Unit Root Tests with Markov-Switching

Diba and Grossman (1988) and Hamilton and Whiteman (1985) recommended unit root tests for rational bubbles. They argued that if stock prices are not more explosive than dividends, then it can be concluded that rational bubbles are not present. Evans (1991) demonstrated that these tests will fail to detect the class of rational bubbles which collapse periodically. When such bubbles are present, stock prices will not appear to be more explosive than the dividends on the basis of these tests, even though the bubbles are substantial in magnitude and volatility. Hall et al. (1999) show that the power of unit root test can be improved substantially when the underlying process of the sample observations is allowed to follow a first-order Markov process. Our paper applies unit root tests to the property prices of Hong Kong and Seoul, allowing for the data generating process to follow a three states Markov chain. The null hypothesis of unit root is tested against the explosive bubble or stable alternative. Simulation studies are used to generate the critical values for the one-sided test. The time series used in the tests are the monthly price and rent indices of Seoul's housing (1986:1 to 2003:6) and Hong Kong's retail premise (1980:12 to 2003:1). The investigations show that only one state appears to be highly likely in both cases. The switching unit root tests failed to find explosive bubbles in the price series, which might be due to the fact that the power of test is weak in the presence of heteroscedasticityunit root, three states markov switching, explosive rational bubbles

Signal Extraction with Kalman Filter: A Study of the Hong Kong Property Price Bubbles

Since Flood and Garber (1980), the debate surrounding speculative bubbles has never subsided. A key obstacle to resolve this issue is the identification problem. A bubble is usually inferred from some assumed fundamental determinants of a price. These assumptions could be over-simplified. Furthermore, there might be data measurement errors. In this paper, we attempt to capture such errors with a latent state variable. This variable is extracted with Kalman filter. Based on our empirical comparisons, we find that it is possible to attribute the observed large price swings in the property market of Hong Kong during the 1980s and 1990s to a periodically collapsing rational speculative bubble.rational speculative bubble, misspecification or measurement error, Kalman filter

Unit Root Tests With Markov-Switching

Diba and Grossman (1988) and Hamilton and Whiteman (1985) recommended unit root tests for rational bubbles. They argued that if stock prices are not more explosive than dividends, then it can be concluded that rational bubbles are not present. Evans (1991) demonstrated that these tests will fail to detect the class of rational bubbles which collapse periodically. When such bubbles are present, stock prices will not appear to be more explosive than the dividends on the basis of these tests, even though the bubbles are substantial in magnitude and volatility. Hall et al. (1999) show that the power of unit root test can be improved substantially when the underlying process of the sample observations is allowed to follow a first-order Markov process. Our paper applies unit root tests to the property prices of Hong Kong and Seoul, allowing for the data generating process to follow a three states Markov chain. The null hypothesis of unit root is tested against the explosive bubble or stable alternative. Simulation studies are used to generate the critical values for the one-sided test. The time series used in the tests are the monthly price and rent indices of Seoul’s housing (1986:1 to 2003:6) and Hong Kong’s retail premise (1980:12 to 2003:1). The investigations show that only one state appears to be highly likely in all series under investigation and the switching unit root procedure failed to find explosive bubbles in both prices.unit root, bootstrap, Markov-Switching

Markov-switching Unit Root Test: A study of the Property Price Bubbles in Hong Kong and Seoul

Evans (1991) demonstrates that the unit root tests recommended by Hamilton and Whiteman (1985) and Diba and Grossman (1988) will fail to detect periodically collapsing rational bubbles. Hall et al. (1999) however show that the power of this test procedure can be improved by incorporating a Markov-switching state variable. In this paper, we apply both procedures to selected data from Hong Kong and Seoul. Both point to the possible existence of a periodically-collapsing bubble in each price series investigated, with the second procedure more precise on timing the bubble. Our Markovswitching model is validated using a symmetry test and a Wald test.Markov-switching, unit root test, periodically-collapsing bubble, real-estate

Gravito-Electromagnetic coupled perturbations and quasinormal modes of a charged black hole with scalar hair

