TITLE:
Comparison of Two Time Series Decomposition Methods: Least Squares and Buys-Ballot Methods
AUTHORS:
I. S. Iwueze, E. C. Nwogu, V. U. Nlebedim, J. C. Imoh
KEYWORDS:
Decomposition Models, Least Squares Estimates, Buys-Ballot Estimates, Accuracy Measures, Successful Transformation, Trending Curves
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.6,
December
21,
2016
ABSTRACT: This paper discusses comparison of two time
series decomposition methods: The Least Squares Estimation (LSE) and
Buys-Ballot Estimation (BBE) methods. As noted by Iwueze and Nwogu (2014),
there exists a research gap for the choice of appropriate model for
decomposition and detection of presence of seasonal effect in a series model.
Estimates of trend parameters and seasonal indices are all that are needed to
fill the research gap. However, these estimates are obtainable through the Least
Squares Estimation (LSE) and Buys-Ballot Estimation (BBE) methods. Hence, there
is need to compare estimates of the two methods and recommend. The comparison
of the two methods is done using the Accuracy Measures (Mean Error (ME)), Mean
Square Error (MSE), the Mean Absolute Error (MAE), and the Mean Absolute
Percentage Error (MAPE). The results from simulated series show that for the
additive model; the summary statistics (ME, MSE and MAE) for the two estimation
methods and for all the selected trending curves are equal in all the
simulations both in magnitude and direction. For the multiplicative model,
results show that when a series is dominated by trend, the estimates of the
parameters by both methods become less precise and differ more widely from each
other. However, if conditions for successful transformation (using the
logarithmic transform in linearizing the multiplicative model to additive
model) are met, both of them give similar results.