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labquiz_soln - Objective To fit a mixed seasonal arima...

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Objective To fit a mixed seasonal arima model to a time series such that model assumptions are generally not violated, a great deal of the variation is explained by the model, the model is sufficiently parsimonious and interpretable. Data Monthly unemployment rate from 1986 to 2005. Methods and Results Plot of original data (Figure 1) shows the possibility of a general downward trend so it is differenced. Plot of differenced data (Figure 2) shows that the general trend is removed by differencing once, so ACF and PACF are plotted for more information to help decide on a model. Plot of ACF and PACF of differenced data (Figure 2) shows that ACF is tailing off at lags of 12 months, thus the this cyclical behavior is removed by a seasonal differencing at lag 12 and the ACF and PACF of the resulting is plotted in Figure 3. Since neither ACF not PACF cut of the first candidate model of ARIMA(1,1,1)x(0,1,0) 12 is fit. arima(x = data, order = c(1, 1, 1), seasonal = list(order = c(0, 1, 0), period = 12)) Coefficients: ar1 ma1 -0.4096 0.2106 s.e. 0.1929 0.2003 sigma^2 estimated as 0.03702:
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