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

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.

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.

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.

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.