Buys – Ballot Estimates for time series decomposition

Iwueze, IS; Nwogu, Eleazar C.

doi:10.4314/gjmas.v3i2.21356

“…According [11], if a time series contains seasonal affects with period s (length of the periodic interval), we expect observations separated by multiples of to be similar: should be similar to ± , = 1,2,3, … m . To analyze the data, it is helpful to arrange the series in a two -dimensional table (Table 1), according to the period and season, including the totals and/or averages.…”

Section: Methodsmentioning

confidence: 99%

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

Dozie

¹

,

Nwogu

²

,

Ijomah

³

2020

AJPAS

0

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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.

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“…The high level of multicollinearity between two or more powers of the time variable(t) in a polynomial trend model often results in wrong inferences and model selection based on the least squares estimates of the concerned parameters [4,24]. As a consequence, the Buys-Ballot estimation procedure proposed in [12], which is capable of yielding estimates that are robust to multicollinearity, is considered when the multicollinearity problem exists [21]. The Buys-Ballot approach is primarily used for the decomposition 249 of a relatively short series such that the trend and cyclical components are jointly estimated.…”

Section: Introductionmentioning

confidence: 99%

“…where X t is the observed value of the time series at time t, M t is the trend-cycle component at time t, S t is the seasonal component at t and e t is the irregular component or the error term at time t. In (1), e t ∼ N (0, σ Apart from the work of [12] in which the chain base and fixed base estimation techniques were used in accordance with the linear trend-cycle component, the additive and multiplicative models, several studies have been subsequently undertaken within the context of the Buys-Ballot method of analysing time series data. In this regard, [17] developed the Buys-Ballot procedure of analysing time series data with the quadratic trend-cycle component.…”

Section: Introductionmentioning

confidence: 99%

Buys-Ballot Technique for the Analysis of Time Series with a Cubic-Trend Component

Okereke

¹

2018

Stat., optim. inf. comput.

0

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Time series, especially those with the cubic trend component, are encountered in many data analysis situations. The decomposition of such series into various components requires a method that can adequately estimate the cubic trend as well as other components of the series. In this study, the chain base, fixed base and classical methods of decomposition of time series with the cubic trend component are discussed with emphasis on the additive model. Chain base and fixed base estimators of the additive model parameters are derived. Basic properties of these two classes of estimators are equally determined. The derived chain base variables have the autocorrelation structure of an invertible third-order moving average model. The chain base estimators are found to be pairwise-negatively correlated estimators. Though the classical method and chain base method are both used for time series decomposition, the chain base method is recommended when a case of multicollinearity has been established.

show abstract

“…The high level of multicollinearity between two or more powers of the time variable(t) in a polynomial trend model often results in wrong inferences and model selection based on the least squares estimates of the concerned parameters [4,24]. As a consequence, the Buys-Ballot estimation procedure proposed in [12], which is capable of yielding estimates that are robust to multicollinearity, is considered when the multicollinearity problem exists [21]. The Buys-Ballot approach is primarily used for the decomposition of a relatively short series such that the trend and cyclical components are jointly estimated.…”

Section: Introductionmentioning

confidence: 99%

“…Apart from the work of [12] in which the chain base and fixed base estimation techniques were used in accordance with the linear trend-cycle component, the additive and multiplicative models, several studies have been subsequently undertaken within the context of the Buys-Ballot method of analysing time series data. In this regard, [17] developed the Buys-Ballot procedure of analysing time series data with the quadratic trend-cycle component.…”

Section: Introductionmentioning

confidence: 99%

Buys-Ballot Technique for the Analysis of Time Series with a Cubic-Trend Component

Okereke

¹

,

Omekara

²

,

Ekezie

³

2018

J Indian Soc Probab Stat

0

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Time series, especially those with the cubic trend component, are encountered in many data analysis situations. The decomposition of such series into various components requires a method that can adequately estimate the cubic trend as well as other components of the series. In this study, the chain base, fixed base and classical methods of decomposition of time series with the cubic trend component are discussed with emphasis on the additive model. Chain base and fixed base estimators of the additive model parameters are derived. Basic properties of these two classes of estimators are equally determined. The derived chain base variables have the autocorrelation structure of an invertible third-order moving average model. The chain base estimators are found to be pairwise-negatively correlated estimators. Though the classical method and chain base method are both used for time series decomposition, the chain base method is recommended when a case of multicollinearity has been established.

show abstract

Buys – Ballot Estimates for time series decomposition

Cited by 11 publications

References 0 publications

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

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

Buys-Ballot Technique for the Analysis of Time Series with a Cubic-Trend Component

Buys-Ballot Technique for the Analysis of Time Series with a Cubic-Trend Component

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