Characteristic period analysis of the Chinese stock market using successive one-sided HP filter

Yuxia Liu; Qi Zhang; Wei Xiao; Tianguang Chu; Yuxia Liu; Qi Zhang; Wei Xiao; Tianguang Chu

doi:10.3934/era.2023311

Electronic Research Archive

2023, Volume 31, Issue 10: 6120-6133. doi: 10.3934/era.2023311

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Characteristic period analysis of the Chinese stock market using successive one-sided HP filter

1.
College of Engineering, Peking University, Beijing 100871, China
2.
School of Information Technology and Management, University of International Business and Economics, Beijing 100029, China

Received: 03 April 2023 Revised: 22 August 2023 Accepted: 27 August 2023 Published: 13 September 2023

Time series of stock indices usually exhibit nonstationary and chaotic behavior. Analysis of the characteristics of the business cycle can reveal pertinent insights into the evolution of the stock volatility. This paper studies the characteristic periods of three main Chinese stock indices, i.e., the Shanghai composite index (SHCI), the Shenzhen component index (SZCI), and the Hang Seng index (HSI). We propose an approach based on the successive one-sided Hodrick-Prescott (SOHP) filtering and wavelet analysis of the empirical data from the stock markets, to detect their characteristic periods. In particular, the SOHP filter, which preprocesses the time series with a moving-horizon optimization procedure, enables us to extract the volatility cycles in different time scales from a stock time series and reduce noise distortion. The characteristic period of the stock index is then determined by the maxima of the wavelet power spectrum of the filtered data. The evolution of the characteristic period in time demonstrates rich information concerning the period stability of the stock market, as well as the cause and effect of the stock crash. To facilitate solving the moving-horizon optimization issue of the SOHP filter, we also present an incremental HP filtering algorithm, which greatly simplifies the involved inverse matrix operation in the HP-type filters.
- nonlinear time series,
- characteristic period,
- the successive one-sided HP filter,
- incremental HP filtering algorithm,
- Chinese stock market
Citation: Yuxia Liu, Qi Zhang, Wei Xiao, Tianguang Chu. Characteristic period analysis of the Chinese stock market using successive one-sided HP filter[J]. Electronic Research Archive, 2023, 31(10): 6120-6133. doi: 10.3934/era.2023311

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Abstract

Time series of stock indices usually exhibit nonstationary and chaotic behavior. Analysis of the characteristics of the business cycle can reveal pertinent insights into the evolution of the stock volatility. This paper studies the characteristic periods of three main Chinese stock indices, i.e., the Shanghai composite index (SHCI), the Shenzhen component index (SZCI), and the Hang Seng index (HSI). We propose an approach based on the successive one-sided Hodrick-Prescott (SOHP) filtering and wavelet analysis of the empirical data from the stock markets, to detect their characteristic periods. In particular, the SOHP filter, which preprocesses the time series with a moving-horizon optimization procedure, enables us to extract the volatility cycles in different time scales from a stock time series and reduce noise distortion. The characteristic period of the stock index is then determined by the maxima of the wavelet power spectrum of the filtered data. The evolution of the characteristic period in time demonstrates rich information concerning the period stability of the stock market, as well as the cause and effect of the stock crash. To facilitate solving the moving-horizon optimization issue of the SOHP filter, we also present an incremental HP filtering algorithm, which greatly simplifies the involved inverse matrix operation in the HP-type filters.

