OECD ÜLKELERİNDE HİSSE SENEDİ FİYATLARININ ORTALAMAYA DÖNÜŞÜ: FOURİER THRESHOLD BİRİM KÖK TESTİNDEN BULGULAR

Year 2024, , 1 - 17, 27.06.2024

Gökhan Konat , Hüseyin İşlek

https://doi.org/10.54452/jrb.1125225

Abstract

Hisse senedi fiyatlarının birim köke sahip olup olmadığı yani rassal yürüyüş süreci içerip içermediği araştırmacıların odağı halindedir. Hisse senedi fiyatları durağan sürece sahip ise yani ortalamaya geri dönüyorsa şokların etkileri geçicidir ve zamanla trend yoluna döneceği yorumu yapılmaktadır. Eğer hisse senedi fiyatları geçici şoklara sahip ise yatırım açısından geçmiş davranışlara bağlı olarak gelecekteki hareketlerin tahmin edilebilmesini olanak tanımaktadır. Bu çalışma, hisse senedi fiyatlarının ortalamaya dönüp dönmediğini ve dolaysıyla rassal yürüyüş sürecine sahip olup olmadığını araştırmaktadır. Bu amaçla, 26 OECD ülkesi için Ocak 1990-Ocak 2021 dönemi için Caner ve Hansen (2001) test metodolojisine dayanan Fourier Eşik Birim Kök (FTUR) testi ile ele alınan değişkenlerin sınamaları gerçekleştirilmiştir. FTUR testi, hem yapısal kırılmaları hem de doğrusal olmayan durumları dikkate almaktadır. Fourier fonksiyonlarının yapısal değişimleri hesaba katmak için kullanılmasındaki amaç kırılmaların sayısı, yeri ve şeklinden etkilenmemesidir. Böylece, testin gücü artmaktadır. Bu test sonuçlarına göre Avusturya, Kanada, Almanya, İtalya, Yeni Zelanda, İspanya ve İngiltere'de hisse senedi fiyatlarının doğrusal olduğu görülmektedir. Bu nedenle doğrusal olduğu gözlenen bu ülkeler için Fourier Augmented Dickey Fuller (FADF) birim kök analizi yapılmıştır. Diğer ülkeler için FTUR sınaması yapılmıştır. FTUR ve FADF birim kök testi sonuçlarına göre hisse senedi fiyatlarının İtalya dışında bazı ülkelerde birim kök içerdiği bulgusuna erişilmiştir. Bazı ülkelerde hisse senedi fiyatları kısmi bir birim kök yapısına sahiptir. Diğer bir deyişle, şokların etkileri kalıcıdır ve rassal yürüyüş süreci ile bu ülkelerde gelecekteki getirilerin tahmin edilemeyeceği sonucuna varılmaktadır.

Keywords

Hisse senedi fiyatları, ortalamaya dönüş, yumuşak geçişli otoregresif (STAR) model, eşik birim kök, Fourier fonksiyon

TESTING MEAN REVERSION OF STOCK PRICES IN OECD COUNTRIES: EVIDENCE FROM FOURIER THRESHOLD UNIT ROOT TEST

Abstract

Researchers focus on whether stock prices have a unit root, that is, whether they contain a random walk process. If stock prices have a stationary process, that is, if they return to the mean, the effects of shocks are temporary, and it is interpreted that they will return to the trend path over time. If stock prices have transitory shocks, it allows for the prediction of future movements based on past behavior in terms of investment. This study investigates whether stock prices revert to the mean and thus have a random walk process. For this purpose, the Fourier Threshold Unit Root (FTUR) test based on the test methodology of Caner and Hansen (2001) for the period January 1990–January 2021 for 26 OECD countries is applied. The FTUR test takes into account both structural breaks and nonlinearities. The purpose of using Fourier functions to account for structural changes is that they are not affected by the number, location, or shape of breaks. Thus, the power of the test increases. According to the results of this test, stock prices in Austria, Canada, Germany, Italy, New Zealand, Spain, and the UK are linear. Therefore, Fourier Augmented Dickey-Fuller (FADF) unit root analysis was performed for these countries. The FTUR test was performed in other countries. According to the results of FTUR and FADF unit root tests, stock prices are found to contain unit roots in some countries except Italy. In some countries, stock prices have a partial unit root structure. In other words, the effects of shocks are permanent, and it is concluded that future returns cannot be predicted in these countries with the random walk process.

