This is Chapter 6 of a manuscript entitled as Modern Time Series Analysis:Theory and Applications written by the author.We will introduce some popular nonparametric methods,particularly the kernel smoothing method and the local polynomial smoothing method,to estimate functions of interest in time series contexts,such as probability density functions,autoregression functions,spectral density functions,and generalized spectral density functions.Empirical applications of these functions crucially depend on the consistent estimation of these functions.We will discuss the large sample statistical properties of nonparametric estimators in various contexts. Key words:Asymptotic normality,bias,boundary problem,consistency,curse of di- mensionality,density function,generalized spectral density,global smoothing,integrated mean squared error,law of large numbers,local polynomial smoothing,local smoothing, locally stationary time series model,mean squared error,kernel method,regression func- tion,series approximation,smoothing,spectral density function,Taylor series expansion, variance. Reading Materials and References This lecture note is self-contained.However,the following references will be useful for learning nonparametric analysis. (1)Nonparametric Analysis in Time Domain Silverman,B.(1986):Nonparametric Density Estimation and Data Analysis.Chap- man and Hall:London. Hardle,W.(1990):Applied Nonparametric Regression.Cambridge University Press:Cambridge. Fan,J.and Q.Yao (2003),Nonlinear Time Series:Parametric and Nonparametric Methods,Springer:New York. (2)Nonparametric Methods in Frequency Domain Priestley,M.(1981),Spectral Analysis and Time Series.Academic Press:New York. .Hannan,E.(1970),Multiple Time Series,John Wiley:New York 2This is Chapter 6 of a manuscript entitled as Modern Time Series Analysis: Theory and Applications written by the author. We will introduce some popular nonparametric methods, particularly the kernel smoothing method and the local polynomial smoothing method, to estimate functions of interest in time series contexts, such as probability density functions, autoregression functions, spectral density functions, and generalized spectral density functions. Empirical applications of these functions crucially depend on the consistent estimation of these functions. We will discuss the large sample statistical properties of nonparametric estimators in various contexts. Key words: Asymptotic normality, bias, boundary problem, consistency, curse of di￾mensionality, density function, generalized spectral density, global smoothing, integrated mean squared error, law of large numbers, local polynomial smoothing, local smoothing, locally stationary time series model, mean squared error, kernel method, regression func￾tion, series approximation, smoothing, spectral density function, Taylor series expansion, variance. Reading Materials and References This lecture note is self-contained. However, the following references will be useful for learning nonparametric analysis. (1) Nonparametric Analysis in Time Domain  Silverman, B. (1986): Nonparametric Density Estimation and Data Analysis. Chap￾man and Hall: London.  H‰rdle, W. (1990): Applied Nonparametric Regression. Cambridge University Press: Cambridge.  Fan, J. and Q. Yao (2003), Nonlinear Time Series: Parametric and Nonparametric Methods, Springer: New York. (2) Nonparametric Methods in Frequency Domain  Priestley, M. (1981), Spectral Analysis and Time Series. Academic Press: New York.  Hannan, E. (1970), Multiple Time Series, John Wiley: New York. 2