Prediction of transformed time series
Predikce transformovaných časových řad
diploma thesis (DEFENDED)
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http://hdl.handle.net/20.500.11956/14891Identifiers
Study Information System: 43566
Collections
- Kvalifikační práce [10690]
Author
Advisor
Referee
Jarušková, Daniela
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
Probability, mathematical statistics and econometrics
Department
Department of Probability and Mathematical Statistics
Date of defense
15. 5. 2008
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
English
Grade
Excellent
The aim of this thesis is to find prediction for non-linear transformation of time series. First, under certain assumptions regarding the original time series, the autocovariance function and spectral density of the transformed time series are studied. General theorems are applied to concrete ARMA processes. Then general formulas for predictions of the transformed time series, which do not require knowledge of the autocovariance function of the transformed series nor its spectral density are presented. These formulas are applied to three concrete transformations and explicit formulas for ARMA processes are derived. Three types of predictions (optimal, naive and linear) are compared in the terms of proportional increase of mean square prediction error. Explicit formulas for ARMA processes are verified by a simulation.