Research On Abnormal Shocks Of Stock Market And Risk Measurement Based On Wavelet Analysis

Volatility of financial assets is a potential characteristic of all financial time series.It is a necessary part of portfolio management,financial assets pricing;it's also important for risk management such as VaR evaluation and other financial fields.In particular,it is of great significance for investors and regulators to understand the financial volatility model and to study the related anomaly detection.In practice,the characteristics of financial volatility usually come from a series of regressions of financial assets.This paper studies outliers detection of financial return time series through a new method combining wavelet analysis.Firstly,a new method combining wavelet analysis,based on certain financial volatility models,is come up with to detect outliers in financial time series.Through applying discrete wavelet transform to certain mother wave,we get the wavelet coefficient vectors.Secondly,an outlier detection and location method based on wavelet transform is proposed to analyze the time series of financial returns.After using the volatility model for the time series of financial returns,the residual series can be obtained.The location of the maximum value which is greater than the threshold value obtained from Monte Carlo simulation in the series of wavelet coefficients is shown.The convenience and effectiveness of the refered method are empirically demonstrated with the Shanghai Composite Index.The outlier detection and location method based on wavelet is implemented to analyze these series,empirical result shows that it can effectively detects the series' outliers and accurately locates them.From the result of Grane and Veiga(2009),it is known that the existence of outliers,even at a small scale,can lead to deviations in estimating the minimum capital risk requirement(MCRR),a measure of risk used by financial institutions,including part of capital.It should be retained to absorb the predetermined percentage of unforeseen losses.This strengthens the importance of outlier detection,because accurate estimation of MCRR is essential to avoid wasting valuable resources.This paper concentrates on the detection of additive(level and volatility)outliers through wavelet transforming.Innovation outliers are not very important to the dynamic characteristics of a series,because they propagate through the same dynamics,just like other parts of the series.Wavelets are a series of basis functions that allow the representation and approximation of other functions.In fact,the wavelet coefficients can detect variances,horizontal changes and discontinuities in functions.Our method was inspired by Bilen and Huzurbazar(2002).They proposed an outliers detection method based on wavelet transforming,but differed from them in the way of obtaining threshold limits.They used Donoho's and Johnstone's(1994)and Wang's(1995)proposals,which relied on data from standard normal distribution.In addition,because their threshold limits are very conservative,their programs result in very high average false outliers.On the other hand,our method of calculating threshold limits is based on the distribution of the maximum detail coefficient(absolute value)obtained by Monte Carlo.In fact,the threshold is considered to be the 95 th percentile of the maximum distribution.In this way,our program can be applied to estimate the residual of different volatility models with errors that follow any known distribution.We determine the events that cause large shocks in volatility of the Shanghai composite index over the period 1990–2019,using the Wavelet-based detection based on conditional heteroscedasticity models.We find that these large shocks can be associated with particular events(financial events,political events,monetary policies,etc.).We show that some shocks are not identified as extraordinary movements by the investors due to their occurring during high volatility episodes.