URT | Fast Unit Root Tests and OLS regression | GPU library

I have been developing algorithmic trading tools for a while and it is no secret that unit root tests are widely used in this domain to decide whether a time serie is (weakly) stationary or not and construct on this idea a profitable mean-reversion strategy. Nowadays you often have to look at smaller and smaller time frames as minute data to find such trading opportunities and that means on the back-testing side using more and more historical data to test whether the strategy can be profitable on the long term or not. I found frustrating that the available libraries under R and Python, interpreted languages commonly used in the first steps of building a trading algorithm, were too slow or did not offer enough flexibility. To that extent I wanted to develop a library that could be used under higher level languages to get a first idea on the profitability of a strategy and also when developping a more serious back-tester on a larger amount of historical data under a lower level language such as C++. In algorithmic trading we have to find the right sample size to test for stationarity. If we use a too short sample of historical data on a rolling window the back-testing will be faster but the test precision will be smaller and the results will be less reliable, on the contrary if we use a too large sample the back-testing will be slower but the test precision will be greater and the results will be more reliable. Hence, when testing for stationarity we have to always keep this tradeoff in mind. Sample sizes used are usually between 100 to 5000, leading to relatively small size arrays. I have then decided not to use parallelism for matrix and vector operations as it would not bring any speed improvement and on the contrary would slow down the code when applied on such small dimensions. Although Armadillo does not allow for parallelism yet, Blaze and Eigen do, I made sure to turn off this ability. However, parallelism is used to speed up the lag length optimization by information criterion minimization in ADF and DF-GLS tests by enabling OpenMP. All of these libraries are now using vectorization (from SSE to AVX), activating this feature greatly improves the general performance. During my experimentations I have tried to find the correct set up for each C++ linear algebra library (Armadillo, Blaze and Eigen compiled with either Intel MKL or OpenBLAS) in order to get the fastest results on a standard sample size of 1000. If anyone can find a faster configuration for any of them, or more generally, if anyone has anything to propose that could make the C++ code or the Cython and Rcpp wrappers faster, he is more than welcome to bring his contribution to this project.