In this paper, we propose two types of sieve bootstrap, univariate and multivariate approach, for the generalized method of moments estimators of time series data. Compared with the nonparametric block bootstrap, the sieve bootstrap is in essence parametric, which helps fitting data better when researchers have prior information about the time series properties of the variables of interested. Our Monte Carlo experiments show that the performances of these two types of sieve bootstrap are comparable to the performance of the block bootstrap. Furthermore, unlike the block bootstrap, which is sensitive to the choice of block length, these two types of sieve bootstrap are less sensitive to the choice of lag length.

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