Effect of Outliers on Buys-Ballot Estimates of Trend Parameters and Seasonal Indices in Descriptive Time Series Analysis
Anusionwu Collins O. *
Department of Statistics, Imo State University, Owerri, Nigeria.
Nwogu Eleazar C.
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
Ohaegbulem Emmanuel U.
Department of Statistics, Imo State University, Owerri, Nigeria.
Iwueze Iheanyi S.
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Buys-Ballot methodology was developed to, among other things, obtain estimates of trend parameters and seasonal indices in descriptive time series analysis (Iwueze et al, 2011). In developing this method, Iwueze and Nwogu (2004, 2005), Iwueze and Ohakwe (2005), proposed these estimates (of trend parameters and seasonal indices) were derived from row, column and overall averages and standard deviations of the Buys-Ballot table. These averages and standard deviations were known to be affected by outliers. In their proposed methods, Iwueze and Nwogu (2004, 2005), Iwueze and Ohakwe (2005), made no provision for the effects of these outliers on the proposed estimates. Hence, the purpose of this study was to assess the effects of outliers on Buys-Ballot estimates of trend parameters and seasonal indices. Simulated series were used in this study in the absence and presence of outliers. To capture the presence of outliers, 5, 10, and 15 outliers were introduced in the simulations. Comparison of the estimates (in the absence and presence of outliers) was done using the Accuracy Measures (Mean Square Error (MSE), the Mean Absolute Error (MAE), and the Mean Absolute Percentage Error (MAPE)). The accuracy measures were based on the deviations of parameters estimated from the corresponding parameters. The results of the analysis showed MSE is 0.024 in the absence of outliers. The values of the MSE increased as the number of outliers increased to 15.37, 21.23, and 31.23 for 5,10 and 15 outliers respectively. Thus in the presence of outlier, the Buys-Ballot Estimates (BBE) is not effective in estimating the trend parameters and seasonal indices when trend-cycle component is linear for additive model. Hence, it has been recommended that in estimating the trend parameters and seasonal indices using a Buys-Ballot procedure of the Buys-Ballot table, the effect of outlier should be considered and handled before further analysis.
Keywords: Buys-Ballot estimates, linear trend parameters, seasonal indices, outlier, descriptive time series