HETEROSKEDASTİK VERİLERDE BİLİNMEYEN DEĞİŞİM NOKTALARININ TESPİT EDİLMESİ

Year 2023, Volume: 24 Issue: 2, 81 - 98, 31.12.2023

Sıdıka Başçı Asad Ul Islam Khan

https://doi.org/10.24889/ifede.1300907

Abstract

Bilinmeyen değişim noktalarında yapısal değişimi tespit etmek için birkaç test vardır. Andrews Sup F testi (1993) en güçlüsüdür, ancak eş varyans varsayımını gerektirir. Ahmed ve ark. (2017), bu varsayımı gevşeten ve hem regresyon hem de varyans katsayılarındaki değişiklikleri aynı anda test eden Sup MZ testini tanıttı. Bu çalışmada, bilinmeyen değişim noktalarındaki yapısal değişiklikleri tespit etmek için Sup MZ testini kullanan bir model güncelleme prosedürü öneriyoruz. Bu prosedürü, İstanbul Menkul Kıymetler Borsası hisse senedi endeksinin (BIST 100) 21 yıllık (2003-2023) haftalık getirilerini modellemek için uyguluyoruz. Modelimiz, bilinmeyen zamanlarda ortalama veya varyans seviyesinde ara sıra sıçramalar ile basit bir ortalama artı gürültüden oluşur. Amaç, bu sıçramaları tespit etmek ve modeli buna göre güncellemektir. Ayrıca, prosedürümüzdeki tahminleri kullanan ve bunu al ve tut stratejisiyle karşılaştıran bir ticaret kuralı öneriyoruz.

Keywords

yapısal değişim, bilinmeyen değişim noktaları, Sup MZ testi, İstanbul borsası, tahmin

DETECTING UNKNOWN CHANGE POINTS FOR HETEROSKEDASTIC DATA

Abstract

There are several tests to detect structural change at unknown change points. The Andrews Sup F test (1993) is the most powerful, but it requires the assumption of homoskedasticity. Ahmed et al. (2017) introduced the Sup MZ test, which relaxes this assumption and tests for changes in both the coefficients of regression and variance simultaneously. In this study, we propose a model update procedure that uses the Sup MZ test to detect structural changes at unknown change points. We apply this procedure to model the weekly returns of the Istanbul Stock Exchange's common stock index (BIST 100) for a 21-year period (2003-2023). Our model consists simply a mean plus noise, with occasional jumps in the level of mean or variance at unknown times. The goal is to detect these jumps and update the model accordingly. We also suggest a trading rule that uses the forecasts from our procedure and compare it to the buy-and-hold strategy.

Keywords

structual change, unknwn change points, Sup MZ test, Istanbul stock exchange, forecast

References

• Andrews, D. W. (1993). Tests for Parameter Instability and Structural Change with Unknown Change Point. Econometrica, 61(4), 821-856.
• Andrews, D. W., Lee, I & Ploberger W. (1996). Optimal Change Point Tests for Normal Linear Regression. Journal of Econometrics, 70, 9-38.
• Ahmed, M., Haider, G., & Zaman, A. (2017). Detecting structural change with heteroskedasticity. Communications in Statistics -Theory and Methods, 46(21), 10446-10455.
• Basci, E., Basci, S., & Zaman, A. (2000). A method for detecting structural breaks and an application to the Turkish stock market. METU Studies in Development, 27(1-2), 35-45.
• Bai, J. (1994). Least squares estimation of a shift in linear processes. Journal of Time Series Analysis, 15(5), 453-472.
• Boutahar, M. (2012). Testing for change in mean of independent multivariate observations with time varying covariance. Journal of Probability and Statistics, 2012, 1-17.
• Boutahar, M. (2018). Testing for change in mean of heteroskedastic time series. Cornell University, https://arxiv.org/abs/1102.5431.
• Chernoff, H., & Zacks, S. (1964). Estimating the current mean of a normal distribution which is subjected to changes in time. The Annals of Mathematical Statistics, 35(3), 999-1018.
• Chu, C., J. (1990). The Econometrics of Structural Change, Dissertation, University of California, San Diego. Hawkins, D. M. (1977). Testing a sequence of observations for a shift in location. Journal of the American Statistical Association, 72(357), 180-186.
• Hinich, M. J., Foster, J., & Wild, P. (2010). A statistical uncertainty principle for estimating the time of a discrete shift in the mean of a continuous time random process. Journal of Statistical Planning and Inference, 140(12), 3688-3692.
• Hinkley, D. V. (1970). Inference about the change-point in a sequence of random variables. Biometrika, 57(1), 1-17.
• James, B., James, K. L., & Siegmund, D. (1987). Tests for a change-point. Biometrika, 74(1), 71-83.
• James, B., James, K. L., & Siegmund, D. (1992). Asymptotic approximations for likelihood ratio tests and confidence regions for a change-point in the mean of a multivariate normal distribution. Statistica Sinica, 2(1), 69-90.
• Jewell, S., Fearnhead, P., & Witten, D. (2022). Testing for a change in mean after changepoint detection. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84(4), 1082-1104.
• Kasman, A., & Kırkulak, B. (2007). Türk hisse senedi piyasası etkin mi? Yapısal kırılmalı birim kök testlerinin uygulanması. Iktisat Isletme ve Finans, 22(253), 68-78.
• Kim, J. H., & Ryu, J. E. (2006). Test and Estimation for Normal Mean Change. Communications for Statistical Applications and Methods, 13(3), 607-619.
• Lee, B. H., & Wei, W. W. (2017). The use of temporally aggregated data on detecting a mean change of a time series process. Communications in Statistics-Theory and Methods, 46(12), 5851-5871.
• Li, Y. X. (2006). Change-point estimation of a mean shift in moving-average processes under dependence assumptions. Acta Mathematicae Applicatae Sinica, 22(4), 615-626.
• Maasoumi, E., Zaman, A., & Ahmed, M. (2010). Tests for structural change, aggregation, and homogeneity. Economic Modelling, 27(6), 1382-1391.
• Wang, D., Yu, Y., & Rinaldo, A. (2020). Univariate mean change point detection: Penalization, cusum and optimality. Electronic Journal of Statistics, 14, 1917-1961.
• Worsley, K. J. (1979). On the likelihood ratio test for a shift in location of normal populations. Journal of the American Statistical Association, 74(366a), 365-367.