A central limit theorem for quadratic forms in strongly dependent linear (or moving average) variables is proved, generalizing the results of Avram [-1] and Fox and Taqqu [-3] for Gaussian variables. The theorem is applied to prove asymptotical normality of Whittle's estimate of the parameter of strongly dependent linear sequences.
This paper studies a broad class of nonnegative
ARCH(∞) models. Sufficient conditions for the existence
of a stationary solution are established and an explicit
representation of the solution as a Volterra type series
is found. Under our assumptions, the covariance function
can decay slowly like a power function, falling just short
of the long memory structure. A moving average representation
in martingale differences is established, and the central
limit theorem is proved.
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