The Mathematics of Financial Modelingand Investment Management

11-FinEcon-Time Series Page 291 Wednesday, February 4, 2004 12:58 PM

Financial Econometrics: Time Series Concepts, Representations, and Models 291

N

∑

a i

iz =^0

i = 1

have absolute values strictly greater than 1. The inverse operator is an

infinite power series

A –^1 ()L = ψ

∞

∑ iL

i

i = 1

Given two linear functions of the operator L, it is possible to define

their product

M

∑aiL

AL()= i

i = 1

N

∑biL

BL()= i

j = 1

+

∑

MN

i = 1

PL()= AL()BL()= piLi

pi =

i

∑a^ rbir–

r = 1

The convolution product of two infinite series in the lag operator is

defined in a similar way

∞

∑aiL

AL()= i

i = 0

∞

∑biL

BL()= i

j = 0