Examination of ozonesonde data for trends and trend changes incorporating solar and Arctic oscillation signals

One major question that arises with the implementation of the Montreal Protocol and its subsequent conventions is our ability to determine that an ozone “recovery” is in process. Toward this we have utilized a statistical model suggested by Reinsel et al. (2002) that utilizes the idea of a trend and a trend change at a specific time and applied it to 12 ozonesonde stations in the midlatitudes of the Northern Hemisphere. The lower stratosphere, in particular, is of significance as this is where the ozone concentration is a maximum and also where heterogeneous ozone losses have been noted. This statistical methodology suffers, however, from the ambiguities of having to select a specific time for the ozone trend to change and the fact that the Mt Pinatubo volcanic aerosols impacted the ozone amount. Within this paper, we analyze the ozonesonde station data utilizing the above model but examine the statistical stability of the computed results by allowing the point of inflection to change from 1995 through 2000 and also exclude varying amounts of data from the post-Pinatubo period. The results indicate that while the impacts of deleting data and changing the inflection point are nontrivial, the overall results are consistent in that there has been a major change in the ozone trend in the time frame of 1996 and that a reasonable scenario is to utilize a change point in 1996 and exclude 2 years of data after the 1991 Mt. Pinatubo eruption. In addition, we include a term for the Arctic oscillation within the statistical model and demonstrate that it is statistically significant

Elements of Multivariate Time Series Analysis

xvii.;ill.;357 hal.; 30 c

Approximate ML and REML estimation for regression models with spatial or time series AR(1) noise

This paper considers maximum likelihood (ML) and restricted maximum likelihood (REML) estimation of regression models with two-dimensional spatial or one-dimensional time series autoregressive AR(1) noise. Although the exact ML and REML procedures are described, the aim is to develop and present a simple estimation procedure that provides very accurate approximations to the ML and REML estimators and is computationally convenient. An approximation for the bias of the ML estimator of the AR parameters is also investigated. Simulation results are provided to assess the accuracy of our approximations.Bias Maximum likelihood estimator Restricted maximum likelihood estimator Spatial AR model Time series regression model

Asymptotic properties of the score test for autocorrelation in a random effects with AR(1) errors model

The score test developed by Chi and Reinsel (1989) is shown to be asymptotically chi-squared distributed, and the asymptotic power of the score test under local alternatives is derived and found to be reasonably high for moderate values of the autocorrelation coefficient in the AR(1) errors.Asymptotic normality autocorrelation longitudinal data maximum likelihood estimation power