Keywords

Fourier Function, Stock Prices, mean reversion, smooth transition autoregressive (STAR) model, threshold unit root, Fourier function

References

• Ahmad, A. H., Daud, S. N. M., and Azman-Saini, W. N. W. (2010). Efficient market hypothesis in emerging markets: Panel data evidence with multiple breaks and cross sectional dependence. Economics Bulletin, 30(4), 2987–2995.
• Andrews, D.W. (1998). Hypothesis testing with a restricted parameter space. Journal of Econometrics, 84(1), pp. 155–199.
• Balvers, R., Wu, Y. and Gilliland, E. (2000). Mean reversion across national stock markets and parametric contrarian investment strategies, Journal of Finance, 55, 745-772.
• Bose, N. (2005). Endogenous growth and the emergence of equity finance. Journal of Development Economics, 77(1), 173-188.
• Buguk, C. W. and Brorsen, B. W. (2003). Testing weak-form market efficiency: evidence from the Istanbul Stock Exchange, International Review of Financial Analysis, 12(5), 579-590.
• Caner, M. and Hansen, B.E., (2001). Threshold autoregression with a unit root. Econometrica, 69(6), 1555–1596.
• Chaudhuri, K. and Wu, Y. (2003). Random walk versus breaking trend in stock prices: evidence from emerging markets, Journal of Banking & Finance, 27, 575-592.
• Chaudhuri, K. and Wu, Y. (2004). Mean reversion in stock prices: evidence from emerging markets, Managerial Finance, 30, 22-31.
• Choudhry, T. (1997). Stochastic trends in stock prices: evidence from Latin American markets, Journal of Macroeconomics, 19, 285-304.
• Christopoulos, D. K. and León Ledesma, M. A. (2010). Smooth breaks and non–linear mean reversion: Post–Bretton Woods real exchange rates. Journal of International Money and Finance, 29(6), 1076–1093.
• Christopoulos, D. K. and Leon-Ledesma, M. A. (2011). International output convergence, breaks, and asymmetric adjustment. Studies in Nonlinear Dynamics & Econometrics, 15(3).
• Debondt, W. and Thaler, R. (1985). Does the stock market overreact?, Journal of Finance, 40, 793-805.
• Durusu-Ciftci, D., Ispir, M. S., and Kok, D. (2019). Do stock markets follow a random walk? New evidence for an old question. International Review of Economics & Finance, 64, 165-175.
• Enders, W., and Lee, J. (2012a). A unit root test using a Fourier series to approximate smooth breaks. Oxford Bulletin of Economics & Statistics, 74, 574–599.
• Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383–417.
• Fama, E. F. (1990). Term-structure forecasts of interest rates, inflation and real returns, Journal of Monetary Economics, 25, 59-76.
• Fama, E. F. and French, K. R. (1988a). Dividend yields and expected stock returns, Journal of Financial Economics, 22, 3-25.
• Fama, E. F. and French, K. R. (1988b). Permanent and temporary components of stock prices, Journal of Political Economy, 96, 246-273.
• Gozbasi, O., Kucukkaplan, I., and Nazlioglu, S. (2014). Re-examining the Turkish stock market efficiency: Evidence from nonlinear unit root tests. Economic Modelling, 38, 381-384.
• Grieb, T.A. and Reyes, M. G. (1999). Random walk tests for Latin American equity indexes and individual firms, Journal of Financial Research, 22, 371-383.
• Huber, P. (1997). Stock market returns in thin markets: evidence from the Vienna stock exchange, Applied Financial Economics, 7, 493-498.
• Kawakatsu, K. and Morey, M.R. (1999). An empirical examination of financial liberalization and the efficiency of the emerging market stock prices, Journal of Financial Research, 22, 358-411.
• Kilian, L. an dTaylor, M. P. (2003). Why is it so difficult to beat the random walk forecast of exchange rates?, Journal of International Economics, 60, 85-107.
• Kim, M. J., Nelson, C. R. and Startz, R. (1991), Mean reversion in stock prices? A reappraisal of the empirical evidence, The Review of Economic Studies, 58, 515-528.
• Lean, H. H., and Smyth, R. (2007). Do Asian stock markets follow a random walk? Evidence from LM unit root tests with one and two structural breaks. Review of Pacific Basin Financial Markets and Policies, 10(01), 15-31.
• Lee, J., and Strazicich, M. C. (2003). Minimum LM Unit Root Test with One Structural Break. Manuscript, Department of Economics, Appalachian State University, 1-16.
• Lee, C. C., Lee, J. D., and Lee, C. C. (2010). Stock prices and the efficient market hypothesis: Evidence from a panel stationary test with structural breaks. Japan and the world economy, 22(1), 49-58.
• Lee, C. C., Tsong, C. C., and Lee, C. F. (2014). Testing for the efficient market hypothesis in stock prices: International evidence from nonlinear heterogeneous panels. Macroeconomic Dynamics, 18, 943–958.
• Li, C. A. and Chen, T. H. (2010). Revisiting mean reversion in the stock prices for both the U. S. and its major trading partners: Threshold unit root test, The International Review of Accounting, Banking and Finance, 2, 23-38.
