Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods1

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Nonparametric dynamic panel data models: Kernel estimation and specification testing (2013, methodology): “In fact, one can also use noniterative method to solve a Fredholm integral equation of the second kind; see, e.g., Linton and Mammen (2005), Darolles, Fan, Florens, and Renault (2011).”
EFFICIENT SEMIPARAMETRIC ESTIMATION OF THE FAMA-FRENCH MODEL AND EXTENSIONS (2012, methodology): “…2jt(11) + 1 T T∑ t=1 ∑ k =j fjtfktE[gk(Xki)|Xji = xj] Doing this for each j = 1 J, we obtain a system of implicit linear equations for g given f , that is, a system of integral equations (of type 2) in the functional parameter g; see Mammen, Linton, and Nielsen (1999) and Linton and Mammen (2005).”
News - Good or Bad - and its Impact on Volatility Predictions over Multiple Horizons (2011, methodology): “12 12The practical implementation of the above estimator is basically the same as in Linton and Mammen (2005), and therefore omitted.”
A flexible semiparametric forecasting model for time series (2015, methodology): “Linton and Mammen (2005) considered the semiparametric (volatility) regression model E(Y 2t |Yt−1, Yt−2 . . .) = ∞∑ j=1 ψj(θ)m(Yt−j), where m(·) is an unknown function and the parametric family {ψj(θ), θ ∈ Θ, j = 1, . . . ,∞} satisfies some regularity conditions.”