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F-Transform In View Of Trend Extraction, Irina Perfilieva, Vladik Kreinovich, Vilém Novák
F-Transform In View Of Trend Extraction, Irina Perfilieva, Vladik Kreinovich, Vilém Novák
Departmental Technical Reports (CS)
In the analysis of time series, it is important to decompose the original values into trend, cycle, seasonal component, and noise. In this paper, we provide a theoretical justification of the fact that the F-transform can be used for this purpose. We formulate "natural" requirements on the trend extraction procedure and then show that the inverse F-transform fulfils all of them.