The University of Western Australia School of Mathematics & Statistics…

The University of Western Australia School of Mathematics & Statistics
4S5: Time Series Methods and Applications Project 1 (2012) The following data show quarterly expenditure on non-beer alcohol based drinking in a certain country. The units are zillions of dollars. (Read the data row by row!) Submit your report by end of April.
Year Q1 Q2 Q3 Q4 1985 50 67 71 113 1986 56 65 74 122 1987 57 68 77 129 1988 62 72 81 129 1989 61 75 83 150 1990 58 87 92 154 1991 72 96 104 164 1992 64 108 106 173 1993 66 116 119 182 1994 89 121 134 213 1995 88 130 143 220 1996 101 144 150 228 1997 104 149 159 242
(a) Fit a trend plus seasonal means model by direct regression. Is a linear trend adequate, or quadratic, or … ? Justify your choice. (b) Fit a trend plus trigonometric seasonal model to these data, giving explicit reasons for your choice of f . Think very carefully about which harmonic components should form part of your model. (c) In both cases use diagnostic tools to comment on how well your model fits the data, and the degree to which the residuals mimic Gaussian white noise. I expect to see residual histograms, ACF charts, Q-Q type plots and associated goodness of fit tests, model selection criteria. You may like to think about whether a preliminary transformation gives you a better fit. (d) Forecast 1998 quarterly expenditures. Report confidence and prediction limits. (e) Comment on similarities/differences of the two models you select as ‘hest’. Present your work in a ‘report’ style, explaining why you do what you do and support this with appropriate displays. (Don’t forget to centre your final seasonal estimates at zero.) Do not submit nothing other than annotated computer print-out. If you use the computers in the MCL, then make sure you can save your work to your own memory device. User files are deleted from computer memory at the end of each day.
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