Ch. 23 Cointegration 1 Introduction An important property of (1) variables is that there can be linear combinations of theses variables that are I(O). If this is so then these variables are said to be cointegrated. Suppose that we consider two variables Yt and Xt that are I(1) (For example, Yt= Yt-1+ St and Xt= Xi-1+nt.)Then, Yt and Xt are said to be cointegrated if there exists a B such

Ch. 13 Difference Equations 1 First-Order Difference Equations Suppose we are given a dynamic equation relating the value y takes on at date t to another variables Wt and to the value y took in the previous period: where o is a constant. Equation(1)is a linear first-order difference equation a difference equation is an expression relating a variable yt to its previous values

Chapter 4 Operations in Relational Model 4. 1 An Algebra of relational operations Operation运算,操作 Operator算子 Operand操作数

This paper is an updated version of a previous working paper, Capital Budgeting in the Presence of Managerial Overconfidence and Optimism, by the same authors. Financial support by the Rodney L. white Center for Financial Research is gratefully acknowledged. The authors would like to thank Andrew Abel, Jonathan Berk, Domenico Cuoco, David Denis, Janice Eberly, Robert Goldstein, Peter Swan, and seminar

This lecture presents results describing the relation between existence of Lyapunov or storage functions and stability of dynamical systems 6.1 Stability of an equilibria

Lyapunov analysis, which uses monotonicity of a given function of system state along trajectories of a given dynamical system, is a major tool of nonlinear system analysis It is possible, however, to use monotonicity of volumes of subsets of the state space to predict certain properties of system behavior. This lecture gives an introduction to suc methods

he variable t is usually referred to as the\time Note the use of an integral form in the formal definition(2.2): it assumes that the function tHa(a(t), t)is integrable on T, but does not require =a(t)to be differentiable at any particular point, which turns out to be convenient for working with discontinuous

4.1 Addition of hx to Alkenes. p100 Hydrohalogenation General reaction mechanism: electrophilic addition Attack of electrophile(such as hBr)on T bond of alkene Produces carbocation and bromide ion Carbocation is an electrophile, reacting with nucleophilic bromide ion

Introduction Objective: To compare the different imaging configurations for a Separated Spacecraft Interferometer operating from an Earths orbit

Routing Must choose routes for various origin destination pairs o/d pairs) or for various sessions Datagram routing: route chosen on a packet by packet basis Using datagram routing is an easy way to split paths Virtual circuit routing: route chosen a session by session basis Static routing: route chosen in a prearranged way based on O/D pairs Eytan Modiano