References

[1]	N. Salmon, I. SenGupta, Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging, Ann. Finance, 17 (2021), 529–558. https://doi.org/10.1007/s10436-021-00394-4 doi: 10.1007/s10436-021-00394-4
[2]	M. Lin, I. SenGupta, Analysis of optimal portfolio on finite and small-time horizons for a stochastic volatility market model, SIAM J. Financ. Math., 12 (2021), 1596–1624. https://doi.org/10.1137/21M1412281 doi: 10.1137/21M1412281
[3]	T. Mo, C. Xie, K. Li, Y. Ouyang, Z. Zeng, Transmission effect of extreme risks in China's financial sectors at major emergencies: empirical study based on the GPD-CAViaR and TVP-SV-VAR approach, Electron. Res. Arch., 30 (2022), 4657–4673. https://doi.org/10.3934/era.2022236 doi: 10.3934/era.2022236
[4]	X. Hui, B. Sun, I. SenGupta, Y. Zhou, H. Jiang, Stochastic volatility modeling of high-frequency CSI 300 index and dynamic jump prediction driven by machine learning, Electron. Res. Arch., 31 (2023), 1365–1386. https://doi.org/10.3934/era.2023070 doi: 10.3934/era.2023070
[5]	N. T. Vu, Stock market volatility and international business cycle dynamics: evidence from OECD economies, J. Int. Money Finance, 50 (2015), 1–15. https://doi.org/10.1016/j.jimonfin.2014.08.003 doi: 10.1016/j.jimonfin.2014.08.003
[6]	F. Verona, Time–frequency characterization of the U.S. financial cycle, Econ. Lett., 144 (2016), 75–79. https://doi.org/10.1016/j.econlet.2016.04.024 doi: 10.1016/j.econlet.2016.04.024
[7]	P. A. Samuelson, W. D. Nordhaus, Macroeconomics, 18^th edition, Posts & Telecom Press: McGraw-Hill Education (Asia) Co, 2007.
[8]	T. Choudhry, F. I. Papadimitriou, S. Shabi, Stock market volatility and business cycle: evidence from linear and nonlinear causality tests, J. Banking Finance, 66 (2016), 89–101. https://doi.org/10.1016/j.jbankfin.2016.02.005 doi: 10.1016/j.jbankfin.2016.02.005
[9]	R. Bisoi, P. K. Dash, A hybrid evolutionary dynamic neural network for stock market trend analysis and prediction using unscented Kalman filter, Appl. Soft Comput., 19 (2014), 41–56. https://doi.org/10.1016/j.asoc.2014.01.039 doi: 10.1016/j.asoc.2014.01.039
[10]	X. L. Li, J. Yan, X. Wei, Dynamic connectedness among monetary policy cycle, financial cycle and business cycle in China, Econ. Anal. Policy, 69 (2021), 640–652. https://doi.org/10.1016/j.eap.2021.01.014 doi: 10.1016/j.eap.2021.01.014
[11]	R. J. Hodrick, E. C. Prescott, Postwar US business cycles: an empirical investigation, J. Money Credit Banking, 29 (1997), 1–16. https://doi.org/10.2307/2953682 doi: 10.2307/2953682
[12]	J. H. Stock, M. W. Watson, Forecasting inflation, J. Monetary Econ., 44 (1999), 293–335. https://doi.org/10.1016/S0304-3932(99)00027-6 doi: 10.1016/S0304-3932(99)00027-6
[13]	P. C. B. Phillips, Z. Shi, Boosting: why you can use the HP filter, Int. Econ. Rev., 62 (2021), 521–570. https://doi.org/10.1111/iere.12495 doi: 10.1111/iere.12495
[14]	P. Krusell, T. Mukoyama, A. Şahin, Labour-market matching with precautionary savings and aggregate fluctuations, Rev. Econ. Stud., 77 (2010), 1477–1507. https://doi.org/10.1111/j.1467-937X.2010.00700.x doi: 10.1111/j.1467-937X.2010.00700.x
[15]	K. R. Gerdrup, A. B. Kvinlog, E. Schaanning, Key Indicators for a Countercyclical Capital Buffer in Norway - Trends and Uncertainty, 2013. Available from: http://hdl.handle.net/10419/210284.
[16]	Yahoo Finance, Stock data, [EB/OL], 2020. Available from: https://hk.finance.yahoo.com/.
[17]	E. Kočenda, A. Černý, Elements of Time Series Econometrics: An Applied Approach, Charles University in Prague, Karolinum Press, 2015.
