Learning objectives
The course aims to delve into the concepts related to the estimation and use of the linear model. In the second part, fundamental notions for the analysis of time series and forecasting are introduced.
Prerequisites
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Course unit content
First Module: Regression Model
1) Introduction and review of basic concepts
- The relationship between variables
- The regression line and parameter calculation: least squares method
- Introduction of random elements: simple regression model.
- Parameter estimation
- Inference on parameters
2) Multiple Regression Model
- Introduction of additional regressors in the model
- Matrix notation of the multiple regression model
- Parameter estimation: generalization of the least squares method.
- Adjusted coefficient of determination and the problem of overfitting.
Second Module: Time Series Models
3) Analysis of Time Series
- Dependent data
- Preliminary transformations: contemporaneous and intertemporal
- Temporal variations and aggregations
- Temporal dependence: autocovariance and autocorrelation
- Identification of cycles: periodogram
- Models for latent components decomposition
- Local polynomial regression and moving averages
- Stochastic models for time series: ARIMA processes
3) Forecasting with Time Series Models
- The problem of forecasting
- Forecast errors and loss functions
- Evaluation of predictive performance
- Forecasting using exponential smoothing models
- Forecasting with ARIMA models
Full programme
First Module: Regression Model
1) Introduction and review of basic concepts
- The relationship between variables
- The regression line and parameter calculation: least squares method
- Introduction of random elements: simple regression model.
- Parameter estimation
- Inference on parameters
2) Multiple Regression Model
- Introduction of additional regressors in the model
- Matrix notation of the multiple regression model
- Parameter estimation: generalization of the least squares method.
- Adjusted coefficient of determination and the problem of overfitting.
Second Module: Time Series Models
3) Analysis of Time Series
- Dependent data
- Preliminary transformations: contemporaneous and intertemporal
- Temporal variations and aggregations
- Temporal dependence: autocovariance and autocorrelation
- Identification of cycles: periodogram
- Models for latent components decomposition
- Local polynomial regression and moving averages
- Stochastic models for time series: ARIMA processes
3) Forecasting with Time Series Models
- The problem of forecasting
- Forecast errors and loss functions
- Evaluation of predictive performance
- Forecasting using exponential smoothing models
- Forecasting with ARIMA models
Bibliography
Riani M. et al. - Data Science con MATLAB, Seconda
Edizione, Giappichelli, 2023. Capitolo 15: Analisi
delle serie storiche.
Teaching methods
Lectures and laboratory with Matlab.
Assessment methods and criteria
Project Work and oral exam
Other information
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