A Comparative Study on Additive and Mixed Models in Descriptive Time Series

Dozie, Kelechukwu C. N.; Ijomah, Maxwell Azubuike

doi:10.11648/j.ajmcm.20200501.12

Cited by 5 publications

(3 citation statements)

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“…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 [7], Iwueze et.al [8], Nwogu et.al [5], Dozie and Ihekuna [9], Dozie et.al [6], Dozie and Nwanya [10], Dozie [1], Dozie and Ijeomah [11], Dozie and Ibebuogu [12], Dozie and Uwaezuoke [13], Dozie and Ihekuna [14] Dozie and Ibebuogu [15].…”

Section: Methodsmentioning

confidence: 99%

Buys-Ballot Estimates for Overall Sample Variances and Their Statistical Properties: A Mixed Model Case

Dozie

2023

AJARR

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This article proposes an estimation procedure of overall sample variances for the mixed model while comparing them with those of the additive and multiplicative models. The estimation procedure is based on the row, column and overall means and variances of time series data arranged in a Buys-Ballot table. The procedure 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 either linear or quadratic and (3) the decomposition method is either multiplicative or mixed. Statistical properties of the overall sample variances of the Buys-Ballot table are also considered in this study. Result indicates that, under the stated assumptions, the expected value of the overall sample variances involve sum of square and cross-product of trend parameters and seasonal indices.

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Section: Methodsmentioning

confidence: 99%

Buys-Ballot Estimates for Overall Sample Variances and Their Statistical Properties: A Mixed Model Case

Dozie

2023

AJARR

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“…This method adopted in this study assumed that the data are arranged in a Buys-Ballot table with m rows and s columns. For details of this method see Wei [7], Iwueze et al [5], Nwogu et al [8], Dozie and Ihekuna [9], Dozie et al [10], Dozie and Ijeomah [11], Dozie and Ibebuogu [12], Dozie and Uwaezuoke [13], Dozie and Ihekuna [14], Dozie and Ibebuogu [15] For the multiplicative model, the row, column and overall averages and variances obtained with the error terms are given in equations ( 8) to (10). From equation (12) it is clear that the column variances ( 2 j  ) depends on the seasons j only through the square of the seasonal indices ( 2 j S ) and the trending curves through the square of seasonal average with the error variance.…”

Section: Methodsmentioning

confidence: 99%

Statistical Properties of Buys-Ballot Estimates for Multiplicative Model with the Error Terms

Dozie,

Ibebuogu

2023

AJRCoS

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In this study, we discuss statistical properties of Buys-Ballot estimates for multiplicative model with their error terms. The aim of this study is to characterize the properties of the row, column and overall means and variances of the Buys-Ballot table for multiplicative model with the error terms. The properties of Buys-Ballot estimates in this study are used for (1) estimation of trend parameters (2) estimation of seasonal effect (3) choice of model for decomposition. The results indicate that (1) the column variance (\(\hat{\sigma}^2_j\)) of the Buys-Ballot depends on the seasonal indices (\(S^2_j\)) of the jth seasons. (2) the model that best describe the pattern in the transformed series is additive. This further confirms that the appropriate model of the original series is multiplicative.

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“…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].…”

Section: Buys-ballot Proceduresmentioning

confidence: 99%

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

Dozie,

Ibebuogu

2023

AJPAS

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This study examines the comparison of trend cycle and seasonal components in the presence and absence of missing observations. The method adopted in this study is based on the row, column and overall means of the time series arranged in a Buys-Ballot table with m rows and s columns. The method assumes that (1) Only one data is missing at a time in the Buys-Ballot table (2) the trending curve is exponential (3) the modal structure is additive. The study indicates that, the estimation of the missing observations as they occur consecutively with the errors being normally distributed. Results indicate that, the differences in the trend parameters for both situations are insignificant because they are approximately the same. In the case of corresponding seasonal effects, significant differences existed on the points in which there are missing values in the column of the Buys-Ballot table.

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A Comparative Study on Additive and Mixed Models in Descriptive Time Series

Cited by 5 publications

References 0 publications

Buys-Ballot Estimates for Overall Sample Variances and Their Statistical Properties: A Mixed Model Case

Buys-Ballot Estimates for Overall Sample Variances and Their Statistical Properties: A Mixed Model Case

Statistical Properties of Buys-Ballot Estimates for Multiplicative Model with the Error Terms

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

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