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Transformation and Trend-Seasonal Decomposition
Transformation and Trend-Seasonal Decomposition
Abstract
Many time series, particularly monthly economic and official time series, are both non-linear and seasonal. In practice simple power transformations are often used to transform such series to additive linear models and standard trend-seasonal decomposition procedures are then applied for various purposes including seasonal adjustment, trend extraction, and forecasting.
This paper considers the effects of trend-seasonal decomposition on transformed time series which are then transformed back to provide season and trend components in the original scale of the data. It is shown that this approach leads to ambiguities in the resulting decomposition which result in systematic biases to these components. These effects are particularly evident when there is significant variation about the trend, due to either or both of the seasonal and irregular components.
A new trend seasonal decomposition is proposed which largely free of these biases. Results are illustrated by simulation and with reference to NZ official time series.
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Page Last Revised - October 8, 2021
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