Detecting joint tendencies of multiple time series
Fábio Mace do Mendes, Anníbal Dias Figueiredo, Paul M. Goggans, Chun-Yong Chan · AIP conference proceedings · 2009
The moving average smoother decomposes time‐series data x(t) into a systematic part plus fluctuations, i.e., x(t) = x̄(t)+δx(t). In the language of Bayesian inference, smoothing can be understood as the inverse problem of finding the systematic component x̄(t). from the noisy time‐series data x(t) This can be accomplished by a straightforward Bayesian analysis after assigning a prior probability to the functions x̄(t) and δx(t). We use Gaussian probabilities and approximate the calculations using a free field theory. This contribution generalizes a previous work in order to deal with multidimensional time‐series. The full solution is obtained: the posterior, the predictive probability and the evidence.