|
|
Cusp catastrophe theory: Application to the housing market
Kořínek, Vojtěch ; Kukačka, Jiří (advisor) ; Nevrla, Matěj (referee)
The bachelor's thesis applies the stochastic cusp catastrophe model to the housing market of the United States. Weekly data over the period from 2007 to 2017 are used. The current catastrophe theory literature related to the housing market is reviewed, the models found are assessed and expanded. Specifically, we have identified three deficiencies of the catastrophe models applied to housing market in the current literature and our contribution lies in the elimination of these deficiencies. In order to satisfy the constant volatility assumption of the model, the state variable is normalized by the estimated volatility derived from GARCH. Furthermore, multiple control variables are added to the model to represent the activity of fundamentalists and chartists. The results suggest that the cusp catastrophe model fits the data better than the linear and logistic models. The normalization of the state variable improves the model performance while the introduction of the additional control variables does not produce better results. Keywords Housing market, catastrophe theory, stochastic cusp catastrophe model, hous- ing bubble, real estate, fundamental investors, speculation. 1
|
|
|
Quantal and thermal phase transitions in atomic nuclei
Dvořák, Martin ; Cejnar, Pavel (advisor) ; Knapp, František (referee)
In this bachelor work phase transitions in atomic nuclei are studied. The main attention is paid to quantal phase transitions between nuclear ground states of different symmetry. First, the interacting boson model in its simplest version, IBM-1, is introduced. The correspondence between the IBM and the geometric model of nuclei is indicated and possible shapes of the nucleus in the ground state are introduced. In the next step, critical and degenerated critical points of the potential derived from the IBM-1 are investigated in detail, especially their dependence on parameter values of the potential. Degenerated critical points are classified using the catastrophe theory. The special values of potential parameters are found for which phase transitions of the first and second order occur. Finally, the possibility of substitution of the potential by canonical catastrophic functions in a vicinity of degenerated critical points is discussed.
|
|
|
Cusp catastrophe theory: Application to the housing market
Kořínek, Vojtěch ; Kukačka, Jiří (advisor) ; Nevrla, Matěj (referee)
The bachelor's thesis applies the stochastic cusp catastrophe model to the housing market of the United States. Weekly data over the period from 2007 to 2017 are used. The current catastrophe theory literature related to the housing market is reviewed, the models found are assessed and expanded. Specifically, we have identified three deficiencies of the catastrophe models applied to housing market in the current literature and our contribution lies in the elimination of these deficiencies. In order to satisfy the constant volatility assumption of the model, the state variable is normalized by the estimated volatility derived from GARCH. Furthermore, multiple control variables are added to the model to represent the activity of fundamentalists and chartists. The results suggest that the cusp catastrophe model fits the data better than the linear and logistic models. The normalization of the state variable improves the model performance while the introduction of the additional control variables does not produce better results. Keywords Housing market, catastrophe theory, stochastic cusp catastrophe model, hous- ing bubble, real estate, fundamental investors, speculation. 1
|
|
|
Quantal and thermal phase transitions in atomic nuclei
Dvořák, Martin ; Cejnar, Pavel (advisor) ; Knapp, František (referee)
In this bachelor work phase transitions in atomic nuclei are studied. The main attention is paid to quantal phase transitions between nuclear ground states of different symmetry. First, the interacting boson model in its simplest version, IBM-1, is introduced. The correspondence between the IBM and the geometric model of nuclei is indicated and possible shapes of the nucleus in the ground state are introduced. In the next step, critical and degenerated critical points of the potential derived from the IBM-1 are investigated in detail, especially their dependence on parameter values of the potential. Degenerated critical points are classified using the catastrophe theory. The special values of potential parameters are found for which phase transitions of the first and second order occur. Finally, the possibility of substitution of the potential by canonical catastrophic functions in a vicinity of degenerated critical points is discussed.
|
guest ::
