Buys – Ballot Estimates for time series decomposition

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

“…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.…”

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

“…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.…”

“…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.…”

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

“…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.…”

“…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.…”