Description:
| Aims & Learning Objectives: Aims: To introduce a variety of statistical models for time series and cover the main methods for analysing these models. To facilitate an in-depth understanding of the topic.
Objectives:
At the end of the course, the student should be able to:
* Compute and interpret a correlogram and a sample spectrum;
* derive the properties of ARIMA and state-space models;
* choose an appropriate ARIMA model for a given set of data and fit the model using an appropriate package;
* compute forecasts for a variety of linear methods and models;
* demonstrate an in-depth understanding of the topic.
Content: Introduction: Examples, simple descriptive techniques, trend, seasonality, the correlogram.
Probability models for time series: Stationarity; moving average (MA), autoregressive (AR), ARMA and ARIMA models.
Estimating the autocorrelation function and fitting ARIMA models.
Forecasting: Exponential smoothing, Forecasting from ARIMA models.
Stationary processes in the frequency domain: The spectral density function, the periodogram, spectral analysis.
State-space models: Dynamic linear models and the Kalman filter.
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