###### Outliers and anomalous values
• Introduce the mathematical formalism necessary to understand some of the most used algorithms in Forecasting through regressions and time series.

• Invite the student to understand the need and the advantages of regularization in linear regressions.

• Motivate the use of time series as a method to correctly model some phenomena.

• Teach the statistical and computational qualities of the proposed algorithms.

• Introduce the concept of anomaly and those algorithms useful in its detection.

Syllabus

Course One: Time Series Anomalies and Regressions

Part I. Regularization

• Ridge

• Statistical qualities

• Geometric interpretation and relationship with PCA

Part II Linear regression abnormalities

• Regression abnormalities

• Robust regression

• Linear programming: a solution to robust regression

Part III Time series and anomaly detection

• Basic definitions

• Buys-Ballot model: relationship with regressions

• Exponential smoothing

• Anomaly detection

Course Two: Other Methods in Detecting Anomalies for Time Series

Part I. ARIMA

• Moving average

• White noise

• Invitation to stochastic processes

• Anomaly detection and ARIMA

Part II Mahalanobis distance and anomalies

• Basic definitions

• Geometric interpretation

• DCM

• Applications to anomaly detection

Part III. Time series anomalies via Elastic Search

• Non-Gaussian distributions and other problems

• Formal definition of the algorithm

• Anomaly detection