Tutorial on Time Series Analysis

Abstract 

Time series analysis is a large research field that finds applications in several disciplines. Essential to time series analysis theory and practice are the three steps of model identification, estimation and diagnostic checking. Techniques are available that allows both the researcher and the practitioner to develop novel devices to analyse time series data and selecting and testing the effectiveness of models for explanatory or forecasting purpose. Theory will be presented in three parts, in ascending order of difficulty, from basics linear models to testing and modeling non linear and non stationary behavior, up to vector models and time series interaction problems as the obvious consequence. Whatever would be the model complexity or the difficulty of taking properly into account unusual or unexpected time series sequences,  identification, estimation and diagnostics will have to be performed anyway adopting the techniques that will best fit the data. 

Each part A, B and C will be contained within approximately 50 minutes. Necessarily not many details will be given and the appropriate references will be offered to the interested reader. A due space will be given instead to examples of applications to real time series so that the reader could appreciate the usefulness of so many models and methods and operate as much as possible a correct choice between them. 

Part A. Basics. 
Markov Chains.
Linear Models. 
            Autoregressive. 
            Moving-average.
Mixed Models.
Model Selection.
(Subset Models.)

Part B. Non Stationary Non Linear Models
Integrated Models.
Seasonal Models.
(Fractionally Differenced Models.)
Structural Breaks.
Markov Switching Models.
(Heteroscedasticity.)
State Dependent Models.
            (Threshold.
             Piecewise Linear.
             Smooth Transition.
             Exponential Autoregressive.
             Bilinear.)
Artificial Neural Networks.

Part C. Vector Models.
Linear Vector Models.
Vector Autoregressive.
Vector Moving-average.
Mixed Vector models.
Cointegration.
Causality.
(Threshold Vector Error Correction.)
(Outliers.)

NOTE: Arguments in parentheses will be skipped if there will be no time to develop them in a reasonable way.