takehome W10

takehome W10 - 1). DESCRIPTIVE ABSTRACT: Monthly number of...

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1). DESCRIPTIVE ABSTRACT: Monthly number of unemployed persons in Australia. Feb 1978 - Aug 1995. YOUR TASK: To forecast unemployment rate for the first eight months of 1995, i.e. from January to August 1995. You should a) Construct a linear regression model of the unemployment rate vs. time using dummy variables for seasonality, if required. You can apply variance stabilizing transformations if you think that such transformations are appropriate. b)Provide diagnostics of the assumptions (white noise normality)for your model, i.e. verify that residuals are homoscedastic (residual plots), uncorrelated (acf plot, the Ljung-Box test/plot, the runs tests) and normally distributed (Shapiro-Wilk test, QQ plot). C) construct 90% and 95% predictive intervals for the first eight months of 1995, i.e. from January to August 1995, using your regression model; does the observed data fall into the constructed predictive intervals? d)write your conclusion on the aptness of the obtained model; Justify all your conclusions. 5. US monthly sales of petroleum and related products. Jan 1971 - Dec 1991. Use data from January 1971 to September 1991 as a training set. You should a) Provide a scatter (time series) (Yt versus t) and acf plot of vehicles sales and discuss your findings; b) construct a linear regression of vehicle sales vs. other available regressors; select the best model and check whether your residuals satisfy assumption of white noise and normality; c) if your residuals do not satisfy the assumptions, try to fix the issue(s) by running a model with correlated residuals; 1
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d) provide 95% and 99% prediction intervals for the vehicles sales in October, November and December 1991 using your best model. Which of these prediction intervals are wider? Check whether actual observations fall within the constructed predictive intervals. Discuss your results. f) write your conclusion on the aptness of the obtained model. How can the model be improved? "Date" "Chemicals" "Coal" "Petrol" "Vehicles" JAN71 3.896 49.780 5.154 4.367 FEB71 4.346 47.059 5.550 5.147 MAR71 4.318 56.950 5.165 5.418 APR71 4.536 54.336 5.553 4.897 MAY71 4.454 50.445 5.190 5.005 JUN71 4.554 49.598 5.588 5.359 JUL71 4.058 39.537 5.550 3.537 AUG71 4.345 56.185 5.551 3.940 SEP71 4.693 54.449 5.581 5.556 OCT71 4.389 11.857 5.350 5.459 NOV71 4.589 56.357 5.585 5.400 DEC71 3.997 56.035 5.579 4.446 JAN75 4.353 49.680 5.319 5.075 FEB75 4.609 49.115 5.396 5.707 MAR75 4.794 54.438 5.397 5.760 APR75 4.975 49.814 5.465 5.807 MAY75 4.859 55.879 5.368 5.865 JUN75 5.057 50.083 5.505 5.909 JUL75 4.385 40.964 5.490 3.681 AUG75 4.798 55.169 5.553 3.895 SEP75 5.076 49.374 5.611 6.547 OCT75 4.979 51.671 5.558 6.659 NOV75 4.845 50.597 5.618 6.670 DEC75 4.740 44.904 5.685 5.550 JAN73 4.885 49.379 5.649 6.710 FEB73 5.579 45.893 5.753 7.134 MAR73 5.741 50.547 5.675 7.097 APR73 5.910 46.999 5.753 6.741 MAY73 5.784 51.450 5.781
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takehome W10 - 1). DESCRIPTIVE ABSTRACT: Monthly number of...

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