Assignment_3_S07

Assignment_3_S07 - Homework 3 STAT 443 Spring 2007 1....

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Homework 3 STAT 443 Spring 2007 1. Consider an ARMA(2,2) model with et ~ WN(0,1) Zt=aZt-2 +et + bet-2. What assumptions do we need to ensure that Z_t is a weakly stationary process? Derive a formula for 2-steps ahead predictor of Zt. 2. DESCRIPTIVE ABSTRACT: Stock prices of the company G in US dollars over the period from July 9, 1998 through December 31, 1999. (Only business days are shown.) YOUR TASK: To forecast stock prices for the company G for December 27, 28, 29, 30 and 31 of 1999. So the training set is from July 9, 1998 through December 23, 1999. You should a) provide an acf and pacf plots of the stock data and interpret these plots; b) difference the data and/or apply variance stabilizing transformations if needed; repeat (a); c) suggest an AR, MA or ARMA model for the stock prices (possibly preprocessed) and estimate the chosen model; d) justify your model by comparing with other models (for example, using AIC); e) provide diagnostics of the assumptions (white noise + normality), i.e. verify that residuals are homoscedastic (residual plots), uncorrelated (acf plot, the Ljung-Box test/plot, the runs test) and normally distributed (Shapiro-Wilk test, QQ plot). f) predict stock prices for the company G for December 27, 28, 29, 30 and 31 of 1999. and construct 99% prediction intervals. g) write your conclusion on the aptness of the obtained model. Company G data: data stock 1 19980709 16.000 1
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2 19980710 18.375 3 19980713 17.875 4 19980714 18.250 5 19980715 18.188 6 19980716 16.625 7 19980717 17.625 8 19980720 16.688 9 19980721 14.938 10 19980722 15.250 11 19980723 13.313 12 19980724 12.875 13 19980727 11.438 14 19980728 9.938 15 19980729 9.938 16 19980730 10.031 17 19980731 9.938 18 19980803 9.250 19 19980804 9.813 20 19980805 9.750 21 19980806 9.813 22 19980807 9.750 23 19980810 9.625 24 19980811 8.500 25 19980812 10.063 26 19980813 10.000 27 19980814 9.875 28 19980817 9.125 29 19980818 8.688 30 19980819 8.875 31 19980820 8.250 32 19980821 7.875 33 19980824 6.938 34 19980825 6.875 35 19980826 6.938 36 19980827 6.625 37 19980828 6.250 38 19980831 5.188 39 19980901 6.375
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Assignment_3_S07 - Homework 3 STAT 443 Spring 2007 1....

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