Trend detection under erroneous observations: application to quantitative financial strategies

In this paper, we show how to handle the problem of trend detection, in the context of financial strategies, when the data is potentially erroneous. We focus on the case of a filtering method based on wavelets. This is used, for instance, to build an estimator of a given security at a future time horizon, or to construct trading signals based on extreme variations from the trend. We study how the erroneous observation of past data is incorporated into the filter method and, therefore, into the estimator built with it. The techniques of error calculus with Dirichlet forms are applied to see how the errors affect the estimation: they define an expansion of the estimator in terms of its first- and second-order moments, interpreted as statistical variance/covariance and bias.