This study considers test for seasonality in the additive model using the Buys-Ballot table and the nature of trending curves (linear, quadratic and exponential). The test is applied to the periodic and overall sample variances of the Buys-Ballot table to detect the presence and absence of seasonal indices in time series.
The purpose of this study is to present the linear trend cycle component with the emphasis on the choice between mixed and multiplication models in time series analysis. Most of the existing studies have adequately dwelt more on choice of model between additive and multiplicative, with little or no regards to the mixed model. The main aim of this study is to compare the row, column and overall means and variances for mixed and multiplicative models using Buys-Ballot table for seasonal time series. Specific objectives are 1) to obtain and compare the expected values of means for mixed and multiplicative models 2) to estimate and compare trend parameters and seasonal indices (when there is no trend, that is (b = 0)). The study indicate that column variances ( ) of the Buys-Ballot table depends on the season j only through the square of the seasonal effect for mixed model and it is for multiplicative model, a quadratic function of the column j and square of the seasonal effect .
The procedure for estimation of lineartrend cycle and seasonal components and accepts additive model is examined in this study. Estimates of the periodic, seasonal and overall means and variances with error terms and error variances are obtained for additive model. Empirical example based on short series in which trend cycle component is jointly estimated for the linear case is applied to determine suitable model for decomposition of the study series.
Road traffic offences in time series analysis when trend-cycle component is quadratic is discussed in this study. The study is to investigate the variance stability, trend pattern, seasonal indices and suitable model for decomposition of study data. The study shows that, the series is seasonal with evidence of upward trend or downward trend. There is an upsurge of the series in the months of March, August and November and a drop in January, June and December. The periodic standard deviations are stable while the seasonal standard deviations differ, suggesting that the series requires transformation to make the seasonal indices additive.
This study looks at the effects of replication on prediction variance performances of inscribe central composite design especially those without replication on the factorial and axial portion (ICCD1), inscribe central composite design with replicated axial portion (ICCD2) and inscribe central composite design whose factorial portion is replicated (ICCD3). The G-optimal, I-optimal and FDS plots were used to examine these designs. Inscribe central composite design without replicated factorial and axial portion (ICCD1) has a better maximum scaled prediction variance (SPV) at factors k = 2 to 4 while inscribe central composite design with replicated factorial portion (ICCD3) has a better maximum and average SPV at 5 and 6 factor levels. The fraction of design space (FDS) plots show that the inscribe central composite design is superior to ICCD3 and inscribe central composite design with replicated axial portion (ICCD2) from 0.0 to 0.5 of the design space while inscribe central composite design with replicated factorial portion (ICCD3) is superior to ICCD1 and ICCD2 from 0.6 to 1.0 of the design space for factors k = 2 to 4.
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