Testing for Cointegration with Nonstationary Volatility

The paper generalises recent unit root tests for nonstationary volatility to a multivariate context. Persistent changes in the innovation variance matrix lead to size distortions in conventional cointegration tests, and possibilities of increased power by taking the time-varying volatilities and correlations into account. The testing procedures are based on a likelihood analysis of the vector autoregressive model with a conditional covariance matrix that may be estimated nonparametrically. We find that under suitable conditions, adaptation with respect to the volatility matrix process is possible, in the sense that nonparametric volatility estimation does not lead to a loss of asymptotic local power

Limiting distributions for explosive PAR(1) time series with strongly mixing innovation

This work deals with the limiting distribution of the least squares estimators of the coefficients a r of an explosive periodic autoregressive of order 1 (PAR(1)) time series X r = a r X r--1 +u r when the innovation {u k } is strongly mixing. More precisely {a r } is a periodic sequence of real numbers with period P \textgreater{} 0 and such that P r=1 |a r | \textgreater{} 1. The time series {u r } is periodically distributed with the same period P and satisfies the strong mixing property, so the random variables u r can be correlated

Unit roots in periodic autoregressions

Abstract. This paper analyzes the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series. First, we consider various representations of such models, including a new parametrization which facilitates imposing a unit root restriction. Next, we propose a class of likelihood ratio tests for a unit root, and we derive their asymptotic null distributions. Likelihood ratio tests for periodic parameter variation are also proposed. Finally, we analyze the impact on unit root inference of misspecifying a periodic process by a constant-parameter model

Quantification of carotid plaque composition with a multi-contrast atherosclerosis characterization (MATCH) MRI sequence

Background and purposeCarotid atherosclerotic plaques with a large lipid-rich necrotic core (LRNC), intraplaque hemorrhage (IPH), and a thin or ruptured fibrous cap are associated with increased stroke risk. Multi-sequence MRI can be used to quantify carotid atherosclerotic plaque composition. Yet, its clinical implementation is hampered by long scan times and image misregistration. Multi-contrast atherosclerosis characterization (MATCH) overcomes these limitations. This study aims to compare the quantification of plaque composition with MATCH and multi-sequence MRI.MethodsMATCH and multi-sequence MRI were used to image 54 carotid arteries of 27 symptomatic patients with ≥2 mm carotid plaque on a 3.0 T MRI scanner. The following sequence parameters for MATCH were used: repetition time/echo time (TR/TE), 10.1/4.35 ms; field of view, 160 mm × 160 mm × 2 mm; matrix size, 256 × 256; acquired in-plane resolution, 0.63 mm2× 0.63 mm2; number of slices, 18; and flip angles, 8°, 5°, and 10°. Multi-sequence MRI (black-blood pre- and post-contrast T1-weighted, time of flight, and magnetization prepared rapid acquisition gradient echo; acquired in-plane resolution: 0.63 mm2 × 0.63 mm2) was acquired according to consensus recommendations, and image quality was scored (5-point scale). The interobserver agreement in plaque composition quantification was assessed by the intraclass correlation coefficient (ICC). The sensitivity and specificity of MATCH in identifying plaque composition were calculated using multi-sequence MRI as a reference standard.ResultsA significantly lower image quality of MATCH compared to that of multi-sequence MRI was observed (p < 0.05). The scan time for MATCH was shorter (7 vs. 40 min). Interobserver agreement in quantifying plaque composition on MATCH images was good to excellent (ICC ≥ 0.77) except for the total volume of calcifications and fibrous tissue that showed moderate agreement (ICC ≥ 0.61). The sensitivity and specificity of detecting plaque components on MATCH were ≥89% and ≥91% for IPH, ≥81% and 85% for LRNC, and ≥71% and ≥32% for calcifications, respectively. Overall, good-to-excellent agreement (ICC ≥ 0.76) of quantifying plaque components on MATCH with multi-sequence MRI as the reference standard was observed except for calcifications (ICC = 0.37–0.38) and fibrous tissue (ICC = 0.59–0.70).Discussion and conclusionMATCH images can be used to quantify plaque components such as LRNC and IPH but not for calcifications. Although MATCH images showed a lower mean image quality score, short scan time and inherent co-registration are significant advantages