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Tests for Multiple Changes in Linear Regression Models
Marušiaková, Miriam ; Hušková, Marie (vedoucí práce) ; Prášková, Zuzana (oponent) ; Picek, Jan (oponent)
We consider tests for multiple structural changes in linear regression models. The tests are based on F-type test statistics for the null hypothesis of no change against k changes or against an unknown number of changes with a given upper bound. We extend the existing results to linear regression models with deterministically trending regressors. Moreover, we introduce a generalized M-type test statistic which is based on functionals of weighted M-residuals. In change-point analysis approximations to critical values are usually obtained through the limit behavior of the respective test statistic under the null hypothesis. However, these approximations are often not satisfactory. Either the convergence of the test statistic to its limit distribution is rather slow or the limit distribution itself is very complex. An alternative approach is to apply resampling methods. We explore this possibility for F-type and M-type test statistics in the presence of multiple change points. We prove that the bootstrap method provides asymptotically correct critical values for the studied tests. We conduct several simulation experiments to show that the bootstrap based approximations are reasonable also in nite sample situations. Moreover, these approximations are often better than the asymptotic critical values. Finally, we...
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Aplikace Markowitzovy teorie portfolia na kapitálové trhy
Tyl, Tomáš ; Hurt, Jan (vedoucí práce) ; Marušiaková, Miriam (oponent)
Nazev prace: Aplikace Markowitzovy tcorie portfolia na kapitalovc trhy Autor: Tomas Tyl Katedra : Katedra pravdcpodobnosti a matematicke statistiky Vedouci diplomove prace: Doc. RNDr. Jan Hurt, CSc. e-mail vedouciho: Jan.IIurt@mff.cuni.cz Abstrakt: Prace pojednava o Markowitzove teorii portfolia a jeho aplikaci na realnych historickych datech pfi pouziti zakladnfch tri'd aktiv (jednotlive svetove akciove a dluhopisove trhy, hotovost, komodity). Cflem bude porovnat optimalm portfolia sestavena ze vstupnich udaju v historickych obdobich s ruznymi charakteristikami vynosu a rizika. Vysledkem by melo byt potvrzcnf, nebo vyvraceni hypotezy, ze pfi pouziti historickych dat je Markowitzuv model prakticky uzitecny pro bezncho investora. Prace se zameff na testovani Markowitzova modelu pro tfi typy drobnych investoru - konzcrvativniho, vyvazeneho a dynamickeho. Markowitzova teorie bude testovana pro rocnf a petilete vynosy. Klfcova slova:Teorie portfolia, Investovani, Skladba portfolia Title: Applications of the Markowitz portfoliotheory to capital markets Author: Tomas Tyl Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Jan Hurt, CSc. Supervisor's e-mail address: Jan.Hurt@mff.cuni.cz Abstract: This work discusses the Markowitz's stock portfolio theory and its application for...
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Strukturální změny ekonomických veličin
Nerglová, Eva ; Prášková, Zuzana (vedoucí práce) ; Marušiaková, Miriam (oponent)
Nazev prace: Strukturalni zmeny ekonomickych vclicin Autor: Eva Nerglova Katedra: Katedra pravdepodobnosti a,matematickc statistiky Vcdouci diplomove prace: Doc. RNDr. Zuzana Praskova,CSc. e-mail vedouciho: Zuxana.PraskovHMmff.runi.c-/, Abstrakt: Tato prace se zabyva. detekci zmen ve stfedni hodnote (v poloze) v posloupnosti nonnalne rozdelenych nahodnych vclicin a detckci zmen v jednoduchem inodelu linearni regrese (dvoufazovy rcgresni model). Vedle tcstovani hypote/y o ])fitoniuosti /nieny v uvazovanein inodelu se zabyva i od- hadeni bodu zineiiy a odhadein ])aranictru modelu prod a po zinene. Zabyva se zejmena bayesovsk_yni ])fistupein, v zaveru prace je zininen i pfistuj) zalozcny na metode inaximalni verohodnosti. Oba pfistii])y jsou porovnariy na shnulovaiiych i realnych datecli. Klicova slova: Strukturalni zmena. bod zineny, test stability, bayesovska analyza, inenici se nonnalni poslou]>nost7 dvoufazovy regresni model, metoda niaximalni verohodnosti Title: Structural changes of economic variables Author: Eva Nerglova Department: Department of Probability and Mathematical Statistics Supervisor: Doc. KXDr. Zuzana Prasko\a, CSc. Supervisor's e-mail address: Zuzana.Praskova^nifl.cimi.c/, Abstract: This thesis deals with detection of changes in the mean value (location) of a sequence of normally...
