Data-Mining

Assignment 2- Question 2

Question: Fit a seasonal model to the variable HSTARTS in the construction data set.

Step 1: We selected the Construction dataset from the FETS Library. We selected the variable Housing starts.

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Step 2: Below is the graph of Housing starts. The graph clearly shows a seasonal trend in the data.

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Step 3: Below is the White noise test and Unit root test for the data.

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Step 4: In order to understand which model is considered the best by SAS I first ran an automatic model fit and below is the fitted model. The model selected was Log exponential Smoothing model.

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Step 5: The distribution of residuals is random and it does not show any kind of trend towards the end as well.

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Step 6: Below is the auto correlation plots for the log exponential model and it shows no lag in the residual and this we can conclude there is no correlation between the residuals.

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Step 7: The White noise test is insignificant thus we can say that the residuals are random. The unit root test and seasonality test show that the model is stationary.

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Step 8:  Below are the estimates of the model which include all the seasonal dummies.

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Step 9: Below are the various fit criteria for the log seasonal smoothing model.

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Step 10: We can see how close the forecast is from the below graph.

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Step 11: I then fit a number of custom models on the data using seasonality and boiled down to the below model which is a Seasonal Dummy+ Quadratic Model fitted by custom fit.

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Step 12: Below is the residual plot for the Seasonal Dummy+ quadratic model and we can see a random distribution of residuals.

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Step 13: From the auto correlation plot we can see some considerable lags between the residuals and thus there is correlation in the residuals.

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Step 14: Below graph shows significant white noise test which shows that the residuals are not random and also from the other graphs we can say the model is not doing well on stationarity as well compared to the log seasonal smoothed model.

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Step 15: Below are the estimates of the seasonal dummies +quadratic model with values of the seasonal dummies.

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Step 16: The various fit parameters are shown below for the seasonal dummies +quadratic model.

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Step 17: We can see the forecast graph as below.