The Proposed Buys-Ballot Estimates for Multiplicative Model with the Error Variances
Issue: 2023 - Volume 25 [Issue 8]
K. C. N. Dozie *
Department of Statistics Imo State University, Owerri, Imo State, Nigeria.
M. U. Uwaezuoke
Department of Mathematics Imo State University, Owerri, Imo State, Nigeria.
*Author to whom correspondence should be addressed.
This article presents the condition(s) under which the multiplicative model with the error variances best describes the pattern in an observed time series, while comparing it with those of the additive and mixed models. The method of estimation is based on the periodic, seasonal and overall averages and variances of time series data arranged in a Buys-Ballot table. The method assumes that (1) the underlying distribution of the variable, X i j , i = 1, 2, ..., m , j = 1 , 2 , ..., s , under study is normal. (2) the trending curve is linear (3) the decomposition method is either additive or multiplicative or mixed. For multiplicative model, the error variance is not known and needs to be estimated with time series data. For additive and mixed models, the error variances are known and assumed to be equal to 1. Result shows that, under the stated assumptions, the seasonal variances of the Buys-Ballot table, for multiplicative model, a function of column ( j ) through the seasonal component S2j with error variance.
Keywords: Time series decomposition, trend-cycle component, multiplicative model, error variances, buys-ballot estimates, appropriate model
How to Cite
Alder HL, Roesslar EB. Introduction to Probability and Statistics, W.H. Freeman and Company, San Francisco; 1990.
Chatfield C. The analysis of time Series: An introduction. Chapman and Hall,/CRC Press, Boca Raton; 2004 .
Iwueze IS, Nwogu EC. Buys-Ballot estimates for time series decomposition, Global Journal of Mathematics. 2004; 3(2):83-98.
Puerto J, Rivera MP. Descriptive analysis of time series applied to housing prices in Spain, Management Mathematics for European Schools 94342-CP-2001- DE – COMENIUS – C21; 2001.
Iwueze IS, Nwogu EC. Framework for choice of models and detection of seasonal effect in time series. Far East Journal of Theoretical Statistics. 2014; 48(1):45– 66.
Wei WWS. Time series analysis: Univariate and multivariate methods, Addison-Wesley publishing Company Inc, Redwood City; 1989.
Nwogu EC, Iwueze IS, Dozie KCN, Mbachu HI. Choice between mixed and multiplicative models in time series decomposition. International Journal of Statistics and Applications. 2019;9(5):153-159.
Dozie KCN, Ihekuna SO. Buys-Ballot estimates of quadratic trend component and seasonal indices and effect of incomplete data in time series. International Journal of Science and Healthcare Research. 2020;5(2):341- 348.
Dozie KCN, Nwogu EC, Nwanya JC. Buys-Ballot technique for analysis of time Series model. International Journal of Scientific Research and Innovative Technology. 2020;7(1):63-78.
Dozie KCN, Nwanya JC. Comparison of mixed and multiplicative models when trend-cycle component is liner. Asian Journal of Advanced Research and Report. 2020;12(4):32-42.
Dozie KCN. Estimation of seasonal variances in descriptive time series analysis. Asian Journal of Advanced Research and Reports. 2020;10(3):37- 47.
Dozie KCN, Ijomah MA. A comparative study on additive and mixed models in descriptive time series. American Journal of Mathematical and Computer Modelling. 2020;5(1):12-17.
Dozie KCN, Ibebuogu CC. Road traffic offences in Nigeria: An empirical analysis using buys-ballot approach. Asian Journal of Probability and Statistics. 2021;12(1):68-78.
Dozie KCN, Uwaezuoke MU. Procedure for estimation of additive time series model. International Journal of Research and Scientific Innovation. 2021;8(2):251-256.
Dozie KCN, Ihekuna SO. Additive seasonality in time series using row and overall sample variances of the buys-ballot table. Asian Journal of Probability and Statistics. 2022;18(3):1-9.
Dozie KCN, Ibebuogu CC. Decomposition with the mixed model in time series analysis using Buy-Ballot procedure. Asian Journal of Advanced Research and Report. 2023;17(2):8-18.
Akpanta AC, Iwueze IS. On applying the Bartlett transformation method to time series data. Journal of Mathematical Sciences. 2009;20(5):227-243.