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

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Wywiał J., Department of Econometrics A. o. E.

Acta Universitatis Lodziensis. Folia Oeconomica

1997

vol. 141

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.

Bayesian estimation of a shift point in a two-phase regression model

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Jadamus-Hacura M., Department of Econometrics A. o. E.

Acta Universitatis Lodziensis. Folia Oeconomica

1997

vol. 141

The purpose of this paper is to carry out the Bayesian analysis of a two-phase regression model with an unknown break point. Essentially, there are two problems associated with a changing linear model. Firstly, one will want to be able to detect a break point, and secondly, assuming that a change has occurred, to be able to estimate it as well as other parameters of the model. Much of the classical testing procedure for the parameter constancy (as the Chow test, CUSUM, CUSUMSQ, tests and their modifications, predictions tests for structural stability) indicate only that the regression coefficients shifted, without specifying a break point. In this study we adopt the Bayesian methodology of investigating structural changes in regression models. The break point is identified as the largest posterior mass density, the peak of the posterior discrete distribution of a break point. It seems to work well with artificially generated data. The Bayesian framework also seems to be promising for extending the analysis of a single break to that of multiple breaks.

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2 Acta Universitatis Lodziensis. Folia Oeconomica

2 Department of Econometrics A. o. E.

1 Jadamus-Hacura M.

1 Wywiał J.

2 1997

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

Bayesian estimation of a shift point in a two-phase regression model