• 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.

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Syllabus

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Linear regressions

Part I. Regularization

1. 1. Ridge

   2. Lasso

   3. Geometric interpretation

   4. Statistical qualities

   5. Ridge and logistic regression

 

 

Part II Regression abnormalities

1. 1. Anomalies in classification problems

   2. Regression abnormalities

   3. Robust regression

   4. Linear programming: a solution to robust regression

   5. Robust Ridge Regression

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Time series

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Part I. Time series

1. Basic definitions and motivation: Fourier analysis
2. Buys-Ballot model: relationship with regressions

3. Moving-Average

4. Local regressions

5. Exponential smoothening

 

Part II Time series abnormalities

1. Classic approach
2. An invitation to stochastic processes: Markov and Martingale chains

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