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Fortune, Timothy; Peligrad, Magda; Sang, Hailin

A local limit theorem for linear random fields. (English) Zbl 1477.60046

J. Time Ser. Anal. 42, No. 5-6, 696-710 (2021).
Summary: In this article, we establish a local limit theorem for linear fields of random variables constructed from i.i.d. innovations each with finite second moment. When the coefficients are absolutely summable we do not restrict the region of summation. However, when the coefficients are only square-summable we add the variables on unions of rectangle and we impose regularity conditions on the coefficients depending on the number of rectangles considered. Our results are new also for the dimension 1, that is, for linear sequences of random variables. The examples include the fractionally integrated processes for which the results of a simulation study is also included.

Cited in 4 Documents

MSC:

60F05 Central limit and other weak theorems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60G10 Stationary stochastic processes
62G05 Nonparametric estimation

Keywords:

linear random fields; local limit theorem; long memory; regularity condition
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References:

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