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

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.

Buys-Ballot Estimates for Linear Model with the Expected Values in Time Series Decomposition

“…This method is based on the row, column and overall means of the Buys-Ballot table with m rows and s columns. For details of this method see Wei [6], Nwogu et.al [7], Dozie and Ihekuna [8], Dozie et.al [9], Dozie and Nwanya [10], Dozie [5], Dozie and Ijeomah [11], Dozie and Ibebuogu (12), Dozie and Uwaezuoke [13], Dozie and Ihekuna [14], Dozie and Ibebuogu [15], Akpanta and Iwueze [16], Dozie and Uwaezuoke [17] and Dozie [18]. 2.…”

“…Nwogu, et al, [7] and Dozie et al [9] proposed "chi-square test for choice between the multiplicative and mixed models is based on the column variances". According to them, the null hypothesis to be tested is H0:…”

Decomposition with the Additive Model Using Buys-Ballot Technique of Quadratic Trend-Cycle Component in Descriptive Time Series Analysis

“…The resulting time series after elimination the trend-cycle ( t M ) is the de-trended series and expresses the effects of the season and irregular components. The de-trended series is expressed mathematically as: tt XM − (7) for the additive model or / tt XM (8) for the multiplicative model or / tt XM (9) for the mixed model…”

“…This method adopted in this study assumed that the series are arranged in a Buys-Ballot table with m rows and s columns. For details of this method see Wei [6], Nwogu et.al [7], Iwueze and Ohakwe [8], Dozie and Ijeomah [9], Dozie and Uwaezuoke [10], Dozie et.al [11], Dozie and Nwanya [12], Dozie [4], Dozie and Ibebuogu [13], Dozie and Uwaezuoke [14], Dozie and Ihekuna [15], Dozie and Ibebuogu [16], Dozie and Uwaezuoke [17], Dozie [18], and Dozie and Ihekuna [19]…”

Comparison of Trend Parameters and Seasonal Indices in the Presence and Absence of Missing Values of Exponential Trend-Cycle in Time Series Analysis

“…The method adopted for this article is the Buys-Ballot method. For details of this method, see Iwueze et.al [4], Nwogu et.al [9], Dozie and Uwaezuoke [10], Dozie and Ibebuogu [11], Dozie et.al [12], Dozie and Ijomah [13], Dozie and Nwanya [14], Dozie [15], Dozie and Uwaezuoke [16], Dozie and Ihekuna [17], Dozie and Ibebuogu [18], Akpanta and Iwueze [19]. Dozie and Ihekuna [20], Dozie [21] and Dozie and Uwaezuoke [22].…”