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Vícefázová regrese
Marušiaková, Miriam
We consider linear regression models with structural changes occurring at unknown time points. We describe F type tests for detection of changes. For calculation of approximations to the corresponding critical values we suggest a method based on the application of the permutation principle. We prove that the method is applicable to the F type test statistics. The simulation study shows that the permutation arguments provide satisfactory approximations to the critical values when the change in parameters is not too large. For estimation of the number of changes present we use information criteria and a method based on sequential testing. All discussed methods are applied to Klementinum data.
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Strukturální změny ekonomických veličin
Nerglová, Eva ; Marušiaková, Miriam (oponent) ; Prášková, Zuzana (vedoucí práce)
Nazev prace: Strukturalni zmeny ekonomickych vclicin Autor: Eva Nerglova Katedra: Katedra pravdepodobnosti a,matematickc statistiky Vcdouci diplomove prace: Doc. RNDr. Zuzana Praskova,CSc. e-mail vedouciho: Zuxana.PraskovHMmff.runi.c-/, Abstrakt: Tato prace se zabyva. detekci zmen ve stfedni hodnote (v poloze) v posloupnosti nonnalne rozdelenych nahodnych vclicin a detckci zmen v jednoduchem inodelu linearni regrese (dvoufazovy rcgresni model). Vedle tcstovani hypote/y o ])fitoniuosti /nieny v uvazovanein inodelu se zabyva i od- hadeni bodu zineiiy a odhadein ])aranictru modelu prod a po zinene. Zabyva se zejmena bayesovsk_yni ])fistupein, v zaveru prace je zininen i pfistuj) zalozcny na metode inaximalni verohodnosti. Oba pfistii])y jsou porovnariy na shnulovaiiych i realnych datecli. Klicova slova: Strukturalni zmena. bod zineny, test stability, bayesovska analyza, inenici se nonnalni poslou]>nost7 dvoufazovy regresni model, metoda niaximalni verohodnosti Title: Structural changes of economic variables Author: Eva Nerglova Department: Department of Probability and Mathematical Statistics Supervisor: Doc. KXDr. Zuzana Prasko\a, CSc. Supervisor's e-mail address: Zuzana.Praskova^nifl.cimi.c/, Abstract: This thesis deals with detection of changes in the mean value (location) of a sequence of normally...
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Aplikace Markowitzovy teorie portfolia na kapitálové trhy
Tyl, Tomáš ; Marušiaková, Miriam (oponent) ; Hurt, Jan (vedoucí práce)
Nazev prace: Aplikace Markowitzovy tcorie portfolia na kapitalovc trhy Autor: Tomas Tyl Katedra : Katedra pravdcpodobnosti a matematicke statistiky Vedouci diplomove prace: Doc. RNDr. Jan Hurt, CSc. e-mail vedouciho: Jan.IIurt@mff.cuni.cz Abstrakt: Prace pojednava o Markowitzove teorii portfolia a jeho aplikaci na realnych historickych datech pfi pouziti zakladnfch tri'd aktiv (jednotlive svetove akciove a dluhopisove trhy, hotovost, komodity). Cflem bude porovnat optimalm portfolia sestavena ze vstupnich udaju v historickych obdobich s ruznymi charakteristikami vynosu a rizika. Vysledkem by melo byt potvrzcnf, nebo vyvraceni hypotezy, ze pfi pouziti historickych dat je Markowitzuv model prakticky uzitecny pro bezncho investora. Prace se zameff na testovani Markowitzova modelu pro tfi typy drobnych investoru - konzcrvativniho, vyvazeneho a dynamickeho. Markowitzova teorie bude testovana pro rocnf a petilete vynosy. Klfcova slova:Teorie portfolia, Investovani, Skladba portfolia Title: Applications of the Markowitz portfoliotheory to capital markets Author: Tomas Tyl Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Jan Hurt, CSc. Supervisor's e-mail address: Jan.Hurt@mff.cuni.cz Abstract: This work discusses the Markowitz's stock portfolio theory and its application for...
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Tests for Multiple Changes in Linear Regression Models
Marušiaková, Miriam ; Hušková, Marie (vedoucí práce) ; Prášková, Zuzana (oponent) ; Picek, Jan (oponent)
We consider tests for multiple structural changes in linear regression models. The tests are based on F-type test statistics for the null hypothesis of no change against k changes or against an unknown number of changes with a given upper bound. We extend the existing results to linear regression models with deterministically trending regressors. Moreover, we introduce a generalized M-type test statistic which is based on functionals of weighted M-residuals. In change-point analysis approximations to critical values are usually obtained through the limit behavior of the respective test statistic under the null hypothesis. However, these approximations are often not satisfactory. Either the convergence of the test statistic to its limit distribution is rather slow or the limit distribution itself is very complex. An alternative approach is to apply resampling methods. We explore this possibility for F-type and M-type test statistics in the presence of multiple change points. We prove that the bootstrap method provides asymptotically correct critical values for the studied tests. We conduct several simulation experiments to show that the bootstrap based approximations are reasonable also in nite sample situations. Moreover, these approximations are often better than the asymptotic critical values. Finally, we...
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