Learning models of time series and their forecasting methods.
Prerequisites
Probability Theory, Mathematical Statistics.
Scope
Lecture
Linear difference equations, polynomial characteristic; solution form; G-Transform (4 hours)
Time series as a stochastic proces and statistical data;Classical decomposition of time series; .Modelling of trend and seasonality; Smoothing methods (moving-avagrege, exponential smoothing, Holt method). ex ante and ex post. forecastings (4 hours.)
Linear time series: Autocovariance and autocorrelation function, weakly and strictly stationary time series, estimation of autocovariance and autocorrelation function, spectra properties of stationary models, periodogram and its relationship with estimation of autocovariance function; sampling spectrum; power spectrum and spectral density function; generating function of autocovariance; conditions of stationarity and invertibility. (8 hours.)
Autoreggresive models AR(p): stationarity and invertibility conditions, Autocorrelation; spectrum, Yule-Walker equations; Partial autocorrelation function; identification of models AR; estimation of parameters and forecasting. (4 hours.)
Moving average models MA(q): stationary and invertibility conditions, Autocorrelation function, spectrum, identyfication of models MA, estymation of parameters, forecasting. (4 hours.)
Mixed models of autoregression and moving average ARMA(p,q): stationarity and invertibility conditions; autocorrelation function; spectrum; identification of ARMA; forecasting (2 hours)
Linear stationary models ARIMA(p,d,q): representation in difference form, random impulses and inverse form, identification of models ARIMA, forecastings. (4 godz.)
Class
Solving difference equations. (4 hours.)
Smothing of time series (analytic and mechanics metods). (3 hours.)
Computing of seasonal indicators. (2 hours.)
Computing of ex post and ex ante forecasts. (3 hours.)
Verification of stability of linear filters. (4 hours.)
Verification of weak and strict stationarity of time series. (4 hours)
Computing of autocorrelation and partial autocorrelation function in models AR, MA, ARMA, ARIMA. (4 hours.)
Calculation of parameters of models using Yule-Walker equations. (2 hours)
Calculation of forecastings of models AR, MA, ARMA, ARIMA. (4 hours)
Laboratory
Polynomial models of trend. (3 hours)
Seasonal variation models. (2 hours)
Prediction based on trend and seasonall models. (3 hours)
AR(p) models. (4 hours)
MA(q) models. (4 hours)
ARMA(p,q) models. (4 hours)
Verification of stationarity of model: unit root test. (2 hours)
ARIMA(p,d,q) models. (4 godz.)
Procedurs of elimination of seasonality. (4 godz.)
Teaching methods
Lecture. Class. On laboratory – solving tasks using computer package GRETL, R.
Learning outcomes and methods of theirs verification
Outcome description
Outcome symbols
Methods of verification
The class form
Assignment conditions
A student performs a report (laboratory) in which selects and solves a forecasting problem using time series models. The positive mark from laboratory is possible if the mark from report is positive. A student not attending to laboratory is not classified. Two tests (class) with mathematical tasks. The person not attending to class is not classified. One test (lecture) multiple choice.
Final mark O is a weighted average of marks from laboratory OL, from class OC and lecture OW, and is determined by the formula: O=0.4*OL+0.4*OC+0.2*OW.
Recommended reading
P. J. Brockwell, R. A. Davis, Introduction to time series and forecasting, Springer, New York, 2002.
G. Kirchgaessner, J. Wolters, Introduction to modern time series analysis, Springer, Berlin, 2007.
R. S. Tsay, Analysis of Financial Time Series, Wiley&Sons, New Jersey, 2005.
Further reading
G. E. P. Box, G. M. Jenkins, Analiza szeregów czasowych. Prognozowanie i sterowanie, PWN, Warszawa, 1983.
T. Kufel, Ekonometria. Rozwiązywanie problemów z wykorzystaniem programu Gretl, PWN, Warszawa, 2007.
Notes
Modified by dr Alina Szelecka (last modification: 18-09-2020 13:46)
