Arbitrage is a widely sought after phenomenon in financial markets: profit without any risk is very desirable. Statistical arbitrage is a related concept: the idea is to take advantage of market inefficiencies using statistical techniques and mathematical models. It is by no means risk-free however. We focus on the statistical arbitrage technique ”pairs trading” utilizing both cointegration and minimum distance pairs. We discuss the algorithms involved and simulate these based on data from the NASDAQ 100.There have been recent forages into financial applications and time series with wavelets. However, ideas surrounding pairs trading through the use of wavelets have been little to non-existent. Our contribution is the application of wavelets and costationarity as an approach to pairs trading. We applied the concept of estimating the evolutionary wavelet spectrum, which is analogous to the spectrum for time series but for wavelets. Following the estimation of the evolutionary wavelet spectrum, we find variance stationary linear combinations of the differenced stock prices. This is essentially the concept of costationarity: finding variance stationary linear combinations from non-stationary processes using time-varying coefficients. We then compare the results of the application of the costationarity method to the minimum distance method and to the cointegration method. We find that there are significant improvements on the minimum distance method, but that it does not have a large improvement over the cointegration method.
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