Conditions for convergence of random coefficient AR(1) processes and perpetuities in higher dimensions
نویسندگان
چکیده
A d-dimensional RCA(1) process is a generalization of the d-dimensional AR(1) process, such that the coefficients {Mt; t = 1, 2,. . .} are i.i.d. random matrices. In the case d = 1, under a nondegeneracy condition, Goldie and Maller gave necessary and sufficient conditions for the convergence in distribution of an RCA(1) process, and for the almost sure convergence of a closely related sum of random variables called a perpetuity. We here prove that under the condition n t=1 Mt a.s.
منابع مشابه
Complete convergence of moving-average processes under negative dependence sub-Gaussian assumptions
The complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. As a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.
متن کاملApproximations for the Distribution of Perpetuities with Small Discount Rates
General perpetuities (i.e. random variables of the formD = R∞ 0 e −Γ(t−)dΛ (t), also known as infinite horizon discounted rewards) play an important role in several application settings (e.g. insurance, finance and time series analysis). Our focus is on developing approximations for the distribution of D that are asymptotically valid when the “accumulated short rate process” or “accumulated for...
متن کاملBaxter’s Inequality and Sieve Bootstrap for Random Fields
The concept of the autoregressive (AR) sieve bootstrap is investigated for the case of spatial processes in Z. This procedure fits AR models of increasing order to the given data and, via resampling of the residuals, generates bootstrap replicates of the sample. The paper explores the range of validity of this resampling procedure and provides a general check criterion which allows to decide wh...
متن کاملNonparametric estimation of the distribution of the autoregressive coefficient from panel random-coefficient AR(1) data
We discuss nonparametric estimation of the distribution function G(x) of the autoregressive coefficient from a panel of N random-coefficient AR(1) data, each of length n, by the empirical distribution of lag 1 sample correlations of individual AR(1) processes. Consistency and asymptotic normality of the empirical distribution function and a class of kernel density estimators is established unde...
متن کاملOn distributional properties of perpetuities
We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously singular. We further provide necessary and sufficient criteria for the finiteness of p-moments, p > 0 as well as exponential moments. In particular, a formula fo...
متن کامل