The Expected Values of Buys-Ballot Estimates for Multiplicative Model with the Error Terms
Kelechukwu C. N. Dozie *
Department of Statistics, Imo State University Owerri, Imo State, Nigeria.
Christian C. Ibebuogu
Department of Computer Science, Imo State University Owerri, Imo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The expected values of Buys-Ballot estimates with the error terms for multiplicative model in time series decomposition when trend-cycle component is linear is discussed. The expected values of Buys-Ballot estimates of row, column and overall means with the error terms are derived. A real example for the linear case is applied to determine the estimation of trend parameters, seasonal indices, choice of appropriate transformation and choice of model of the Buys-Ballot table. Results show that, the expected values of periodic and seasonal means of the Buys-Ballot table are; (1) periodic mean mimic the shape of the trending curves of the original series and contains seasonal indices (2) seasonal mean is a function of the trending parameters of the original series and contain seasonal indices.
Keywords: Descriptive time series, multiplicative model, linear trend, Buys-Ballot estimates, expected values, choice of appropriate model
How to Cite
Downloads
References
Chatfield C. The analysis of time Series: An introduction. Chapman and Hall,/CRC Press, Boca Raton; 2004.
Iwueze IS, Nwogu EC, Ohakwe J, Ajaraogu JC. Uses of the Buys – Ballot table in time series analysis. Applied Mathematics Journal. 2011;2:633 –645
Dozie KCN. Estimation of seasonal variances in descriptive time series analysis. Asian Journal of Advanced Research and Reports. 2020;10(3):37 – 47
Oladugba AV, Ukaegbu EC, Udom AU, Madukaife MS, Ugah TE, Sanni SS, Principles of applied statistic, University of Nigeria Press Limited; 2014
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, Ijeomah MA. Effect of missing observations on Buys-Ballot estimates of time series components. Asian Journal of Probability and Statistics. 2020;6(3):13-24
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, 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
Dozie KCN, Uwaezuoke MU. The Proposed Buys-Ballot estimates for multiplicative model with the error variances. Journal of Engineering Research and Reports. 2023;25(8): 94-106.
Dozie KCN.Buys-Ballot estimates for overall sample variances and their statistical properties. A mixed model case. Asian Journal of Advanced Research and Reports. 2023;17(10):213-223.