Bernstein polynomial estimation of a spectral density
Kakizawa, Y.
2006 Journal of Time Series Analysis, 27(2)
Kakizawa, Y., (2006), "Bernstein polynomial estimation of a spectral density", Journal of Time Series Analysis, 27(2).
Abstract:
We consider an application of Bernstein polynomials for estimating a spectral density of a stationary process. The resulting estimator can be interpreted as a convex combination of the (Daniell) kernel spectral density estimators at m points, the coefficients of which are probabilities of the binomial distribution bin(m???1,?|¦Ë|/¦Ð), ¦Ë?¡Ê?¦°?¡Ô?[?¦Ð,?¦Ð] being the frequency where the spectral density estimation is made. Several asymptotic properties are investigated under conditions of the degree m. We also discuss methods of data-driven choice of the degree m. For a comparison with the ordinary kernel method, a Monte Carlo simulation illustrates our methodology and examines its performance in small sample.
