Time Series Modeling of Extreme Losses Values Based on a Spectral Analysis Approach

Document Type : Research Paper


1 , Assistant Prof., Department of Financial Management, Faculty of Management, Payame Noor University, Yazd, Iran.

2 Assistant Prof., Department of Statistics, Faculty of Statistics, Payame Noor University, Yazd, Iran.


Objective: Because data analysis for modeling extreme values ​​in financial literature is of interest to researchers and in financial markets and is considered by market risk managers, identifying new and appropriate approaches can provide analysts with insight into predicting very rare events. Analyzing very rare events by time distribution is one of the most appropriate approaches to risk analysis. This study aims to combine the time analysis and spectral analysis approach to identify and present a new approach in extracting and analyzing overt and covert fluctuations along all possible longitudinal wavelengths, to identify stock price behavior and its fluctuations.
Methods: According to the defined algorithm, the extreme losses are extracted for each share in the period under review and are defined as a time series according to the time distribution. For the time series obtained, the iterative structural model was performed using a multi-harmonic analysis and variance analysis approach and the hidden fluctuations in maximum loss yields were identified with varying degrees of quality and then estimated with the highest quality period according to a sinusoidal relationship. For this purpose, the stock price has been used for the statistical period of 1998-1997 (20 years) and includes 105 companies listed on the Tehran Stock Exchange.
Results: The results showed that using the findings of the proposed 460-day cycle method, the most appropriate and high-quality cycle in detecting fluctuations in the time series can be examined. Besides, based on the mentioned cycle, the parameters of the estimated sinusoidal pattern are significant. The fitness test also showed that 78% of the yield changes could be identified by the proposed model.
Conclusion: Applying a combined approach to time-series analysis and spectral analysis has the necessary competence in describing the time-series behavior of corporate stock returns. Therefore, the proposed model can be used for forecasting and analysis in the capital market.


Barkish, A. (2015). Analysis of downwards waves in Tse with wavelets. Financial engineering and security management, 6(25), 155-174. (in Persian)
Dorodi, D. & Abrahimi, B. (2017). Presenting a new hybrid method for predicting the Stock Exchange price index. Financial Research Journal, 18(4), 613-632. (in Persian)
Fallahpour, S., & Tabasi, H. (2020). Estimation of Expected Shortfall Based on Conditional Extreme Value Theory Using Multifractal Model and Intraday Data in Tehran Stock Exchange. Financial Research Journal, 22(1), 27-43. (in Persian)
Jeon, S., Hong, B., Chang, V. (2017). Pattern graph tracking-based stock price prediction using big data. Future Generation Computer Systems, 80, 171-187.
Jung, A., Young, D., Hue, S. (2019). Handling Black Swan Events in Deep Learning with Diversely Extrapolated Neural Networks. Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence, 2140-2147
Lomb, N.R. (1976). Least-squares frequency analysis of unequally spaced data. Astrophysics and Space Science, 39, 447-462.
Manhire, J. (2018). Measuring Black Swans in Financial Markets. Journal of Mathematical Finance, 8(1), 277-239.
Nikusokhan, M. (2018). An Improved Hybrid Model with Automated Lag Selection to Forecast Stock Market. Financial Research Journal, 20(3), 389-408. (in Persian)
Pazoki, N., Hamidian, A., Mohammadi, Sh., & Mahmoudi, V. (2013). Correlation Analysis of Stock Exchange Index, Oil price, Exchange Rate and Gold price: A Wavelet Decomposition Method. Knowledge investment, 2(7), 131-148. (in Persian)
Sabrina, M. & Levo, D. (2017). The Neural Basis of Loss Aversion in Decision-Making under Risk. Science, 18(315), 255-269.
Sadeghi, H. & Behboodi, S. (2016). Using Extreme Value Theory to Estimate Value at Risk (Case Study: Foreign Exchange rate). Asset management & financing, 4(2), 77-794.
(in Persian)
Sadeghi, H. & Dehghani firoozabadi, Z.(2017). Denoising of financial time series using wavelet analysis. Financial engineering and portfolio management, 8(33), 299-315. (in Persian)
Sajjad, R., Hedayati, Sh., Hedayati, Sh. (2013). Estimation of Value at Risk by using Extreme Value Theory. Knowledge investment, 3(9), 133-156. (in Persian)
Saranj, A., Nourahmadi, M. (2017), Statistical ranking of different VaR and ES models by using Model Confidence Set approach for the banking industry: With an emphasis on Conditional Extreme Value Theory. Financial engineering and security management, 8(30), 131-146. (in Persian)
Scargle, J. D. (1982). Studies in astronomical time series analysis. Astrophysical Journal, 343, 835-853.
Schwarzenberg, A., Czerny, P. (1998). The distribution of empirical periodograms: Lomb–Scargle and PDM spectra. Monthly Notices of the Royal Astronomical Society, 3(21), 831-840.
Shahrzadi, M., Foroghi, D., & Amiri, H. (2019). The Effect of Left Tail Risk on Expected Excess Returns and Its Consequences on the Persistence of Left Tail Returns. Financial Research Journal, 21(4), 593-611. (in Persian)