Statistical and Machine Learning Models for Time Series Analysis
Prerequisiti
The course is aimed at PhD students of mathematics, physics, computer science, and other scientific subjects, but is also accessible to students in the master's programme. It is also largely accessible to students in the area of economics and finance.
Programma
Introduction.
Deterministic and stochastic models. Ergodicity, weak and strong mixing. Delay map. Takens theorem. Reconstruction of attractors from time series.
Components of a time series (trend, cycle, seasonal, irregular), stationarity, autocorrelation and dependencies, approaches to time series analysis. Review of estimation methods (Least Squares, Maximum Likelihood, Generalized Method of Moments).
Linear models. ARMA processes, partial autocorrelation, invertibility, ARIMA models for non-stationary series. Inference of linear models: identification and fitting, diagnostics, Ljung-Box statistic; model selection. Vector AutoRegressive models, reduced form, structural form e identification issues. Granger causality.
State space models. Filtering, prediction and smoothing; Kalman recursions; local level models. Particle filtering and smoothing, Score Driven models, Hidden Markov Models.
Neural networks for time series. Introduction to (Deep) Neural Networks, Inference of time series models with Machine Learning methods. Overview of time series forecasting via ML and Deep Learning Libraries: TensorFlow, Keras. Autoencoders
Recurrent Neural Networks (RNN), Gated Architectures (LSTMs, GRUs), Bi-directional RNNs, Deep RNN. Reservoir computing and Echo State Networks. Generative Adversarial Networks (GANs). Overview of synthetic time series generation with GANs.Applications and examples.
Introduction to Reinforcement Learning.
Obiettivi formativi
The objective of the course is to provide the main elements of the theory of time series analysis by using methods from statistics, econometrics, and machine learning. The course also provides working knowledge for the computational modeling of empirical time series as well as for the simulation and inference of statistical models.
Riferimenti bibliografici
J. Hamilton, Time Series Analysis, Princeton University Press
J. Durbin and S.J. Koopman, Time Series Analysis by State Space Models, Oxford University Press
F. Lazzeri, Machine Learning for Time Series Forecasting with Python, Wiley
Additional material (notes, slides, papers) will be provided during the course