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Conditional Information in Projections of Gaussian Vectors

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Conditional information measures the information in a sample for an interest parameter in the presence of nuisance parameter. In the context of Gaussian likelihoods this paper first derives conditions under which a projection of the data may reduce conditional information to zero. These are then applied in the context of time series regressions, and inference on a covariance parameter, such as with either autoregressive or moving average errors. It is shown that regressing out very common regressors, such as a linear trend or dummy variable, can imply that conditional information is zero in the case of non-stationary autoregressions or non-invertible moving averages, respectively.

Keywords: Autoregression; Conditional information; Moving average; Regression

Document Type: Research Article

Affiliations: Department of Economics, University of York, Heslington, York, UK

Publication date: January 1, 2009

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