This note proposes a tool to investigate and demonstrate the adequacy of the central limit theorem in small samples. The suggested testing procedure provides a method to investigate if the mean estimator is approximately normally distributed, given data and sample size at hand. This is important...

This paper proposes a stylized model that reconciles several seemingly conflicting findings on financial security returns and option prices. The model is based on a pure jump Levy process, wherein the jump arrival rate obeys a power law dampened by an exponential function. The model allows for...

Consider the d-dimensional unit cube [0,1]d and portion it into n regions, A1,..., An. Select and fix a point in each one of these regions so we have x1,..., xn. Consider observable variables Yi, i = 1,..., n, satisfying the multivariate regression model Yi = g(xi) + [var epsilon]i, where g is...

Standardized slowly varying regressors are shown to be $L_p$-approximable. This fact allows one to relax the assumption on linear processes imposed in central limit results by P.C.B. Phillips, as well as provide alternative proofs for some other statements.

Portfolio credit risk measurement is greatly affected by data constraints, especially when focusing on loans given to unlisted firms. Standard methodologies adopt convenient, but not necessarily properly specified parametric distributions or simply ignore the effects of macroeconomic shocks on...

Let (Xn) be a sequence of integrable real random variables, adapted to a filtration (Gn). Define: Cn = n^(1/2) {1/n SUM(k=1:n) Xk - E(Xn+1 | Gn) } and Dn = n^(1/2){ E(Xn+1 | Gn)-Z } where Z is the a.s. limit of E(Xn+1 | Gn) (assumed to exist). Conditions for (Cn,Dn) -- N(0,U) × N(0,V) stably...

An urn contains balls of d = 2 colors. At each time n = 1, a ball is drawn and then replaced together with a random number of balls of the same color. Let An =diag (An,1, . . . ,An,d) be the n-th reinforce matrix. Assuming EAn,j = EAn,1 for all n and j, a few CLT’s are available for such urns....

This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B | X1, . . . ,Xn)} , where (Xn) is a sequence of random variables and µn = (1/n)SUM(i=1,..,n) d(Xi) the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution)...