• Liu, X., Song, H. and Romilly, P. (1997). Are Chinese stock markets efficient? A cointegration and causality analysis, Applied Economics Letters, 4, 511-515.
• Lo, A. W. and MacKinlay, A. C. (1988). Stock market prices do not follow random walks: evidence from a simple specification test, Review of Financial Studies, 1, 41-66.
• Lumsdaine, R. L., and Papell, D. H. (1997). Multiple Trend Breaks and the Unit-Root Hypothesis. The Review of Economics and Statistics, 79(2), 212-218.
• Mishra, A. and Mishra, V. (2011). Is the Indian stock market efficient? Evidence from a TAR model with an autoregressive unit root, Applied Economics Letters, 18, 467-472.
• Mishra, A., Mishra, V., and Smyth, R. (2015). The random-walk hypothesis on the Indian stock market. Emerging markets finance and trade, 51(5), 879-892.
• Moghaddam, M., and Li, Y. (2017). Searching for the P/E mean reversion affinity–An application of the flexible Fourier approximation. The Journal of Business Inquiry, 16(2), 102-111.
• Munir, Q., and Mansur, K. (2009). Is Malaysian stock market efficient? Evidence from threshold unit root tests. Economics Bulletin, 29(2), 1359-1370.
• Murthy, V. N. R., Washer, K. and Wingender, J. (2011). Do U.S. stock prices exhibit mean reversion? Evidence from recent nonlinear unit root tests, International Research Journal of Finance and Economics, 68, 46-49.
• Narayan, P. K., and Smyth*, R. (2005). Are OECD stock prices characterized by a random walk? Evidence from sequential trend break and panel data models. Applied Financial Economics, 15(8), 547-556.
• Narayan, P. K. (2006). The behaviour of US stock prices: Evidence from a threshold autoregressive model. Mathematics and computers in simulation, 71(2), 103-108.
• Narayan, P., and Prasad, A. (2007). Mean reversion in stock prices: New evidence from panel unit root tests for seventeen European countries. Economics Bulletin, 3(34), 1-6.
• Narayan, P. K. (2008). Do shocks to G7 stock prices have a permanent effect?: Evidence from panel unit root tests with structural change. Mathematics and Computers in Simulation, 77(4), 369-373.
• Nartea, G. V., Valera, H. G. A., and Valera, M. L. G. (2021). Mean reversion in Asia-Pacific stock prices: New evidence from quantile unit root tests. International Review of Economics & Finance, 73, 214-230.
• Perron, P. (1989). The Great Crash, The Oil Price Shock, And The Unit Root Hypothesis. Econometrica: Journal Of The Econometric Society, 1361-1401.
• Poterba, J. M. and Summers, L. H. (1988), Mean reversion in stock prices: evidence and implications, Journal of Financial Economics, 22, 27-59.
• Qian, X. Y., Song, F. T., and Zhou, W. X. (2008). Nonlinear behaviour of the Chinese SSEC index with a unit root: Evidence from threshold unit root tests. Physica A: Statistical Mechanics and Its Applications, 387(2-3), 503-510.
• Richards, A. J. (1995). Comovements in national stock market returns: evidence of predictability but not cointegration, Journal of Monetary Economics, 36, 631-654.
• Richards, A. J. (1997). Winner-loser reversals in national stock market indices: can they be explained?, Journal of Finance, 52, 2129-2144.
• Shively, P. A. (2003). The nonlinear dynamics of stock prices. The Quarterly Review of Economics and Finance, 43(3), 505-517.
• Shen, X., and Holmes, M. J. (2014b). Are stock prices stationary? Some new evidence from a panel data approach. Studies in Economics and Finance.
• Tan, S. H., Habibullah, M. S., and Khong, R., (2010). ''Non-linear unit root properties of stock prices: Evidence from India, Pakistan and Sri Lanka''. Economics Bulletin, 30(1), 274-281.
• Taylor, M. P. and Peel, D. A. (2000). Nonlinear adjustment, long-run equilibriumand exchange rate fundamentals, Journal of International Money and Finance, 19, 33-53.
• Urrutia, J. L. (1995). Test of random walk and market efficiency for Latin American emerging equity markets, Journal of Financial Research, 18, 299-309.
• Wang, J., Zhang, D., and Zhang, J. (2015). Mean reversion in stock prices of seven Asian stock markets: Unit root test and stationary test with Fourier functions. International Review of Economics & Finance, 37, 157-164.
• Yilancı, V. (2012). Mean Reversion In Stock Prices Of G7 Countrıes: Evidence From Panel SURADF And Panel SURKSS Tests. Actual Problems of Economics, 5, 380-385.
• Yilanci, V., Ozkan, Y., and Altinsoy, A. (2020). Testing the Unemployment Hysteresis in G7 Countries: A Fresh Evidence from Fourier Threshold Unit Root Test. Romanian Journal of Economic Forecasting, 23(3), 49.
• Zhu, Z. (1998). The random walk of stock prices: evidence from a panel of G7 countries, Applied Economics Letters, 5, 411-3.
• Zivot, E. and 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.