1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. Mathematics - pierwszego stopnia z tyt. licencjata
5. Time Series Modeling

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Time Series Modeling - opis przedmiotu

Cel przedmiotu

Familiarization with time series models and forecasting methods based on them.

Wymagania wstępne

Zapisz zmiany

Probability Calculus, Mathematical Statistics.

Zakres tematyczny

Lecture

1. The multiple linear regression linear models. Explanatory variables, explained variables, tests of significance of single and groups of variables; (4 hours)
2. Classical decomposition model. Moving average and exponential smoothing for data preparations, estimation of seasonality, final estimation of parameters of trend, forecasting. (4 hours)
3. Linear time series. Stationary time series, Autocorrelation Function, Partial Autocorrelation Function, spectral properties of time series, spectrum, spectral density, periodogram.  (8 hours)
4. Autoregressive models AR(p), stationarity conditions, Autocorrelation Function, spectrum,  Yule’a-Walker formula,  Partial Autocorrelation Functions, identifications of AR models, preliminary estimation of parameters. (4 hours)
5. Moving average models MA(q), invertibility conditions, Autocorrelation Function, spectrum, identifications of MA models, preliminary estimation of parameters. (4 hours)
6.  Mixed models ARMA(p,q): stationarity and invertibility conditions, Autocorrelation, Partial Autocorrelation, spectrum, identification of ARMA, final estimation of parameters, forecasting. (2 hours)
7. Linear nonstationary models ARIMA(p,d,q). (4 hours.)

Laboratory

1.  Polynomial trend models. (4 hours)
2.  Seasonal fluctuation models. (4 hours)
3.  Prediction based on trend and seasonality models. (4 hours)
4.  AR(p) models. (6 hours)
5.  MA(q) models. (6 hours)
6.  ARMA(p,q) models. (6 hours)
7.  Verification of model stationarity: unit root test. (3 hours)
8.  ARIMA(p,d,q) models. (6 hours)
9.  Seasonality elimination procedures. (6 hours)

Metody kształcenia

Traditional lecture. In the laboratory, solving tasks using selected computer packages.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

To evaluate the laboratory, the student prepares a report with an example of a forecasting model and solves it by applying time-series analysis. To evaluate the lecture, the student passes a test of multiple choice.  The final mark is equal to the arithmetic mean of marks from the laboratory and lecture, provided both are positive. 

Literatura podstawowa

1. P .J. Brockwell, R. A. Davis, Introduction to time series and forecasting, Springer, New York, 2002.
2. G. Kirchgaessner, J. Wolters, Introduction to modern time series analysis, Springer, Berlin, 2007.

Literatura uzupełniająca

Uwagi

Zmodyfikowane przez dr Ewa Sylwestrzak-Maślanka (ostatnia modyfikacja: 15-03-2024 12:29)