Bernstein polynomial estimation of a spectral density

Yoshihide Kakizawa

Journal of Time Series Analysis, 2006, vol. 27, issue 2, 253-287

Abstract: 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, |λ|/π), λ ∈ Π ≡ [−π, π] 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.

Date: 2006
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https://doi.org/10.1111/j.1467-9892.2005.00465.x

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