Nonstationary Process Monitoring Based on Alternating Conditional Expectation and Cointegration Analysis

Independence Tests based on the Conditional Expectation

In this paper we propose a new procedure for testing independence of random variables, which is based on the conditional expectation. As it is well known, the behaviour of the conditional expectation may determine a necessary condition for stochastic independence, that is, the so called mean independence. We provide a necessary and sufficient condition for independence in terms of conditional e...

CONDITIONAL EXPECTATION IN THE KOPKA'S D-POSETS

The notion of a $D$-poset was introduced in a connection withquantum mechanical models. In this paper, we introduce theconditional expectation of  random variables on theK^{o}pka's $D$-Poset and prove the basic properties ofconditional expectation on this  structure.

Bayesian Conditional Cointegration

Cointegration is an important topic for timeseries, and describes a relationship between two series in which a linear combination is stationary. Classically, the test for cointegration is based on a two stage process in which first the linear relation between the series is estimated by Ordinary Least Squares. Subsequently a unit root test is performed on the residuals. A well-known deficiency o...

Conditional Expectation

Let μ and λ be two positive bounded measures on the same meaurable space (Ω,F). We call μ and λ equivalent, and write μ ≡ λ, if they have the same null sets— so, if they were probability measures, the notion of “a.s.” would be the same for both. More generally, we call λ absolutely continuous (AC) w.r.t. μ, and write λ μ, if μ(A) = 0 implies λ(A) = 0, i.e., if every μ-null set is also λ-null. W...

Conditional expectation