Distance test method for dynamic simulation results

A concept of mean Mahalanobis distance between time series and its simulation result is presented. Based on the concept, a distance test method for dynamic simulation results is established. The rejection regions for dynamic simulation results in normal distributions are given, and a two-step simulation method of determining the rejection regions in non-normal distributions is presented. By the method, dynamic simulation results can be tested at a high confidence level according to one measured sample function or multiple measured sample functions. This method has no limitation for time series, namely suitable for the stationary and the non-stationary time series. Furthermore, test method for equality between covariance matrixes of time series and its simulation result is given in the normal and the non-normal distribution respectively. A standardized distance test method for dynamic simulation results is also established.