Effect of Missing Observations on Buys-Ballot Estimates of Time Series Components

Main Article Content

Kelechukwu C. N. Dozie
Eleazar C. Nwogu
Maxwell A. Ijomah

Abstract

This study discusses the effects of missing observations on Buys-Ballot estimate when trend-cycle component of time series is linear. The method adopted in this study is Decomposing Without the Missing Value (DWMV) which is used to estimate missing observations in time series decomposition when data are arranged in a Buys-Ballot table. The model structure used is multiplicative. Results show that the trend parameters with and without missing observations have insignificant effect while there are significant differences in the seasonal indices only at the season points where missing observations occurred in the Buys-Ballot table.

Keywords:
Time series decomposition, missing observation, trend parameter, seasonal effect, multiplicative model, buys-ballot table.

Article Details

How to Cite
N. Dozie, K. C., C. Nwogu, E., & A. Ijomah, M. (2020). Effect of Missing Observations on Buys-Ballot Estimates of Time Series Components. Asian Journal of Probability and Statistics, 6(3), 13-24. https://doi.org/10.9734/ajpas/2020/v6i330161
Section
Original Research Article

References

Pratama I, Permanasari AE, Ardiyanto I, Indrayani R. International Conference on Information Technology Systems and Innovation (ICITSI) Bandung – Bali, October 24 – 27, 2016; 2018.

Brockwell PJ, Davis RA. Time series: Theory and methods. New York, USA: Springer-Verlag; 1991.

Chatfield C. The analysis of time series: An introduction. Chapman and Hall,/CRC Press, Boca Raton; 2004.

Iwueze IS, Nwogu EC, Nlebedim VU, Nwosu IU, Chinyem UE. Comparison of methods of estimating missing values in time series. Open Journal of Statistics. 2018;8:390-399.

Okereke EW, Omekara CO, Ekezie CK. Buys-Ballot estimators of the parameters of the cubic polynomial trend model and their statistical properties. Statistics Opt. Inform. Comput. 2018;6(6):248–265.

Ferreiro O. Methodologies for the estimation of missing observations in time series. Statistical and Probability Letters. 1987;5(1):65-69.

Kohn R, Ansely CF. Estimation, prediction and interpolation of ARIMA models with missing data. Journal of the American Statistical Association. 1986;81(395):751-761.

Ansely CF, Kohn R. Estimation, filtering and smoothing in state space models with incompletely specified initial conditions. Annals of Statistics. 1985;13:1286-1316.

Robinson PM, Dunsmuir W. Estimation of time series models in the presence of missing data. Journal of the Royal Statistical Association. 1981;76(375):560-568.

Nwosu UI. Comparison of methods of estimating missing values in descriptive time series. MSc. Thesis, Department of Statistics, Federal University of Technology, Owerri; 2015.

Iwueze IS, Nwogu EC. Buys-Ballot estimates for time series decomposition. Global Journal of Mathematics. 2004;3(2):83-98.

Wold H. A study in the analysis of stationary time series. Almqvist and Wiksell, Sweden; 1938.

Buys-Ballot CHD. Leo Claemert Periodiques de Temperature, Kemint et Fils, Utrecht; 1847.

Iwueze IS, Nwogu EC, Ohakwe J, Ajaraogu JC. Best linear unbiased estimate using Buys-Ballot procedure when trend-cycle component is linear. Journal of Applied Statistics. 2011;2.