Keywords
time series analysis, trend test, wavelets, stochastic model, farima
Start Date
1-7-2004 12:00 AM
Abstract
The assessment of trends in meteorology and/or hydrology still is a matter of debate. Capturing typical properties of time series, like trends, is highly relevant for the discussion of potential impacts (e.g. global warming or ood occurrence). In order to enhance capabilities of analytical strategies run-off data from river gauges in southern Germany are analysed systematically regarding their trend behaviour. The trend is assumed to be a slowly varying deterministic component caused e.g. by human impact like global warming. Its detection is dif cult since it might be superimposed by natural variability also present on large time scales. In an innovative approach a polynomial trend component and a stochastic model part are combined. With the stochastic model long-term and short-term correlations in time series data are considered. A reliable test for a signi cant trend can be performed via three steps: First, a stochastic fractional ARIMA model is tted to the empirical data. In a second step, wavelet analysis is applied to separate the variability of small and large time-scales, assuming that the trend component is part of the latter. A comparison of the overall variability to that restricted to small scales results in a test for a trend. For the analysed series no signi cant trend could be found under the assumption of the models presented. The extraction of the large scale behavior by wavelet analysis provides valuable hints concerning the shape of the trend.
Trend Assessment of Correlated Data
The assessment of trends in meteorology and/or hydrology still is a matter of debate. Capturing typical properties of time series, like trends, is highly relevant for the discussion of potential impacts (e.g. global warming or ood occurrence). In order to enhance capabilities of analytical strategies run-off data from river gauges in southern Germany are analysed systematically regarding their trend behaviour. The trend is assumed to be a slowly varying deterministic component caused e.g. by human impact like global warming. Its detection is dif cult since it might be superimposed by natural variability also present on large time scales. In an innovative approach a polynomial trend component and a stochastic model part are combined. With the stochastic model long-term and short-term correlations in time series data are considered. A reliable test for a signi cant trend can be performed via three steps: First, a stochastic fractional ARIMA model is tted to the empirical data. In a second step, wavelet analysis is applied to separate the variability of small and large time-scales, assuming that the trend component is part of the latter. A comparison of the overall variability to that restricted to small scales results in a test for a trend. For the analysed series no signi cant trend could be found under the assumption of the models presented. The extraction of the large scale behavior by wavelet analysis provides valuable hints concerning the shape of the trend.
