residual time series seems to suggest that it is indeed tradable. We now run
the bootstrap procedure on it and obtain the population. A quick look sug-
gests that in the extreme the time between zero crossings can be as long as
14 to 26 days with a median value of about 5 days. The pair definitely
seems to be in tradable category. However, it might be better to liquidate the
position on reversion to zero instead of waiting for an excursion of magni-
tude in the other direction.
SUMMARY
Tradability testing is a two-step process consisting of evaluating the lin-
ear relationship and measuring the degree of mean reversion of the
residual.
The linear relationship between the log-price series of the two stocks is
characterized by the cointegration coefficient and the stock premium.
They may be estimated in a multifactor framework or by ordinary least
squares regression.
The spread series can be calculated by applying the linear relationship.
The degree of mean reversion of a series is quantifiable in terms of the
zero-crossing frequency.
The zero-crossing frequency can be directly estimated using the boot-
strap procedure.
The reciprocal of the zero-crossing frequency is indicative of the trading
period, and a pair may be deemed tradable if we are satisfied with the
range of trade periods or zero crossing frequencies generated by the
bootstrap.116 STATISTICAL ARBITRAGE PAIRS
FIGURE 7.2B Residual Time Series.Time02040 60 800.2Residual0.10.0–0.1