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With a Fourier transform on the kernel function and the projection method, it is shown that, under certain mild conditions, the estimator \\[ \\frac{2}{n(n-1)h_n} \\sum_{1\\le i<j\\le n}K\\left(\\frac{X_i-X_j}{h_n}\\right) \\] has similar asymptotical properties as the i.i.d. case studied in Gin\\'{e} and Nickl (2008) if the linear process $\\{X_n: n\\in \\mathbb{N}\\}$ has the defined short range dependence. 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