Final_1.pdf

trends model is that of a time series being expressed as a simple sum of two
component time series: a stationary component and a nonstationary com-
ponent. If two series are cointegrated, then the cointegrating linear compo-
sition acts to nullify the nonstationary components, leaving only the
stationary components. To see what we mean, consider two time series

(5.2)

where and are the random walk (nonstationary ) components of the
two time series, and and are the stationary components of the time
series. Also, let the linear combination yt–gztbe the cointegrating combi-

εyt εzt

nyt nzt

yn

zn

tyy

tzz

tt

tt

=+

=+

ε

ε

78 STATISTICAL ARBITRAGE PAIRS

FIGURE 5.2A Spread.

10 30 50 70 90

–2

0

2

4

6

8

–6

–4

FIGURE 5.2B Spread ACF.

0510 15 20

Lag

–0.2

–0.0

0.2

0.4

0.6

0.8

1.0

Auto Correlation