The Exact Region for the Successful Application of Square Root Transformation in Time Series Decomposition using the Multiplicative Model

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Abstract

Abstract: In time series decomposition using multiplicative model, the basic assumption required to proceed with a parametric time series analysis is that the error component is normally distributed with unit mean and constant variance . However, in practice there are cases where there are clear evidences of departure from normality and homogeneity of variance. As a remedial measure, such data sets require an appropriate transformation. Considering that successful transformation is one in which the original desired properties necessary for parametric data analysis are maintained after the transformation and considering that in this context, it is desired that the error component must be normally distributed with unit mean after a square root transformation, therefore the exact region in terms of the standard deviation, , for a successful square root transformation of a multiplicative time series model is investigated. From the study, it was established that normality and unit mean are actually achieved in the region . Furthermore, the use of second order approximation for the infinite series obtained in the establishment of the functional expressions for the first and second moments of the square root transformed left truncated normal (1, 2) distribution was justified in this article. Finally, the established results were validated using a real-life data.

Keywords: Data transformation, Multiplicative time series model, Left- truncated - Normal distribu,,

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