Detecting and estimating long-range dependecy are important in the analysis of many environmental time series. The paper introduces Periodogram roughness and describes its uses for testing and estimating the long-range dependence parameter. Asymptotic critical values are generated for performing the derived test. Goodness of fit for appropriateness of chosen spectral densities for modeling the observed dependence structure is obtained. Change in the spectral domain is tested using a simple test statistic that has  22(n-1) distribution. Wavelet coefficients for fractional difference processes are used to detect variance changes. Smaller forecasting errors are obtained by using fractional Brownian motion model. The conventional short-memory model AR(2) is less parsimonious. MLE and semi-parametric estimatorare also implemented. The methods are illustrated using Swedish wind speed measurements. These data were collected every three hours at 10 different locations and during the period 1985 to 1998.

ABDALLA ELBERGALI
Department of Biochemistry & Biophysics
Chalmers University of Technology
P. O. Box 462
Götebog, SE-405 30, Sweden
abdalla@bcbp.gu.se
 
 

Time series of environmental data are often strongly influenced by random fluctuations in temperature, precipitation, runoff, etc. This article shows how Mann-Kendall (M-K) tests for monotone trends can be modified to facilitate hypothesis testing regarding human impacts on the environment in the presence of arbitrary covariates. The proposed procedure involves estimation of the multivariate distribution of several Mann-Kendall (M-K) statistics. This multivariate distribution is then used to derive the conditional distribution of the M-K statistic of the studied response variable, given the M-K statistics of one or several covariates. In particular, we derive conditional variants of the ordinary Mann-Kendall test and the Hirsch-Slack test for monotone trend in seasonal, serially correlated data. A Monte-Carlo study of empirical power functions of different types of conditional Mann-Kendall tests showed that: (i) the loss of power due to introduction of irrelevant covariates is small compared to the possible gain in power that may be achieved by introducing relevant covariates; (ii) the distribution of the test statistic is approximately normal also for moderately large data sets. Case studies of water quality and discharge data showed that conditional Mann-Kendall tests were able to correct for rather complex time-lagged relationships between covariates and the response variable under consideration. The generic character of the tests introduced in this article facilitates standardised trend assessment of a great variety of time series of environmental data.

ANDERS GRIMVALL
Department of Mathematics
Linköping University
Linköping 58183, Sweden
angri@mai.liu.se
 
 

We are dealing with time series occurring in forest health inventories. The response variable is tree damage measured on an ordinal scale and is recorded together with time- and space-varying covariates. The conditional expectations are modelled as a regression model in a GLM-type manner, the parameters are estimated via likelihood- or quasi-likelihood approaches. Our main concern are diagnostic methods for such time series models. The tools are based on the notion of global and partial residual measures and can be found in the literature for special instances, see Landwehr et al (1984) for the case of a binary
logistic model or Pruscha (1994) for the case of a cumulative logistic model. We apply our methods to a data set on 80 beech sites in the Spessart (Bavaria) covering the 15 years period of 1983-1997, see Goettlein and Pruscha (1996) for details.
(i) Partial residual measures are employed to assess the significance of subsets of covariates. We will test the relevance of variables related to topography as well as to soil conditions.
(ii) Global residual measures (after adjustment for the covariates) are plotted over the observation period and over the grid of observation sites to assess the influence of time and space on the response variable of tree damage. In a reversed procedure, global residual measures (after adjustment for time and space) are used to elaborate the (remaining) significance of covariates.

HELMUT PRUSCHA
Mathematical Institute
University of Munich
Theresienstr. 39
Muenchen, D 80333, Germany
pruscha@rz.mathematik.uni-muenchen.de