I'm doing outlier detection (Conditional Outliers) on a multivariate time series. The outliers appear every 2 weeks $\pm$ 4 days.
How can I incorporate this prior in my models, to reduce the number of false positive? Alternatively, how should I filter the results of my models with this prior knowledge?
All my models use sliding windows and calculate an anomaly score of a series of points.
My rough idea: If an outlier is detected, model a Gaussian distribution where $\mu$ is set 14 days later and $\sigma$ is 4 days wide. Then multiply future predictions with the pmf of the distribution. Assuming the model has some kind of anomaly score, we are reducing the score of points which are unlikely outliers.