Abstract
Let r(j) denote the jth autocorrelation based on a sample of N consecutive observations on a stationary linear stochastic process. Under mild regularity conditions on the process, an iterated logarithm result is given for the convergence of r(j) as N → ∞ to the corresponding process autocorrelation ρ( j).
Received December 7, 1972; revised June 21, 1973.
AMS 1970 subject classification. Primary: 62M10; Secondary: 60F15.
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Hannan, E. J. (1960). Time Series Analysis. Methuen, London.
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Heyde, C. C and Scott, D. J. (1973). Invariance principles for the law of the iterated logarithm for martingales and processes with stationary increments. Ann. Probability 1 428–436.
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Heyde, C.C. (2010). An Iterated Logarithm Result for Autocorrelations of a Stationary Linear Process. In: Maller, R., Basawa, I., Hall, P., Seneta, E. (eds) Selected Works of C.C. Heyde. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5823-5_35
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DOI: https://doi.org/10.1007/978-1-4419-5823-5_35
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