Removing Bias in Whittle Estimators

• Activity Number: 299
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Adam Sykulski*+ and Sofia Olhede and Jonathan Lilly and Jeffrey Early
• Companies: and University College London and NorthWest Research Associates and NorthWest Research Associates
• Keywords: Whittle likelihood ; frequency domain ; locally stationary ; stochastic process ; time series ; Fourier transform

Abstract

We present a modification of Whittle likelihood inference for time series analysis. The Whittle likelihood estimates parameters of a process from modelling its spectral density, and is commonly used due to its computational speed and accuracy. Our modification, referred to as the blurred Whittle likelihood, accounts for the estimation bias inherent to standard Whittle likelihood for moderate sample sizes. This bias is attributed to blurring - the phenomena of leakage and aliasing when estimating the spectrum from periodograms or tapered versions thereof. Addressing this bias is particularly important when short windows of data are used, which will be the case if a time series is locally and not globally stationary. The bias-correction is performed explicitly in the likelihood equation by evaluating the finite sample properties of the spectral estimate. We demonstrate both theoretically and empirically the importance of this bias-correction. The blurred Whittle likelihood is also computationally faster than standard Whittle likelihood, as aliased frequencies are naturally treated correctly. Finally, we outline extensions to complex-valued and bivariate time series.