Testing linear cointegration against smooth-transition cointegration

This paper studies a smooth-transition (ST) type cointegration. The proposed ST cointegration allows for regime switching structure in a cointegrated system. It nests the linear cointegration developed by Engle and Granger (1987) and the threshold cointegration studied by Balke and Fomby (1997). We develop F-type tests to examine linear cointegration against ST cointegration in ST-type cointegrating regression models with or without time trends. The null asymptotic distributions of the tests are derived with stationary transition variables in ST cointegrating regression models. And it is shown that our tests have nonstandard limiting distributions expressed in terms of standard Brownian motion when regressors are pure random walks, while have standard asymptotic distributions when regressors contain random walks with nonzero drift. Finite-sample distributions of those tests are studied by Monto Carlo simulations. The small-sample performance of the tests states that our F-type tests have a better power when the system contains ST cointegration than when the system is linearly cointegrated. An empirical example for the purchasing power parity (PPP) data (monthly US dollar, Italy lira and dollar-lira exchange rate from 1973:01 to 1989:10) is illustrated by applying the testing procedures in this paper. It is found that there is no linear cointegration in the system, but there exits the ST-type cointegration in the PPP data.

Self-reported symptoms and motor tests via telemetry in a 36-month levodopa-carbidopa intestinal gel infusion trial

Objective To investigate if a home environment test battery can be used to measure effects of Parkinson’s disease (PD) treatment intervention and disease progression. Background Seventy-seven patients diagnosed with advanced PD were recruited in an open longitudinal 36-month study at 10 clinics in Sweden and Norway; 40 of them were treated with levodopa-carbidopa intestinal gel (LCIG) and 37 patients were candidates for switching from oral PD treatment to LCIG. They utilized a mobile device test battery, consisting of self-assessments of symptoms and objective measures of motor function through a set of fine motor tests (tapping and spiral drawings), in their homes. Both the LCIG-naïve and LCIG-non-naïve patients used the test battery four times per day during week-long test periods. Methods Assessments The LCIG-naïve patients used the test battery at baseline (before LCIG), month 0 (first visit; at least 3 months after intraduodenal LCIG), and thereafter quarterly for the first year and biannually for the second and third years. The LCIG-non-naïve patients used the test battery from the first visit, i.e. month 0. Out of the 77 patients, only 65 utilized the test battery; 35 were LCIG-non-naïve and 30 LCIG-naïve. In 20 of the LCIG-naïve patients, assessments with the test battery were available during oral treatment and at least one test period after having started infusion treatment. Three LCIG-naïve patients did not use the test battery at baseline but had at least one test period of assessments thereafter. Hence, n=23 in the LCIG-naïve group. In total, symptom assessments in the full sample (including both patient groups) were collected during 379 test periods and 10079 test occasions. For 369 of these test periods, clinical assessments including UPDRS and PDQ-39 were performed in afternoons at the start of the test periods. The repeated measurements of the test battery were processed and summarized into scores representing patients’ symptom severities over a test period, using statistical methods. Six conceptual dimensions were defined; four subjectively-reported: ‘walking’, ‘satisfied’, ‘dyskinesia’, and ‘off’ and two objectively-measured: ‘tapping’ and ‘spiral’. In addition, an ‘overall test score’ (OTS) was defined to represent the global health condition of the patient during a test period. Statistical methods Change in the test battery scores over time, that is at baseline and follow-up test periods, was assessed with linear mixed-effects models with patient ID as a random effect and test period as a fixed effect of interest. The within-patient variability of OTS was assessed using intra-class correlation coefficient (ICC), for the two patient groups. Correlations between clinical rating scores and test battery scores were assessed using Spearman’s rank correlations (rho). Results In LCIG-naïve patients, mean OTS compared to baseline was significantly improved from the first test period on LCIG treatment until month 24. However, there were no significant changes in mean OTS scores of LCIG-non-naïve patients, except for worse mean OTS at month 36 (p<0.01, n=16). The mean scores of all subjectively-reported dimensions improved significantly throughout the course of the study, except ‘walking’ at month 36 (p=0.41, n=4). However, there were no significant differences in mean scores of objectively-measured dimensions between baseline and other test periods, except improved ‘tapping’ at month 6 and month 36, and ‘spiral’ at month 3 (p<0.05). The LCIG-naïve patients had a higher within-subject variability in their OTS scores (ICC=0.67) compared to LCIG-non-naïve patients (ICC=0.71). The OTS correlated adequately with total UPDRS (rho=0.59) and total PDQ-39 (rho=0.59). Conclusions In this 3-year follow-up study of advanced PD patients treated with LCIG we found that it is possible to monitor PD progression over time using a home environment test battery. The significant improvements in the mean OTS scores indicate that the test battery is able to measure functional improvement with LCIG sustained over at least 24 months.