From the quantum point of view, singularity should not exist. Recently, Bah and Heidmann constructed a five-dimensional singularity free topology star/black hole [Phys. Rev. Lett. 126, 151101 (2021)]. By integrating the extra dimension, a four-dimensional static spherical black hole with a magnetic charge and scalar hair can be obtained. In this paper, we study the quasinormal modes (QNMs) of the magnetic field and gravitational field on the background of this four-dimensional charged black hole with scalar hair. The odd parity of the gravitational perturbations couples with the even parity of the magnetic field perturbations. Two coupled second-order derivative equations are obtained. Using the matrix-valued direct integration method, we obtain the fundamental QNM frequencies numerically. The effect of the magnetic charge on the QNMs is studied. The differences of the frequencies of the fundamental QNMs between the charged black hole with scalar hair and the Reissner-Norstr\"{o}m black hole are very small for the angular number $l=2$. However, some new interesting results are found for higher angular number.Comment: 10 pages, 3 figures, 2 tables, some mistakes have been correcte

Axial gravitational quasinormal modes of a self-dual black hole in loop quantum gravity

We study the axial gravitational quasinormal modes of a self-dual black hole in loop quantum gravity. Considering the axial perturbation of the background spacetime, we obtain the Schr\"{o}dinger-like master equation. Then we calculate the quasinormal frequencies with the Wentzel-Kramers-Brillouin approximation and the asymptotic iteration method. We also investigate the numerical evolution of an initial wave packet on the self-dual black hole spacetime.~We find the quantum correction parameter $P$ positively affects the absolute values of both the real and imaginary parts of quasinormal frequencies. We derive the relation between the parameters of the circular null geodesics and quasinormal frequencies in the eikonal limit for the self-dual black hole, and numerically verify this relation.Comment: 13 pages, 5 figures, 5 table

Gravitational resonances on f(T)f(T)-branes

In this work, we investigate the gravitational resonances in various $f(T)$-brane models with the warp factor $\text{e}^{A(y)}=\tanh\big(k(y+b)\big)-\tanh\big(k(y-b)\big)$. For three kinds of $f(T)$, we give the solutions to the system. Besides, we consider the tensor perturbation of vielbein and obtain the effective potentials by the Kaluza-Klein (KK) decomposition. Then, we analyze what kind of effective potential can produce the gravitational resonances. Effects of different parameters on the gravitational resonances are analysed. The lifetimes of the resonances could be long enough as the age of our universe in some ranges of the parameters. This indicates that the gravitational resonances might be considered as one of the candidates of dark matter. Combining the current experimental observations, we constrain the parameters for these brane models.Comment: 12 pages, 14 figure

Characteristic modes of thick brane model: resonances and quasinormal modes

In this work, we investigate the gravitational quasinormal modes (QNMs) and the gravitational resonances of a thick brane model. We use the asymptotic iteration and shooting methods to obtain the quasinormal frequencies (QNFs) of the brane. On the other hand, we investigate the resonances and their evolution numerically. The results show that the oscillations of the resonances equal (up to numerical error) to the real parts of the QNFs, while the damping rates of the resonances equal to the imaginary parts of the QNFs. The QNMs and resonances, both of them can be regarded as the characteristic modes of the thick brane, are closely related with each other. In addition, the lifetimes of the QNMs might reach the age of our universe. Such a long-lived Kaluza-Klein modes could be a candidate for dark matter.Comment: 10 pages, 6 figure

Evolution of Fermion Resonance in Thick Brane

In this work, we investigate numerical evolution of massive Kaluza-Klein (KK) modes of a Dirac field on a thick brane. We deduce the Dirac equation in five-dimensional spacetime, and obtain the time-dependent evolution equation and Schr\"odinger-like equation of the extra-dimensional component. We use the Dirac KK resonances as the initial data and study the corresponding dynamics. By monitoring the decay law of the left- and right-chiral KK resonances, we compute the corresponding lifetimes and find that there could exist long-lived KK modes on the brane. Especially, for the lightest KK resonance with a large coupling parameter and a large three momentum, it will have an extremely long lifetime.Comment: 26 pages, 12 figure

Hemiballism-hemichorea induced by ketotic hyperglycemia: case report with PET study and review of the literature

Hemiballism-hemichorea (HB-HC) is commonly used to describe the basal ganglion dysfunction in non-ketotic hyperglycemic elderly patients. Here we report two elderly female patients with acute onset of involuntary movements induced by hyperglycemia with positive urine ketones. We described the computed tomography and magnetic resonance imaging findings in these two patients, which is similar to that of non-ketotic hyperglycemic HB-HC patients. FDG-PET was performed and the glucose metabolism in the corresponding lesion in these two patients was contradictory with each other. We tried to clarify the underlying mechanisms of HB-HC and explain the contradictory neuroradiological findings in FDG-PET as being performed at different clinical stages