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Introduction
In Chapter 6 we discussed the process of choosing potential stock pairs. In
this chapter we will focus on whether the identified candidate pairs are ac-
tually tradable. Based on the discussions so far, we can state that a pair is
tradable if the stocks making up the pair are cointegrated. We need to bear
in mind, however, that in most cases we are dealing with systems that are not
exactly cointegrated. As a matter of fact, in the course of examining the can-
didate pairs, we can almost always expect to have a residual factor exposure
causing the phenomenon of mean drift, thereby resulting in the signal to be
nonstationary. However, if the signal-to-noise ratio is good enough, then for
all practical purposes we could treat the residual series as stationary for the
time period of the trade. Based on the preceding observations we could refine
the phrasing of our question as follows: How do we decide that a pair is
tradable even though it deviates from ideal conditions of cointegration? To
seek out an approach to answer that, we could draw on the insights gleaned
from cointegration testing procedures. With that in mind, let us outline the
process of verifying that two stocks are indeed cointegrated.
Most verification processes are based on the “If it walks like a duck and
quacks like a duck, it must be a duck” philosophy. Needless to add, the ap-
proach to cointegration testing is also along the same lines. We identify the
properties that must be satisfied if cointegration were indeed true and check
to see if the properties hold. If they do, then the stock pair in question is de-
clared cointegrated. Let us therefore review some properties of cointegrated
systems that could be potentially of use in the testing process.
We start off with the Stock-Watson characterization of cointegrated
systems. Each individual stock series is modeled as a sum of a trend compo-
nent and a stationary component. The property characteristic of cointe-
grated systems is that the trend components of the two stocks must be the
same. If the trend component is the same and the stationary component just
oscillates about some value, then there must be a strong correlation between
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