Topics in applied time-series analysis

Models, seasonal adjustment, imputation

This page contains the slides and numerical simulation codes for the lectures delivered in 2023 during my employment as a post-doctoral researcher at the University of Luxembourg.

Course syllabus

Day 1: Introduction to time-series analysis (2024-04-03)

• Introduction to time-series analysis: PDF slides (0.8 MB)

Day 2: Forecasting and non-stationarity (2024-04-08)

• Forecasting and non-stationarity: PDF slides (1.0 MB)

Day 3: Seasonality in time series (2024-04-15)

• Seasonality in time series: PDF slides (0.6 MB)

Day 4: Seasonal decomposition diagnostics (2024-04-19)

• Seasonal decomposition diagnostics: PDF slides (0.7 MB)

Day 5: Forecasting and imputation (2024-04-22)

• Forecasting and imputation: PDF slides (2.8 MB)

Goal and objectives

The goal of this course is to get Ph.D. students acquainted with the fundamentals of time-series modelling and several applied time-series methods that are actively used at major economic institutions (Eurostat, Statec, central banks etc.). The main focus of the course is on characterising the structural features of macroeconomic time series, on seasonal adjustment, and on the basics of imputation for multiple unbalanced time series. Computations are done in free and open-source software: R and JDemetra+.

Upon successful completion of this course, students will be able to:

• Specify many popular time-series models in the state-space framework to apply unified filtering algorithms and produce short-term signal and state forecasts of multiple macro- economic time series with R;
• Diagnose macroeconomic series and use data-driven methods to detect structural breaks and calendar effects;
• Filter out the seasonal component of time series by parametric and semi-parametric methods and evaluate the quality of seasonal adjustment in compliance with the latest Eurostat guidelines with JDemetra+;
• Extract the common dynamics of multiple time series by modelling a small number of unobserved factors;
• Apply state-of-the-art econometric methods to reconstruct partially incomplete macroeconomic data sets with R.

Topics covered

1. Introduction to time-series analysis (TSA). Stationary and non-stationary processes. Wold decomposition. Linear TS models: non-seasonal and seasonal ARIMA. Estimation of TS models in R.
2. Seasonality and seasonal adjustment (SA). Comparison of SA methods. Determining whether the series need any adjustment. Evaluating SA quality. Basics of model-driven outlier detection.
3. Practical implementation of SA. Producing diagnostic plots and tables in R and JDemetra+. Spectral diagnostics of seasonality.
4. Principal component analysis (PCA). Dynamic factor models (DFM). State-space models and Kalman filtering. Mixed-frequency estimation of coincident indices. Basics of time-series imputation, assumptions, and limitations.
5. Univariate model-based time-series imputation. Multivariate PCA-based imputation. Multiple imputation (MI). Expectation-maximisation (EM) algorithm. Imputation with trends. Bayesian imputation, bootstrapping, and the Amelia II algorithm. Imputation diagnostics.