Abstract
We consider a (nonlinear) autoregressive model with unknown parameters (vector θ). The aim is to estimate the density of the residuals by a kernel estimator. Since the residuals are not observed, the usual procedure for estimating the density of the residuals is the following: first, compute an estimator \(\hat \theta \) for θ; second, calculate the residuals by use of the estimated model; and third, calculate the kernel density estimator by use of these residuals. We show that the resulting density estimator is strong consistent at the best possible convergence rate. Moreover, we prove asymptotic normality of the estimator.
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Liebscher, E. Estimating the Density of the Residuals in Autoregressive Models. Statistical Inference for Stochastic Processes 2, 105–117 (1999). https://doi.org/10.1023/A:1009924821271
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DOI: https://doi.org/10.1023/A:1009924821271