Time Series Analysis

A time series - or time series - is a sequence of observations indexed by time. The temporal and joint dynamics of time series are modelled by discrete-time stochastic processes. The main applications of time series are the modelling of macroeconomic and financial series. They can also be used in other sciences such as physics, biology, geology (Nile floods, Hurst 1951), health (hormone levels in blood), etc.

The objective of this time series course is to review a large number of econometric models without going into mathematical demonstrations: for univariate stationary (ARMA models, application to short-term interest rates), non-stationary (ARIMA models, application to exchange rates), conditional variance (GARCH models, application to stock index volatility), multivariate stationary (VAR models, application to stock returns) and non-stationary (notion of cointegration, VECM model, applications to exchange rates and derivatives) series. For each chapter, there will be an application on real data with the Eviews software.

New: equivalent models with artificial neural networks will be covered.

Chap 1: Introduction to the concept of time series. Chap 2. Autoregressive moving average models (ARMA) Basic model.

• recurrent neural networks. LSTM. Chap 3. Autoregressive conditional heteroskedasticity models (ARCH) Models specific to the returns of financial securities. They take into account periods of volatility observed in financial markets.
• Neural volatility models Chap 4. Notion of unit root and ARIMA models Models for non-stationary series, such as macroeconomic series and price series in finance. Neural networks and non-stationarity. Chap 5. Vector autoregressive models (VAR) Models for jointly treating a set of stationary time series. Chap 6. Notion of cointegration, VECM model Models for joint treatment of a set of non-stationary time series.