Detecting joint tendencies of multiple time series

The moving average smoother decomposes time-series data x(t) into a systematic part plus fluctuations, i.e., x(t) = (x) over bar (t) delta(x)(t). In the language of Bayesian inference, smoothing can be understood as the inverse problem of finding the systematic component (x) over bar (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 (x) over bar (t) and delta(x)(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.