Coefficients are usually difficult to interpret from an economic point of view. There exists a danger of potential overfitting,in the sense that nonparametric method,due to its flexibility,tends to capture non-essential features in a data which will not appear in out-of-sample scenarios. The above two motivating examples are the so-called orthogonal series expansion methods.There are other nonparametric methods,such as splines smoothing,kernel smoothing,k-near neighbor,and local polynomial smoothing.As mentioned earlier, series expansion methods are examples of so-called global smoothing,because the coefficients are estimated using all observations,and they are then used to evaluate the values of the underlying function over all points in the support of Xt.A nonparametric series model is an increasing sequence of parametric models,as the sample size T grows. In this sense,it is also called a sieve estimator.In contrast,kernel and local polynomial methods are examples of the so-called local smoothing methods,because estimation only requires the observations in a neighborhood of the point of interest.Below we will mainly focus on kernel and local polynomial smoothing methods,due to their simplicity and intuitive nature. 2 Kernel Density Method 2.1 Univariate Density Estimation Suppose IXt}is a strictly stationary time series process with unknown marginal PDF g(x). Question:How to estimate the marginal PDF g(r)of the time series process [X)? We first consider a parametric approach.Assume that g(r)is an N(u,o2)PDF with unknown u and o2.Then we know the functional form of g()up to two unknown parameters 0 =(u,o2)': -a -, -00<x<00 10 Coe¢ cients are usually di¢ cult to interpret from an economic point of view.  There exists a danger of potential overÖtting, in the sense that nonparametric method, due to its áexibility, tends to capture non-essential features in a data which will not appear in out-of-sample scenarios. The above two motivating examples are the so-called orthogonal series expansion methods. There are other nonparametric methods, such as splines smoothing, kernel smoothing, k-near neighbor, and local polynomial smoothing. As mentioned earlier, series expansion methods are examples of so-called global smoothing, because the coe¢ cients are estimated using all observations, and they are then used to evaluate the values of the underlying function over all points in the support of Xt . A nonparametric series model is an increasing sequence of parametric models, as the sample size T grows. In this sense, it is also called a sieve estimator. In contrast, kernel and local polynomial methods are examples of the so-called local smoothing methods, because estimation only requires the observations in a neighborhood of the point of interest. Below we will mainly focus on kernel and local polynomial smoothing methods, due to their simplicity and intuitive nature. 2 Kernel Density Method 2.1 Univariate Density Estimation Suppose fXtg is a strictly stationary time series process with unknown marginal PDF g(x): Question: How to estimate the marginal PDF g(x) of the time series process fXtg? We Örst consider a parametric approach. Assume that g(x) is an N(; 2 ) PDF with unknown  and  2 : Then we know the functional form of g(x) up to two unknown parameters  = (; 2 ) 0 : g(x; ) = 1 p 22 exp  ￾ 1 2 2 (x ￾ ) 2  ; ￾1 < x < 1: 10