Decomposition of time series on the basis of modified grouping method of Ward

• Authors: Wywiał, Janusz

Title variants

EN

Dekompozycja szeregów czasowych oparta na zmodyfikowanej metodzie Warda

Abstracts

EN

The trend of time series can change its direction. It is assumed that the time interval is divided into subintervals where the trend is given as particular linear function. The problem is how to divide the observation of time series into disjoint and coherent groups where they have linear trend. That is why the problem of the scatter of multivariable observation was first considered. The degree of data spread is measured by means of a coefficient called a discriminant of multivariable observation. It is equal to the sum of volumes of the parallelotops spanned on multidimensional observations. On the basis of it the modifications of the well known generalized variance were introduced. Geometrical properties of those parameters were investigated. The obtained results are used to generalize well-known clustering methods of Ward. One of the advantages of the method is that it finds clusters of high linear dependent multivariate observations. Finally, the results are used to partition a time series into homogeneous groups where observations are close to linear trend. There is considered an example.

Keywords

EN

groupping criterion; agglomeration clustering; multidimensional variable; generalized variance; parallelotop; volume; discriminant; hyperplane; intra group spread; time series; linear trend

• Publisher: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
• Journal: Acta Universitatis Lodziensis. Folia Oeconomica
• Year: 1997
• Volume: 141

Dates

published

1997

Contributors

author

Wywiał, Janusz

other

Department of Econometrics, Academy of Economics, Katowice

Identifiers

URI

http://hdl.handle.net/11089/6262