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Research Article Open access CC BY 4.0

The Proposed Buys-Ballot Estimates for Multiplicative Model with the Error Variances

K. C. N. Dozie, M. U. Uwaezuoke

Journal of Engineering Research and Reports · pp. 94–106 · Published 5 Sep 2023

10.9734/jerr/2023/v25i8962

Abstract

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.

Time series decomposition trend-cycle component multiplicative model error variances buys-ballot estimates appropriate model

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Cited by 6

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

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

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

Kelechukwu C. N. Dozie, Christian Chinwe Ibebuogu · Asian Journal of Probability and Statistics · 2023

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