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Modely celočíselných časových řad s náhodnými koeficienty
Burdejová, Petra ; Prášková, Zuzana (advisor) ; Cipra, Tomáš (referee)
Title: Models of integer-valued time series with random coefficients Author: Petra Burdejová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Zuzana Prášková, CSc. Abstract: In the presented thesis, a generalized integer-valued autoregres- sive process of the order p (GINAR(p)) is considered first. The main aim is taken to introduction of random coefficient integer-valued autoregressive process (RCINAR(p)). We use a thinning operator in order to define the processes. The main characteristics of GINAR(p) and RCINAR(p) are obtained. Condi- tions for stationarity and ergodicity are stated. Three methods of estimation (Yule-Walker, Conditional least squares, Generalized method of moments) are given and compared in simulation with respect to the mean squared error (MSE). At the end, RCINAR(3) model is applied to a real dataset representing a number of earthquakes per year. Keywords: thinning operator, random coefficients, integer-valued time se- ries, GINAR, RCINAR
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Models of integer-valued time series
Houfková, Lucia
13311971730966-1666e6a7843fe8fa35041013336015b3.txt Abstract Title: Models of integer-valued time series Author: Lucia Jarešová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Zuzana Prášková, CSc. Supervisor's e-mail address: praskova@karlin.mff.cuni.cz Abstract: In the presented work the generalized integer valued processes GINAR founded on the Steutel and van Harn generalized operator are studied. Proper- ties of this operator, which are based on the sum of i.i.d. random variables are investigated including the determination of the domain of the operator and sug- gestion of possible construction of this operator. The attention is given on a weak stationary GINAR(p), the main properties of this process are described and it is shown that this process has an AR(p) representation, where the white noise consists of martingale differences. Further, the parameter estimators are descri- bed and consequently tested on extensive simulation with differently distributed innovations. The results are compared according to MSE. The work also contains a real data application. At the end the vector processes VGINAR are mentio- ned, that can also have a VAR representation. The functions for the program environment R are included. Keywords: GINAR, VGINAR, Steutel and van Harn...
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Modely celočíselných časových řad s náhodnými koeficienty
Burdejová, Petra ; Prášková, Zuzana (advisor) ; Cipra, Tomáš (referee)
Title: Models of integer-valued time series with random coefficients Author: Petra Burdejová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Zuzana Prášková, CSc. Abstract: In the presented thesis, a generalized integer-valued autoregres- sive process of the order p (GINAR(p)) is considered first. The main aim is taken to introduction of random coefficient integer-valued autoregressive process (RCINAR(p)). We use a thinning operator in order to define the processes. The main characteristics of GINAR(p) and RCINAR(p) are obtained. Condi- tions for stationarity and ergodicity are stated. Three methods of estimation (Yule-Walker, Conditional least squares, Generalized method of moments) are given and compared in simulation with respect to the mean squared error (MSE). At the end, RCINAR(3) model is applied to a real dataset representing a number of earthquakes per year. Keywords: thinning operator, random coefficients, integer-valued time se- ries, GINAR, RCINAR
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Models of integer-valued time series
Houfková, Lucia
13311971730966-1666e6a7843fe8fa35041013336015b3.txt Abstract Title: Models of integer-valued time series Author: Lucia Jarešová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Zuzana Prášková, CSc. Supervisor's e-mail address: praskova@karlin.mff.cuni.cz Abstract: In the presented work the generalized integer valued processes GINAR founded on the Steutel and van Harn generalized operator are studied. Proper- ties of this operator, which are based on the sum of i.i.d. random variables are investigated including the determination of the domain of the operator and sug- gestion of possible construction of this operator. The attention is given on a weak stationary GINAR(p), the main properties of this process are described and it is shown that this process has an AR(p) representation, where the white noise consists of martingale differences. Further, the parameter estimators are descri- bed and consequently tested on extensive simulation with differently distributed innovations. The results are compared according to MSE. The work also contains a real data application. At the end the vector processes VGINAR are mentio- ned, that can also have a VAR representation. The functions for the program environment R are included. Keywords: GINAR, VGINAR, Steutel and van Harn...
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