Quantile Regression for Location-Scale Time Series Models with Conditional Heteroscedasticity

This paper considers quantile regression for a wide class of time series models including ARMA models with asymmetric GARCH (AGARCH) errors. The classical mean-variance models are reinterpreted as conditional location-scale models so that the quantile regression method can be naturally geared into the considered models. The consistency and asymptotic normality of the quantile regression estimator is established in location-scale time series models under mild conditions. In the application of this result to ARMA-AGARCH models, more primitive conditions are deduced to obtain the asymptotic properties. For illustration, a simulation study and a real data analysis are provided.Comment: 37 pages, 1 figur

The Cusum Test for Parameter Change in Regression with ARCH Errors

In this paper, we concentrate ourselves on Inclán and Tiao (1994)'s cusum test in regression models with ARCH errors. The ARCH and GARCH models have long been popular in financial time series analysis. For a general review, see Gouriéroux (1997).Inclán and Tiao (1994)'s cusum test was originally designed for testing for variance changes and allocating their locations in iid samples. Later, it was demonstrated that the same idea can be extended to a large class of time series models (cf. Lee et all, 2003(a)). Also, the variance change test has been studied in unstable AR models (cf. Lee et al. (2003(b)). In fact, Kim, Cho and Lee (2000) considered to apply the cusum test to GARCH(1,1) models taking account of the fact that the variance is a functional of GARCH parameters, and their change can be detected by examining the existence of the variance change. Although this reasoning was correct, it turned out that the cusum test suffers from severe size distortions and low powers. Hence, there was a demand to improve their cusum test. Here, in order to circumvent such drawbacks, we propose to use the cusum test based on the residuals, given as the squares of observations divided by estimated conditional variances. We intend to use residuals since the residual based test conventionally discard correlation effects and enhance the performance of the test. In fact, a significant improvement was observed in our simulation study. Despite the previous work of Lee et al. (2003(b)) also considers a residual cusum test in time series models, the model of main concern was the autoregressive model with several unit roots. In fact, the mathematical analysis of the cusum test heavily relies on the probabilistic structure of the underlying time series model, and the arguments used for establishing the weak convergence result in unstable models are somewhat different from those in ARCH models. Therefore it is worth to investigate the asymptotic behavior of the residual cusum test in ARCH models. Although the present paper was originally motivated to improve Kim, Cho and Lee (2000)'s test in the GARCH(1,1) model, we consider the cusum test in a more general class of models including regression models with infinite order ARCH errors.Test for parameter change, regression models with ARCH errors, residual cusum test, Brownian bridge, weak convergence

Sequential point estimation of parameters in a threshold AR(1) model

AbstractWe show that if an appropriate stopping rule is used to determine the sample size when estimating the parameters in a stationary and ergodic threshold AR(1) model, then the sequential least-squares estimator is asymptotically risk efficient. The stopping rule is also shown to be asymptotically efficient. Furthermore, non-linear renewal theory is used to obtain the limit distribution of appropriately normalized stopping rule and a second-order expansion for the expected sample size. A central result here is the rate of decay of lower-tail probability of average of stationary, geometrically β-mixing sequences

Fourier-type monitoring procedures for strict stationarity

We consider model-free monitoring procedures for strict stationarity of a given time series. The new criteria are formulated as L2-type statistics incorporating the empirical characteristic function. Asymptotic as well as Monte Carlo results are presented. The new methods are also employed in order to test for possible stationarity breaks in time-series data from the financial sector

A CPW-Fed Rectangular Ring Monopole Antenna for WLAN Applications

We present a simple coplanar waveguide- (CPW-) fed rectangular ring monopole antenna designed for dual-band wireless local area network (WLAN) applications. The antenna is based on a simple structure composed of a CPW feed line and a rectangular ring. Dual-band WLAN operation can be achieved by controlling the distance between the rectangular ring and the ground plane of the CPW feed line, as well as the horizontal vertical lengths of the rectangular ring. Simulated and measured data show that the antenna has a compact size of 21.4×59.4 mm2, an impedance bandwidths of 2.21–2.70 GHz and 5.04–6.03 GHz, and a reflection coefficient of less than −10 dB. The antenna also exhibits an almost omnidirectional radiation pattern. This simple compact antenna with favorable frequency characteristics therefore is attractive for applications in dual-band WLAN

Imaging retinal nerve fiber bundles using optical coherence tomography with adaptive optics

AbstractEarly detection of axonal tissue loss in retinal nerve fiber layer (RNFL) is critical for effective treatment and management of diseases such as glaucoma. This study aims to evaluate the capability of ultrahigh-resolution optical coherence tomography with adaptive optics (UHR-AO-OCT) for imaging the RNFL axonal bundles (RNFBs) with 3×3×3μm3 resolution in the eye. We used a research-grade UHR-AO-OCT system to acquire 3°×3° volumes in four normal subjects and one subject with an arcuate retinal nerve fiber layer defect (n=5; 29–62years). Cross section (B-scans) and en face (C-scan) slices extracted from the volumes were used to assess visibility and size distribution of individual RNFBs. In one subject, we reimaged the same RNFBs twice over a 7month interval and compared bundle width and thickness between the two imaging sessions. Lastly we compared images of an arcuate RNFL defect acquired with UHR-AO-OCT and commercial OCT (Heidelberg Spectralis). Individual RNFBs were distinguishable in all subjects at 3° retinal eccentricity in both cross-sectional and en face views (width: 30–50μm, thickness: 10–15μm). At 6° retinal eccentricity, RNFBs were distinguishable in three of the five subjects in both views (width: 30–45μm, thickness: 20–40μm). Width and thickness RNFB measurements taken 7months apart were strongly correlated (p<0.0005). Mean difference and standard deviation of the differences between the two measurement sessions were −0.1±4.0μm (width) and 0.3±1.5μm (thickness). UHR-AO-OCT outperformed commercial OCT in terms of clarity of the microscopic retina. To our knowledge, these are the first measurements of RNFB cross section reported in the living human eye

On Entropy Test for Conditionally Heteroscedastic Location-Scale Time Series Models

This study considers the goodness of fit test for a class of conditionally heteroscedastic location-scale time series models. For this task, we develop an entropy-type goodness of fit test based on residuals. To examine the asymptotic behavior of the test, we first investigate the asymptotic property of the residual empirical process and then derive the limiting null distribution of the entropy test