The Source And Nature of Long Term Memory in the Business Cycle
The Source And Nature of Long Term Memory in the Business Cycle
Joseph Gerard Haubrich
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Although aware of this bias, Mandelbrot (1972, 1975) did not correct for it since his focus was on the relation of the R/S statistic's logarithm to the logarithm of the sample site, which involves no statistical inference; such a relation clearly is unaffected by short-term dependence 2. 7 - 17 - 8. 89 {A2) suptE\\et\^] 2. {A3) a^ = limn- -ni^U^if exists and a > 0. {A4) {et} is strong-mixing with mixing coefficients a;, that satisfy 19 °° l_i k=l Condition [Al) is standard. Conditions {A2) thr...ough {A4) are restrictions on the maximal degree of dependence and heterogeneity allowable while still permitting some form of the law of large nimibers and the [functional] central limit theorem to obtain. Note that we have not assumed stationarity. Although condition (. 42) rules out infinite variance marginal distributions of et such as those in the stable family with characteristic exponent less than 2, the disturbances may still exhibit leptokurtosis via time-varying conditional moments [e.
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