Behavioural analysis of a time series- A chaotic approach
DSpace at IIT Bombay
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Title |
Behavioural analysis of a time series- A chaotic approach
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Creator |
FATHIMA, TA
JOTHIPRAKASH, V |
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Subject |
Chaos
correlation dimension method false nearest neighbour method phase randomization embedding dimension correlation exponent correlation dimension daily rainfall data India ARTIFICIAL NEURAL-NETWORKS PHASE-SPACE RECONSTRUCTION STRANGE ATTRACTORS EMBEDDING DIMENSION INFLOW PREDICTION DISTRIBUTED DATA DAILY RAINFALL RUNOFF MODEL DYNAMICS |
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Description |
Out of the various methods available to study the chaotic behaviour, correlation dimension method (CDM) derived from Grassberger-Procaccia algorithm and False Nearest Neighbour method (FNN) are widely used. It is aimed to study the adaptability of those techniques for Indian rainfall data that is dominated by monsoon. In the present study, five sets of time series data are analyzed using correlation dimension method (CDM) based upon Grassberger-Procaccia algorithm for studying their behaviour. In order to confirm the results arrived from correlation dimension method, FNN and phase randomisation method is also applied to the time series used in the present study to fix the optimum embedding dimension. First series is a deterministic natural number series, the next two series are random number series with two types of distributions; one is uniform and another is normal distributed random number series. The fourth series is Henon data, an erratic data generated from a deterministic non linear equation (classified as chaotic series). After checking the applicability of correlation dimension method for deterministic, stochastic and chaotic data (known series) the method is applied to a rainfall time series observed at Koyna station, Maharashtra, India for its behavioural study. The results obtained from the chaotic analysis revealed that CDM is an efficient method for behavioural study of a time series. It also provides first hand information on the number of dimensions to be considered for time series prediction modelling. The CDM applied to real life rainfall data brings out the nature of rainfall at Koyna station as chaotic. For the rainfall data, CDM resulted in a minimum correlation dimension of one and optimum dimension as five. FNN method also resulted in five dimensions for the rainfall data. The behaviour of the rainfall time series is further confirmed by phase randomisation technique also. The surrogate data derived from randomisation gives entirely different results when compared to the other two techniques used in the present study (CDM and FNN) which confirms the behaviour of rainfall as chaotic. It is also seen that CDM is underestimating the Correlation dimension, may be due to higher percentage of zero values in rainfall data. Thus, one should appropriately check the adaptability of CDM for time series having longer zero values.
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Publisher |
INDIAN ACAD SCIENCES
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Date |
2014-12-28T09:08:13Z
2014-12-28T09:08:13Z 2014 |
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Type |
Article
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Identifier |
SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES, 39(3)659-676
0256-2499 0973-7677 http://dspace.library.iitb.ac.in/jspui/handle/100/16248 |
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Language |
English
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