Large deviations for moving average processes
نویسندگان
چکیده
منابع مشابه
Moving Average Processes with Infinite Variance
The sample autocorrelation function (acf) of a stationary process has played a central statistical role in traditional time series analysis, where the assumption is made that the marginal distribution has a second moment. Now, the classical methods based on acf are not applicable in heavy tailed modeling. Using the codifference function as dependence measure for such processes be shown it be as...
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Abstract The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change dramatically. We study this phenomenon in the context of functional large, moderate and huge deviation principles.
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متن کاملLarge Deviations for Stochastic Processes
The purpose of these lectures is to introduce you to the basics of large deviation theory. The emphasis will be on the use of compactness ideas (more extensive results are in Puhalskii [13]). Other approaches to large deviation theory are considered in Dembo and Zeitouni [3], den Hollander [4], Deuschel and Stroock [6], Dupuis and Ellis [7], Freidlin and Wentzell [9], Kallenberg [12], Shwartz a...
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Let X(δ) be a Wishart process of dimension δ, with values in the set of positive matrices of size m. We are interested in the large deviations for a family of matrix-valued processes {δ−1X t , t ≤ 1} as δ tends to infinity. The process X(δ) is a solution of a stochastic differential equation with a degenerate diffusion coefficient. Our approach is based upon the introduction of exponential mart...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1995
ISSN: 0304-4149
DOI: 10.1016/0304-4149(95)95687-p