Copula Theory And Its Applications In Dependency Analysis Of The High-frequence Financial Data

Mastering the dependence structure of financial variables is the key to research themode of operation of the financial system and improve the accuracy rate of investmentstrategy. Compare with the traditional correlation analysis methods, Copulas has theability to describe nonlinear, asymmetric dependence structure, especially has obviousadvantage in the ability to describe the tail dependence, which meet the needs ofresearching the dependence structure of financial variables.The paper made a detailed and systematic introduction of Copula theory, includingthe definition, main properties, types, the corresponding correlation measure and so on,summarized the Copula model establishing method and steps,including the method ofdetermining the marginal distribution function, parameter estimation, model selectionand evaluation of model goodness of fit. And this paper focus on studying thecopula parameter estimation method, gave the introduction of Exact MaximumLikelihood estimation (EML), Inference of margins (IFM), Canonical MaximumLikelihood method (CML), Maximum Likelihood based on Kernel Density method(MLK) and Genest&Rivest estimation method, and then get the conclusion throughanalysis and Monte Carlo simulation: when the sample the marginal distributionfunction is difficult to determine, orthe marginal distribution function fitting effect is notgood, MLK is the best parameter estimation method undoubtedly.Apply the copula theory on the analysis of dependency structure of high-frequency financial data. And construct a new model based on BP neural networkmethod and Copula function, demonstrated the this new model can describe thedependence structure between the stock index futures rate of absolute return andtrading volume. First, fitting the calendar effect by the BP neural network method, thenapply the kernel density estimation method to determine the marginal distribution, thenaccording to the frequency histogram of marginal distribution, select Gumbel copulafunction and mixed Archimedes copula function to fit the samples, and evaluated themodel fitting effect from a variety of dependent measure. The results show that: theGumbel copula function whose parameter has the good description of the dependence structure between the stock index futures rate of absolute return per minute and tradingvolume, caught distinct upper tail dependence, and the lower tail dependence is notobvious, explain from the Investment Behavioral Science: when market fluctuations, thetransaction will lead to large gains or losses, investors’ transaction desire will enhancefor the earnings or capital preservation, so the transaction volume increases; and whenthe market volatility is very smooth and steady, investors will maintain a certain amountof trading volume based on the expection of future market.