How Are Shocks to Trend and Cycle Correlated? A Simple Methodology for Unidentified Unobserved Components Models

In this paper, we propose a simple methodology for investigating how shocks to trend and cycle are correlated in unidentified unobserved components models, in which the correlation is not identified. The proposed methodology is applied to U.S. and U.K. real GDP data. We find that the correlation parameters are negative for both countries. We also investigate how changing the identification restriction results in different trend and cycle estimates. It is found that estimates of the trend and cycle can vary substantially depending on the identification restrictions imposed.Business Cycle Analysis, Trend, Cycle, Permanent Component, Transitory Component, Unobserved Components Model

Testing for Coefficient Stability of AR(1) Model When the Null is an Integrated or a Stationary Process

In this paper, we propose a test for coefficient stability of an AR(1) model against the random coefficient autoregressive model of order 1 or RCA(1) model without assuming a stationary nor a non- stationary process under the null hypothesis of constant coefficient. The proposed test is obtained as a modification of the locally best invariant (LBI) test by Lee (1998). We examine finite sample properties of the proposed test by Monte Carlo experiments comparing with other existing tests including the LBI test by McCabe and Tremayne (1995), which is for the null of unit root against the alternative of stochastic unit root.Random Coefficient Autoregressive Model, Stability, Constancy

Inconsistency of a Unit Root Test against Stochastic Unit Root Processes

In this paper, we develop the asymptotic theory of Hwang and Basawa (2005) for explosive random coefficient autoregressive (ERCA) models. Applying the theory, we prove that a locally best invariant (LBI) test in McCabe and Tremayne (1995), which is for the null of a unit root (UR) process against the alternative of a stochastic unit root (STUR) process, is inconsistent against a class of ERCA models. This class includes a class of STUR processes as special cases. We show, however, that the well-known Dickey-Fuller (DF) UR tests and an LBI test of Lee (1998) are consistent against a particular case of this class of ERCA models.Locally Best Invariant Test, Consistency, Dickey-Fuller Test, LBI, RCA, STUR

A note on the relationship between the information matrx test and a score test for parameter constancy

Information matrix (IM) test (White, 1982) has been used for detecting general model misspecification in the applied econometrics literature. Two of the most commonly used asymptotic covariance matrix estimators (ACMEs) for the IM test are the one that White (1982) proposed in his original paper and Chesher (1983)'s ACME. Chesher (1984) showed that the IM test is in effect a score test for parameter constancy. In this note, I show that the IM test with White''s ACME is not only the score test but also a specification robust form of the score test or a score test for quasi-maximum likelihood estimators. Based on this result, it is argued that we should be careful in selecting the ACME for properly interpreting the consequence of the IM test.Hessian matrix

How Are Shocks to Trend and Cycle Correlated? A Simple Methodology for Unidentified Unobserved Components Models

In this paper, we propose a simple methodology for investigating how shocks to trend and cycle are correlated in unidentified unobserved components models, in which the correlation is not identified. The proposed methodology is applied to U.S. and U.K. real GDP data. We find that the correlation parameters are negative for both countries. We also investigate how changing the identification restriction results in different trend and cycle estimates.Unobserved components model, Trend, Cycle, Business Cycle Analysis

Semi-dynamical approach to the shock revival in core-collapse supernovae

We develop a new semi-dynamical method to study shock revival by neutrino heating in core- collapse supernovae. Our new approach is an extension of the previous studies that employ spherically symmetric, steady, shocked accretion flows together with the light bulb approximation. The latter has been widely used in the supernova community for the phenomenological investigation of the criteria for successful supernova explosions. In the present approach, on the other hand, we get rid of the steady-state condition and take into account shock wave motions instead. We have in mind the scenario that not the critical luminosity but the critical fluctuation generated by hydrodynamical instabilities such as SASI and neutrino-driven convection in the post-shock region determines the onset of shock revival. After confirming that the new approach indeed captures the dynamics of revived shock wave qualitatively, we then apply the method to various initial conditions and find that there is a critical fluctuation for shock revival, which can be well fit by the following formula: f_crit ~ 0.8 * (M_in/1.4M_sun) * {1- (rsh/10^8cm)}, in which fcrit denotes the critical pressure fluctuation normalized by the unperturbed post-shock value. Min and rsh stand for the mass of the central compact object and the shock radius, respectively. The critical fluctuation decreases with the shock radius, whereas it increases with the mass of the central object. We discuss the possible implications of our results for 3D effects on shock revival, which is currently controversial in the supernova community.Comment: 15 pages, 10 figures, accepted for publication in Ap

A State Space Approach to Estimating the Integrated Variance and Microstructure Noise Component

We call the realized variance (RV) calculated with observed prices contaminated by microstructure noises (MNs) the noise-contaminated RV (NCRV) and refer to the component in the NCRV associated with the MNs as the MN component. This paper develops a method for estimating the integrated variance (IV) and MN component simultaneously, extending the state space method proposed by Barndorff-Nielsen and Shephard (2002). Our extension is based on the result obtained in Meddahi (2003), namely, when the true log-price process follows a general class of continuous-time stochastic volatility (SV) models, the IV follows an ARMA process. We represent the NCRV by a state space form and show that the state space form parameters are not identifiable; however, they can be expressed as functions of fewer identifiable parameters. We illustrate how to estimate these parameters. The proposed method is applied to yen/dollar exchange rate data. We find that the magnitude of the MN component is, on average, about 21%-48 % of the NCRV, depending on the sampling frequency.Realized Variance, Integrated Variance, Microstructure Noise

The Standing Accretion Shock Instability in the Disk around the Kerr Black Hole

This paper is a sequel to our previous work for accretion onto a Schwarzschild black hole and the so-called standing accretion shock instability (SASI), in this paper we investigate non-axisymmetric perturbations for a Kerr black hole. The linear and non-linear phases for the shock evolution are analyzed in detail by both 2D general relativistic hydrodynamical simulations and linear analysis. Since the structure of steady axisymmetric accretion flows with a standing shock wave is very sensitive to the inner transonic flow, their properties such as Mach numbers, which are important for the stability, depend on the Kerr parameter very much. Although the essential features of the instability do not differ from the previous results for the Schwarzschild black hole, the frame dragging effects specific to the Kerr black hole is also evident. Interestingly, the oscillation periods of the fundamental unstable modes are dependent only on the shock radius irrespective of the injection parameters.Comment: 27 pages, 12 figures, accepted in Ap

Implications of Two Measures of Persistence for Correlation Between Permanent and Transitory Shocks in U.S. Real GDP

Conventionally, shocks to permanent and transitory components in the unobserved components (UC) model for the log of real GDP are assumed to be uncorrelated. This assumption is mainly for identification of model parameters. In this paper, we show important implications of two popular measures of persistence for the correlation between permanent and transitory shocks in the UC model, and demonstrate that the correlation is negative for the log of U.S. real GDP under a very general specification of the cycle process.