Parametric Inference For A Class Of Moving Averages Driven By Brownian Motions

Research on non-independent random variable sequence has a very pro-found theoretical and practical meaning. This paper is concerned with sim-ulation and parameter estimation method for a class of moving averages driven by Brownian motions. The moving average is a Gaussian process with mean O, and whose autocorrelation functions take on both periodic and regressive properties.According to the feature of the moving average, the moving average is simulated by the Davies and Harte method and the Hosking method. The main advantage of the Davies and Harte method is the fast speed. There-fore, the method is more practical in the large sample size. The advantage of the Hosking method is that the simulation can stop at a random time, the sample size does not need to be known in advance. Therefore, when the sample size is very small, the sample path can be accurately simulated with the method.By researching on the relationship between the parameter and auto-covariance function, the moment estimator of the parameter is constructed. By analyzing the spectral density of the discretely sampled trajectory, the properties of the mixing coefficient are captured. Further, the consistency and asymptotic normality of the moment estimator are proved. And the true values of the different parameters are estimated with the moment method of estimation, simulation study shows that the estimator achieves good performance even in the small-sample circumstances. Finally, a set of data from the hull strength detection system are analyzed. The real data analysis evidences that the model can be used to depict the ship hull stress data.For the smaller mean squared error of estimator, the generalized method of moments is constructed. By analyzing the spectral density of the dis-cretely sampled trajectory, the properties of the mixing coefficient are cap-tured. Further the consistency and asymptotic normality of the generalized method of moments estimator are proved. And the true values of the dif-ferent parameters are estimated with the generalized method of moment, simulation study shows that the mean squared error of the generalized method of moments estimator is smaller than the moment estimator’s. Fi-nally, a set of data from the hull strength detection system are analyzed. The real data analysis evidences that the model can be used to depict the ship hull stress data.