Continuous Time Model Of Nonparametric To Set Test Problem

In mathematical finance,there has been the development of a large literature on the estimation of the continuous-time models, however, there is relatively little effort on specification analysis for continuous-times models. Model misspecificaton generally leads to misleading conclusions in inference and hypothesis testing, more, misspecified model can yield large errors in pricing,hedging,and risk management.It is important to develop an effective non-parametric method to test the reliable specification tests for continuous-time models.In this paper, we trying to do something to solve the problem. We reviewed the fruit of continuous-time models estimation in theory and applications, then discussed the nonparametric specification test problem in continuous-time models.At first, we discussed the two nonparametric specification tests for continuous-time models.The first method using the marginal density made by Sahali,the other one using the transition density made by Hong. Then we compared and analyzed these two methods for the four scenarions for simulation analysis by 100 data generated with simulation.Finally,the result show that Hong's method over the trend to accept the null hypothesis. Sahalia's method over the trend to reject the null hypothesis.Secondlly, based on the theoretical basis, in Hong's method we judge whether the series {Zτ}τ=1 n is i.i.d. U[0,1] through chisquare goodness of fit test, and we calculating statistics using a set of smoothing bandwidths instead of a single bandwidth to make the test less dependent on single bandwidth.We select the geometric Brown motion as the original hypothesis, CIR model as alternative hypothesis, calculated by analysis of test statistics, indicating that improve the feasibility.Through simulation analysis,we found the method still over the trend to reject the null hypothesis.Finally, we choose individual stocks and exchange rate as a major raw data improived the method of empirical analysis. We chose a growth stock's closing price as data,the result shows that the stock's closing price can be described by geometric Brown motion.The select the RMB against the U.S. dollar as data, the result shows that the exchange rate can be described by CIR motion...