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Holt-Winters method for exponential smoothing
Koritarová, Lenka ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
"his thesis de-ls with the methods of exponenti-l smoothingF et (rst the prin iE ples of exponenti-l smoothing -re expl-inedF e fo us on -si -ppro- hesX sinE gleD dou le smoothing -nd the rolt¡s methodF "hese pro edures -re suit- le for the modeling time series without se-son-l omponentF rowever in pr- ti e there -re frequent time series with se-son-lityF por su h time series the roltE inter¡s method is usedF "his method is -sed just on the prin iples of exponenti-l smooE thingF sn the l-st p-rt of this thesisD there is demonstr-ted using this methods on re-l d-t-F
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Selected methods of time series analysis with STATISTICA
Indrová, Magdalena ; Hudecová, Šárka (advisor) ; Zichová, Jitka (referee)
This work deals with the use of STATISTICA software for the basic analysis of time series. The thesis is focused on time series decomposition, mainly on the trend elimination. First, the basic methods of the analysis are described theoretically, namely, trend modeling using mathematical curves (polynomial, exponential, logistic and Gompertz) and adaptive approach (moving averages, simple exponential smoothing and Holt's method). These methods are then applied to three selected data sets (unnamed bank's balance sheet from 1998 to 1993, ship construction trends between 1820 and 1997, and CZK/EUR Exchange rate from 1998 to 2012). All analytical procedures are described in detail and individual program outputs are thoroughly explained and commented.
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Some problems of exponential smoothing
Čurda, David ; Hanzák, Tomáš (advisor) ; Komárek, Arnošt (referee)
In this work the several exponential smoothing type methods are briefly described, which are often used to smoothing and forecasting in the time series. Selected problems, that occur in described methods, are presented and in some cases there are the suggestions to their solution, which should tend to more suitable smoothing or to the better forecasts. It's shown how the methods are applied on different data and how the forecasts differ from each other. In conclusion the quality of modifications is evaluated.
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Methods for periodic and irregular time series
Hanzák, Tomáš
Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity
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Seasonal exponential smoothing
Rábek, Július ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This thesis deals with the issues of time series modeling, where seasonal component is present. Principles of basic seasonal exponential smoothing methods: simple and double exponential smoothing, Holt's method, which are applicable on time series without seasonality, are described in the beginning. For seasonal time series, Holt-Winters exponential smoothing is the most suitable method. This method is introduced in both of its versions and the usage of either version depends on the characteristics of the seasonal component. Furthermore, state space modeling is presented as a statistical framework for exponential smoothing methods, joined with a discussion of some selected problems related with practical implementation of these techniques together with suggestions of their solution. Finally, Holt-Winters method on two real data time series with seasonality is presented.
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Analysis of Wages and Salaries in the Pardubice Region
Hanuš, Pavel ; Löster, Tomáš (advisor) ; Šimpach, Ondřej (referee)
This bachelor thesis deals with the study of changes in income of the economically active population in the given region. The main aim of the thesis is to analyze the wage and salary sphere of the population in the Pardubice region and to compare the size of wages and salaries by category. These include age groups, gender, highest education and type of profession. The partial aim is to predict the evolution of hourly earnings using appropriately selected statistical methods. The main benefit of this thesis is to provide a comprehensive overview of the size of the personal income in the Pardubice region for 2015 and 2016.
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Methods for periodic and irregular time series
Hanzák, Tomáš ; Cipra, Tomáš (advisor) ; Arlt, Josef (referee) ; Prášková, Zuzana (referee)
Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity
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Seasonal state space modeling
Suk, Luboš ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
State space modeling represents a statistical framework for exponential smoo- thing methods and it is often used in time series modeling. This thesis descri- bes seasonal innovations state space models and focuses on recently suggested TBATS model. This model includes Box-Cox transformation, ARMA model for residuals and trigonometric representation of seasonality and it was designed to handle a broad spectrum of time series with complex types of seasonality inclu- ding multiple seasonality, high frequency of data, non-integer periods of seasonal components, and dual-calendar effects. The estimation of the parameters based on maximum likelihood and trigonometric representation of seasonality greatly reduce computational burden in this model. The universatility of TBATS model is demonstrated by four real data time series.
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Holt-Winters method for exponential smoothing
Koritarová, Lenka ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
"his thesis de-ls with the methods of exponenti-l smoothingF et (rst the prin iE ples of exponenti-l smoothing -re expl-inedF e fo us on -si -ppro- hesX sinE gleD dou le smoothing -nd the rolt¡s methodF "hese pro edures -re suit- le for the modeling time series without se-son-l omponentF rowever in pr- ti e there -re frequent time series with se-son-lityF por su h time series the roltE inter¡s method is usedF "his method is -sed just on the prin iples of exponenti-l smooE thingF sn the l-st p-rt of this thesisD there is demonstr-ted using this methods on re-l d-t-F
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Methods for periodic and irregular time series
Hanzák, Tomáš
Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity
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