Some Studies On Complex Financial Time Series

Since the complexity and irreversibility analysis of time series have been widely studied in multiple subjects,all kinds of analysis methods have been extensively applied in physics,medicine,biological science,economics and other fields.In this paper,we introduce several novel methods on the measurement of complexity and irreversibility of time series.What is more,we apply these methods on financial time series and discuss the results.First,we put forward the sequence compositional complexity(SCC)method.This method gives us a way to separate a long non-stationary complex time sequence into a set of short stationary time series.What is more,it is also a good method to quantify the complexity of time series.We apply SCC method into stock indices of Chinese stock markets and foreign stock markets.From the results,we find that values of SCC of the foreign stock indices are likely to be lower than the SCC value of Chinese indices data.What is more,we find that,if we classify the indices with the method of SCC,HSI,which is the stock index of Hong Kong,has more similarities with mature foreign markets than Chinese ones.These results show that SCC method is a good tool of complexity quantification.Second,we also introduce another novel method on the quantification of complexity of time series,weighted multiscale Renyi permutation entropy(WMPRE)method.WMPRE method can quantify the amplitude information carried by the signals of stock markets more accurately.For comparison,we also give the introduction of multiscale Renyi permutation entropy(MPRE)method and apply these two methods into the stock indices both in and out of China.We find that,comparing with MPRE,WMPRE method has a better property on distinguish the Chinese stock indices from foreign ones.The results also show a similar consequence with SCC method that HSI has more similarities with mature foreign stock markets instead of Chinese markets.Third,we put forward a new method to define the irreversibility of long non-stationary time series which is based on the visibility graph approach and entropy segmentation.By means of SCC method,visibility graph approach and IOTA,we figure out a way to quantify the irreversibility of time series.We call this approach as HVg-SCC-IOTA method.Different from other methods which are already proposed,HVg-SCC-IOTA creatively combines the visibility graph and IOTA together to measure the irreversibility.What is more,due to the use of SCC method,we expand the irreversibility quantification to long non-stationary time series as the past methods can only method short stationary ones.For practice,we apply the HVg-SCC-IOTA method into financial time series and analyze the results.Finally,we introduce the multivariate Generalized autoregressive conditional heteroskedasticity(MVGARCH)model and apply this model into the Capital asset pricing model(CAPM).The CAPM tells us about the relationship between one single asset and the whole market portfolio with a well-known measurement β.But β cannot explain the relationship as time changes since β is constant with time.What is more,β dose not consider the interaction among different assets.To overcome these drawbacks,we introduce MVGARCH model into the CAPM since it is based on the conditional covariance matrix which makes the model change with time.We apply the CAPM-MVGARCH model into FTSE 100 index and its factor stocks and compare with the CAPM method.From the results,we find that CAPM-MVGARCH model does better in variance control and makes β more explainable on the relationships between single asset and the whole market as β changes with time.What is more,we propose a new idea on the analysis on investment portfolio.