Oesook Lee

An instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models

The unit root tests of Caner and Hansen (Econometrica 69 (2001) 1555) for asymmetric time series models based on the ordinary least squares estimator (OLSE) have asymptotic null distributions that depend on parameters of asymmetry. We resolve this parameter dependency by adopting the instrumental variable estimation of Shin and Lee (J. Business & Economic Statist. 19 (2001) 233) and the recursive mean adjustment of Shin and So (J. Time Series Anal. 22 (2001b) 595). If the threshold parameter is known, the limiting null distribution of the proposed Wald test does not depend on any nuisance parameter and is chi-squared. If the threshold parameter is unknown and is estimated from data, then under threshold effect, the limiting null distributions of the proposed Wald tests are chi-squared as those for model with known threshold parameter whereas, under no threshold effect, they are chi-squared only conditionally on the weak limit of the estimated threshold parameter. Our Wald tests extend to seasonal models retaining the chi-square asymptotics regardless of the parameter of seasonality, which is not the case of the OLSE-based tests. Moreover, the proposed tests can be modified into one-sided Wald tests which are significantly more powerful than the tests of Caner and Hansen (2001). We apply our method to the monthly US unemployment rate and find some evidences of seasonal unit roots, suggesting nonstationarity rather than the strong stationarity of Caner and Hansen (2001).

Ergodicity and central limit theorems for a class of Markov processes

We consider a class of discrete parameter Markov processes on a complete separable metric space S arising from successive compositions of i.i.d. random maps on S into itself, the compositions becoming contractions eventually. A sufficient condition for ergodicity is found, extending a result of Dubins and Freedman [8] for compact S. By identifying a broad subset of the range of the generator, a functional central limit theorem is proved for arbitrary Lipschitzian functions on S, without requiring any mixing type condition or irreducibility.

Probabilistic Properties of a Nonlinear ARMA Process with Markov Switching

ABSTRACT We consider a nonlinear autoregressive moving average (ARMA) process with Markov switching and find sufficient conditions for strict stationarity, geometric ergodicity, and the existence of moments of the process with respect to the stationary distribution. Functional central limit theorem is also obtained.

A note on stationarity of the MTAR process on the boundary of the stationarity region

Abstract We show that the momentum threshold autoregressive (MTAR) process is stationary (ergodic) on the boundary of the region of stationarity corresponding to partial unit roots. This is in contrast with the fact that the self exciting TAR (SETAR) process, as well as the linear autoregressive moving average (ARMA) process, is nonstationary on the boundary of the region of stationarity.

On geometric ergodicity of the MTAR process

We consider the momentum threshold autoregressive (MTAR) process and characterize the region of the autoregressive coefficients for geometric ergodicity. The region is a proper subset of the ergodic region of the TAR process. We show that the process is geometrically ergodic inside the region and is transient outside the closure of the region.

On probabilistic properties of nonlinear ARMA(p,q) models☆

We consider a general nonlinear ARMA(p,q) model Xn+1=h(en-q+1,...,en,Xn-p+1,...,Xn)+en+1, where h : Rp+q-->R is a measurable function and {en: n[greater-or-equal, slanted]1} is an i.i.d. sequence of random variables. Sufficient conditions for stationarity and geometric ergodicity of {Xn} are obtained by considering the asymptotic behaviours of the associated Markov chain.

Geometric Ergodicity and Moment Conditions for a Seasonal GARCH Model with Periodic Coefficients

A seasonal GARCH process with periodic coefficients is considered and conditions for periodic stationarity, geometric ergodicity, β-mixing property with exponential decay rate, and existence of higher-order moments are obtained.

Limit theorems for some doubly stochastic processes

We consider the stochastic processes Xk+1 = [Gamma]k+1(Xk) + Wk+1 where {[Gamma]k} is a sequence of nonlinear random functions and {Wk} is a sequence of disturbances. Sufficient conditions for the existence of a unique invariant probability are obtained. Functional central limit theorem is proved for every Lipschitzian function on R.

Blood Pressure Control During Chronic Kidney Disease Progression

BACKGROUND Hypertension is a major cause of end-stage renal disease, and blood pressure (BP) control is crucial in patients with chronic kidney disease (CKD). However, it is generally inadequately controlled in CKD patients. We investigated the prevalence of CKD patients with inadequate BP control and its related factors, based on the CKD stage. METHODS We analyzed the health examination sample cohort database, which consisted of the randomly selected participants among all the citizens who received the health examination provided by National Health Insurance Service of Korea in 2012 and 2013. RESULTS There were 27,350 CKD patients (7.9%) out of a total of 345,044 participants. As CKD stage progressed, there were more patients with poorly controlled hypertension compared to those with well-controlled hypertension. In addition, systolic BP increased with CKD stage progression, while diastolic BP was not significantly different. Age, female, body mass index, increased pulse pressure, CKD stage, and levels of fasting glucose, total cholesterol, hemoglobin, and proteinuria were significant factors associated with poor control of BP in hypertensive CKD patients. CONCLUSION The proportion of CKD patients with poorly controlled hypertension significantly increased as CKD progressed, mainly associated with the increase in pulse pressure. However, future investigation for causal relationship between poorly controlled hypertension and its related factors is needed.

Asymptotic behaviors of randomly perturbed dynamical systems

We consider the asymptotic behaviors of certain Markov processes which are generated by successive iterations of independent and identically distributed random maps. For the cases that after some number of iterations, iterated maps are Lipschitzian or satisfy the average contraction condition, we find sufficient conditions under which there exists a unique invariant probability. A functional central limit theorem and a strong law of large numbers are proved for Lipschitzian functions