For a student specializing in econometrics and time series analysis (“time series econometrics”, including macroeconometrics and financial econometrics). The aim of this specialization module is to provide essential methodological and empirical skills to analyze time-dependent observations and datasets. In addition to the courses on time series analysis from various perspectives, courses on advanced regression analysis and statistical learning supplement this module. Even though the models and methods are general, this module is designed specifically for students interested in various economic and financial applications.

Our (Department of Mathematics and Statistics) teaching on time series econometrics methods consists of three core courses (see below). These courses are recommended (at least) to students studying:

  • Statistics (as a major or minor subject)
  • Economics and/or finance (generally quantitative methods)
  • Applied Mathematics students, especially if specializing in financial and insurance mathematics
  • Any field where time series and/or advanced machine learning methods will be considered.

The courses introduced below are general, containing typically economic and financial applications


(for the 1. course TILM3541 and for the whole time series econometrics programme)

Students are expected to have basic knowledge of linear regression analysis (including the basics of statistical inference) and the prerequisites for those courses. That is to the extent covered, for example, in the following courses at the UTU:

Statistics students:
Tilastollinen päättely I (TILM3561)
Tilastollinen päättely II (TILM3562)
Lineaariset ja yleistetyt lineaariset mallit (TILM 3588)
These courses are all given in Finnish, alternatives with English language can be inquired from the person in charge.

Economics (finance) students:


Time series analysis / time series econometrics

This course introduces the main concepts of time series analysis. A strong recommendation is to take this course before proceeding to TILM3589 and TILM3586 below (which can be taken in an optional order). The content contains ARMA models and ARCH and GARCH models used in the modelling of conditional variance, including model specification, estimation, evaluation and forecasting among these modelling contexts. After the course, the student has necessary methodological and practical skills for conducting empirical time series analysis independently.

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This course introduces modern nonlinear time series models for the conditional mean, conditional variance and limited dependent variables. The nonlinear models for the conditional mean include, e.g., the threshold autoregressive (TAR) and smooth transition autoregressive (STAR) models. Considering the conditional variance, extensions of the basic conditionally heteroskedastic ARCH and GARCH model will be considered. Limited dependent time series models can be seen as generalizations of generalized linear models to the time series context, including especially models for binary, multinomial and count variables. All the considered nonlinear models and methods are general and can be applied in any field but are highly important especially in various macroeconomic and financial applications.

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This course introduces basics for multiple time series analysis. In particular, a stationary vector autoregressive (VAR) model is introduced, including parameter estimation and forecasting. In addition to the VAR model, special interest will put on structural VAR (SVAR) models and structural analyses commonly made especially in macroeconometrics (partly also financial econometrics) such as impulse response analysis. Cointegrated VAR model and vector error correction modelling used in nonstationary time series analysis are also briefly introduced.

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The course introduces the methods of modern applied macroeconometrics. The main emphasis is on the vector autoregressive (VAR) model and its application in empirical (macro)economics. In addition to the statistical properties and inference of the VAR model, we concentrate on the identification of economic shocks by various methods and the use of the structural vector autoregressive (SVAR) models. Applications in other fields besides macroeconomics may also be discussed. The emphasis is on the practical application of the methods.

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Advanced regression analysis and statistical learning

In addition to the time series econometrics courses introduced above, the following courses on advanced regression analysis and statistical learning are especially highly recommended.

This course contains various extensions of linear and generalized linear models and their connections to statistical learning. These are, among others, parametric nonlinear and nonparametric regression functions and the methods connected to model selection and robust estimation. In statistical learning (cf. machine learning), we emphasize a stronger emphasis on statistics and statistical properties of the methods, with a special attention paid on the predictive performances of the methods. The objective of this course is generally to give starting points for more advanced statistical analyses with statistical learning methods such as various machine learning and neural networks algorithms.

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This course is continuation for the course “TILM3587: Advanced regression analysis and statistical learning” (see above). Knowledge on the topics and methods contained in that (or equivalent) course are assumed as necessary prerequisites. After this course, the student masters a wide range of advanced statistical learning methods including their properties and extensions. These include, among others, the following supervised and unsupervised learning methods including

*Advanced model selection and regularization methods (in large datasets), containing, for example, ridge, lasso and elastic net methods and their extension

* Tree-based methods (regression and decision trees)

* Bagging, boosting and random forest

* Support vector machine and advanced classification-based methods

* Unsupervised learning methods and dimension reduction

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All the above five courses are also partly included in the Economics and Finance study programmes, as well as postgraduate studies in Statistics (UTUGS MATTI school). Moreover, it has been agreed with the UTUGS Doctoral Programme of Turku School of Economics (including Economics and/or Finance) that at least courses TILM3589, TILM3586 and TILM3592 can be included as special courses for general PhD studies

If you like to take an exam on any of the courses above outsides times when they are not lectured, please, be in contact to Associate Professor Henri Nyberg(firstname.surname@utu.fi).

Other courses

See detailed information on courses, especially, in the Statistical inference and Econometrics modules in


Financial and insurance mathematics

In our department, one highly recommended teaching module concerns financial and insurance mathematics. See details: “Vakuutusmatematiikka” and “Stokastiikka ja finanssimatematiikka” in https://opas.peppi.utu.fi/en/degree-programme/6810

UTU Econometrics