Trend of high dimensional time series estimation using low-rank matrix factorization: heuristics and numerical experiments via the TrendTM package

This article focuses on the practical issue of a recent theoretical method proposed for trend estimation in high dimensional time series. This method falls within the scope of the low-rank matrix factorization methods in which the temporal structure is taken into account. It consists of minimizing a penalized criterion, theoretically efficient but which depends on two constants to be chosen in practice. We propose a two-step strategy to solve this question based on two different known heuristics. The performance and a comparison of the strategies are studied through an important simulation study in various scenarios. In order to make the estimation method with the best strategy available to the community, we implemented the method in an R package TrendTM which is presented and used here. Finally, we give a geometric interpretation of the results by linking it to PCA and use the results to solve a high-dimensional curve clustering problem. The package is available on CRAN.