Sieve-Block Bootstrap Sampling Method for Precision Estimation of Time Series AR Model Considering Random Errors of Design Matrix Errors

Objectives The traditional least square method cannot take into account the random errors of design matrix when solving the time series auto-regressive (AR) 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 We introduce 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. We define the Sieve-block Bootstrap sampling method for precision estimation of AR model conside‑ring random errors of design matrix. According to the different blocking criteria and sampling strategies, we give four detailed resampling procedures.

Results The real case of BeiDou satellite navigation system satellite precision clock offsets shows that the root mean square (RMS) of Sieve-moving block Bootstrap method, Sieve-nonoverlapping block Bootstrap method, Sieve-circular block Bootstrap method and Sieve-stationary block Bootstrap method are compared with the RMS of total least squares method, decreased by 70.25%, 78.65%, 70.89% and 79.24%, respectively.

Conclusions The experimental results 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.