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Lecturer(s)
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Boďa Martin, doc. PhDr. Ing. PhD.
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Course content
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1. Stochastic processes and their main characteristics. Stationary stochastic processes. Wold decomposition. 2. Moving average models MA(q). Condition of invertibility. Autoregressive models AR(p). Yull-Worker equations. Stationarity conditions. Autoregressive-moving average models ARMA(p, q). 3. Coefficient estimation in ARMA (p, q) processes. Box-Jenkins methodology to identification of stationary time series models. 4. Forecasting, trend and seasonality in the framework of the Box-Jenkins model 5. Non-stationary time series. Time series with non-stationary variance, non-stationary mean. ARIMA (p, d, q) models. The use of Box-Jenkins methodology to determination of order of integration. 6. The unit root problem. Spurious trends and regressions. Unit root tests. 7. Unit root and structural changes. Non-stationary time series, trend stationarity versus difference stationarity. 8. Regressive dynamic models. Autoregressive models with distributed lags (ARDL).
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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The course seeks to acquaint students with the main concepts of modern time series theory universally applicable in describing the passage of natural and socioeconomic phenomena. Students will master methods of forecasting and analysis of time series based on the Box-Jenkins methodology of ARMA (p,d,q) models. They will understand difficulties associated with non-stationarity, and will learn methods how to tackle its presence. Finally, students will learn the pitfalls of running regressions with non-stationary time series. The course emphasises building of practical skill when working with real-world data in program R.
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Prerequisites
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unspecified
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Assessment methods and criteria
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unspecified
Good knowledge of statistics is prerequisite for this course.
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Recommended literature
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