Abstract: Based on nonstationary bilinear model of Kalman filter,applying the simulated annealing algorithm to calculate the maximum likelihood function value,Monte Carlo simulation shows that BIAS and RMSE of estimator based on Kalman filter is smaller than OLS.By the test of six price index applying the Kalman filter,the null hypothesis of no bilinearity is rejected for one out of six series,except real estate sales price index,but consumer price index,retail price index and export price index are explosive.

Key words: nonstationary bilinear process, kalman filter, simulated annealing, price index, explosive