[18]	M. Fornasier, H. Rauhut, R. Ward, Low-rank matrix recovery via iteratively reweighted least squares minimization, SIAM J. Optim., 21 (2011), 1614–1640. https://doi.org/10.1137/100811404 doi: 10.1137/100811404
[19]	M. I. Stolbov, M. A. Shchepeleva, A. M. Karminsky, A global perspective on macroprudential policy interaction with systemic risk, real economic activity, and monetary intervention, Financ. Innovation, 7 (2021), 41. https://doi.org/10.1186/s40854-021-00257-x doi: 10.1186/s40854-021-00257-x
[20]	H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, 2^nd edition, Cambridge University Press, Cambridge, 2003.
[21]	L. C. Cao, Y. L. Luo, S. H. Qiu, J. X. Liu, A perturbation method to the tent map based on Lyapunov exponent and its application, Chin. Phys. B, 24 (2015), 100501. https://doi.org/10.1088/1674-1056/24/10/100501 doi: 10.1088/1674-1056/24/10/100501
[22]	A. V. Korotayev, S. V. Tsirel, A spectral analysis of world GDP dynamics: Kondratieff waves, Kuznets swings, Juglar and Kitchin cycles in global economic development, and the 2008–2009 economic crisis, Struct. Dyn., 4 (2010). https://doi.org/10.5070/SD941003306 doi: 10.5070/SD941003306
[23]	P. Chen, A random walk or color chaos on the stock market? Time-frequency analysis of S & P indexes, Stud. Nonlinear Dyn. Econom., 1 (1996). https://doi.org/10.2202/1558-3708.1014 doi: 10.2202/1558-3708.1014
[24]	J. B. Bassingthwaighte, L. S. Liebovitch, B. J. West, Fractal Physiology, Springer, New York, (2013).
[25]	T. Ai, R. Zhang, H. W. Zhou, J. L. Pei, Box-counting methods to directly estimate the fractal dimension of a rock surface, Appl. Surf. Sci., 314 (2014), 610–621. https://doi.org/10.1016/j.apsusc.2014.06.152 doi: 10.1016/j.apsusc.2014.06.152
[26]	Z. Q. Jiang, W. X. Zhou, D. Sornette, R. Woodard, K. Bastiaensen, P. Cauwels, Bubble diagnosis and prediction of the 2005–2007 and 2008–2009 Chinese stock market bubbles, J. Econ. Behav. Organ., 74 (2010), 149–162. https://doi.org/10.1016/j.jebo.2010.02.007 doi: 10.1016/j.jebo.2010.02.007
[27]	D. Sornette, G. Demos, Q. Zhang, P. Cauwels, V. Filimonov, Q. Zhang, Real-time prediction and post-mortem analysis of the Shanghai 2015 stock market bubble and crash, in Swiss Finance Institute Research Paper No. 15–31, 2015. https://doi.org/10.2139/ssrn.2693634
[28]	E. C. Chang, J. W. Cheng, Y. Yu, Short‐sales constraints and price discovery: evidence from the Hong Kong market, J. Finance, 62 (2007), 2097–2121. https://doi.org/10.1111/j.1540-6261.2007.01270.x doi: 10.1111/j.1540-6261.2007.01270.x
[29]	I. Yeung, N. Chiu, An outlier analysis of the Hong Kong stock market index, Appl. Econ. Lett., 7 (2000), 531–534. https://doi.org/10.1080/13504850050033328 doi: 10.1080/13504850050033328
[30]	X. Gui, L. Li, J. Cao, L. Li, Dynamic communities in stock market, Abstr. Appl. Anal., 2014 (2014), 723482. https://doi.org/10.1155/2014/723482 doi: 10.1155/2014/723482
[31]	I. Khajar, The global stock exchange and its influence toward the indonesia stock exchange after the global financial crisis in 2008, Int. J. Organ. Innovation, 8 (2015), 133–154.
[32]	G. Zhang, J. Li, Multifractal analysis of Shanghai and Hong Kong stock markets before and after the connect program, Physica A, 503 (2018), 611–622. https://doi.org/10.1016/j.physa.2018.02.139 doi: 10.1016/j.physa.2018.02.139
[33]	K. J. Lee, S. L. Lu, Y. Shih, Contagion effect of natural disaster and financial crisis events on international stock markets, J. Risk Financ. Manag., 11 (2018), 16. https://doi.org/10.3390/jrfm11020016 doi: 10.3390/jrfm11020016
[34]	T. Alexandra, Global woes hit stocks, [EB/OL], 2022. Available from: https://money.cnn.com/2004/03/22/markets/markets_newyork/index.htm.

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