Time Series Analysis and Prediction of AE and Dst Data

Details Time Series Analysis and Prediction of AE and Dst Data Time Series Analysis and Prediction of AE and Dst Data

Dec 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996esasp.392..261t&link_type=abstract

Environment Modelling for Space-based Applications, Symposium Proceedings (ESA SP-392). ESTEC Noordwijk, 18-20 September 1996. E

Statistics

Applications

Scientific paper

A new method to analyse the structure function has been constructed and used in the analysis of the AE time series for the years 1978-85 and Dst time series for 1957-84. The structure function (SF) was defined by S(l) = <|x(ti + lDt) - x(ti)|>, where Dt is the sampling time, l is an integer, and <|.|> denotes the average of absolute values. If a time series is self-affine its SF should scale for small values of l as S(l) is proportional to lH, where 0 < H < 1 is called the scaling exponent. It is known that for power-law (coloured) noise, which has P ~ f-a, a ~ 2H + 1 for 1 < a < 3. In this work the scaling exponent H was analysed by considering the local slopes dlog(S(l))/dlog(l) between two adjacent points as a function of l. For self-affine time series the local slopes should stay constant, at least for small values of l. The AE time series was found to be affine such that the scaling exponent changes at a time scale of 113 (+/-9) minutes. On the other hand, in the SF function analysis, the Dst data were dominated by the 24-hour and 27-day periods. The 27-day period was further modulated by the annual variation. These differences between the two time series arise from the difference in their periodicities in relation to their respective characteristic time scales. In the AE data the dominating periods are longer than that related to the characteristic time scale, i.e. they appear in the flatter part of the power spectrum. This is why the affinity is the dominating feature of the AE time series. In contrast with this the dominating periods of the Dst data are shorter than the characteristic time scale, and appear in the steeper part of the spectrum. Consequently periodicity is the dominating feature of the Dst data. Because of their different dynamic characteristics, prediction of Dst and AE time series appear to presuppose rather different approaches. In principle it is easier to produce the gross features of the Dst time series correctly as it is periodicity dominated. Affinity of the AE time series poses a more difficult challenge; different types of dynamics can lead to affine behaviour. As a first step in the search for the right kind of dynamics it is useful to analyse how autonomous the AE lime series really is. A convenient means for this task is provided by neural networks. The predictive power of different inputs will tell their importance in determining the observed AE time series output. In this analysis multilayer backpropagation neural networks were used. Both an autonomous prediction of the AE data, and an input (vBz) - output (AE) prediction of the AE data were considered. Prediction of the AE time series from the solar wind input was found to be better than that from the previous AE data. However, best results were found by simultaneously using solar wind (vBz) and previous AE inputs. For comparison linear prediction of the AE time series was also made using a simple autoregressive model. This linear prediction model failed already at very short prediction times in accordance with previous results by other methods. In the case both solar wind and previous AE data were used as the input, the trained network could well predict the behaviour of the time series used in the training 20 hours ahead.

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