidence from a simple specification test. The Review of Financial Studies, 1(1), 41–66. https://doi.org/10.1093/rfs/1.1.41
Lothian, J. R., & Taylor, M. P. (1996). Real exchange rate behavior: The recent float from the perspective of the past two centuries. Journal of Political Economy, 104(3), 488–509.
Mishra, V., Mishra, U., & Smyth, R. (2010). The random-walk hypothesis for Indian stock market indices. Empirical Economics Letters, 9(7), 639–646.
Nadarajah, S., & Chu, J. (2017). On the inefficiency of Bitcoin. Economics Letters, 150, 6–9. https://doi.org/10.1016/j.econlet.2016.10.033
Narayan, P. K., & Liu, R. (2015). A GARCH model for testing market efficiency. Applied Economics, 47(47), 5063–5078. https://doi.org/10.1080/00036846.2015.1054067
Nelson, C. R., & Plosser, C. I. (1982). Trends and random walks in macroeconomic time series: Some evidence and implications. Journal of Monetary Economics, 10(2), 139–162. https://doi.org/10.1016/0304-3932(82)90012-5
Okonko, O. J., Ogunmike, O. J., & Adebayo, A. A. (2015). Empirical analysis of unit root and cointegration in the Nigerian financial market: Evidence from stock index, exchange rate, and interest rate. Journal of Economics and Sustainable Development, 6(12), 101–114.
Panopoulou, E. (2005). Long-run relation between interest rates and inflation: Evidence from 14 OECD countries. Journal of Applied Financial Economics, 15(14), 957–968. https://doi.org/:10.1080/09603100500120202
Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica, 57(6), 1361–1401. https://doi.org/10.2307/1913712
Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346. https://doi.org/10.2307/2336182
Pícha, K., Tichá, L., Chuponov, S., Ataev, J., Hudayberganov, D., & Kuziboev, B. (2024). The volatility spillover of global oil price uncertainty. International Journal of Energy Economics and Policy, 14(3), 619–624. https://doi.org/10.32479/ijeep.15803
Rapach, D. E., & Wohar, M. E. (2002). Testing the monetary model of exchange rate determination: New evidence from a century of data. Journal of International Economics, 58(2), 359–385. https://doi.org/10.1016/S0022-1996(02)00054-6
Rogoff, K. S., Rossi, B., & Schmelzing, P. (2024). Rethinking short-term real interest rates and term spreads using very long-run data (NBER Working Paper No. 33079). National Bureau of Economic Research. https://doi.org/10.3386/w33079
Uddin, G. S., & Alam, M. M. (2007). The random walk model of stock prices: Evidence from developing countries. International Review of Business Research Papers, 3(2), 162–174.
Udoh, E., & Ebong, F. (2016). Extreme exchange rate volatility and the Nigeria’s stock market performance. West African Journal of Monetary and Economic Integration, 16(1), 1–25.
Urquhart, A. (2016). The inefficiency of Bitcoin. Economics Letters, 148, 80–82. doi.org
Zivot, E., & Andrews, D. W. K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 10(3), 251–270. https://doi.org/10.1080/07350015.1992.10509904
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