Sieve-Block Bootstrap sampling method for precision estimation of the time series AR model considering random errors of design matrix

Objectives: Since the traditional least square method cannot take into account the random errors of design matrix when solving the time series AR (Auto-Regressive) model. In addition, it is difficult for the existing iterative method of AR model to use the propagation of variance and covariance to give the accurate precision estimation formula. Methods: This paper introduces the Block Bootstrap resampling method into the precision estimation research of the AR model, and on the basis of it, the principle of the Sieve Bootstrap is introduced. This paper defines the Sieve-Block Bootstrap sampling method for precision estimation of the AR model considering random errors of design matrix. According to the different blocking criteria and sampling strategies, this paper gives four detailed resampling procedures. Results:The real case of BeiDou Global Navigation Satellite System satellite precision clock offsets shows that the root mean square (RMS)of the Sieve-Moving Block Bootstrap method, Sieve-Nonoverlapping Block Bootstrap method, Sieve-Circular Block Bootstrap method and Sieve-Stationary Block are given in this paper compared with the RMS of total least squares (TLS)method, decreased by 70.25%, 78.65%, 70.89% and 79.24%, respectively. Conclusions:The experimental research and analysis show that the Sieve-Block Bootstrap sampling method can obtain more reliable autoregressive coefficient standard deviations than the least square method and the classical AR model iterative method, and it has stronger applicability.