Nonparametric tolerance limits for pair trading

Tolerance interval is an important statistical tool for determining the threshold of a certain reference. We propose to utilize nonparametric one-sided tolerance limits with three look-back window sizes for return spreads in order to find trading entry and exit signals. We illustrate how the proposed method help uncover arbitrage opportunities via the daily return spreads of 12 stock pairs in the U.S. markets and then report the performance of pair trading for two out-of-sample periods. The empirical results suggest that combining the minimum squared distance method and nonparametric one-sided tolerance limits generates positive excess returns, relative to the underlying stocks.