Assignment_4_S07

Assignment_4_S07 - Bonus Homework 4(optional STAT 443...

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Bonus Homework 4 (optional) STAT 443 Spring 2007 1. Consider an ARCH(1) model 2 1 1 0 2 , + = = t t t t t X b c e X σ where et is i.i.d. N(0,1), c0 > 0$ and 0< b1 <1. Show that Xt is leptocurtic and larger values of b1 imply larger values of kurtosis. 2. DESCRIPTIVE ABSTRACT: Stock Returns of the company G (SRG) in US dollars over the period from July 10, 1998 through December 31, 1999. (Only business days are shown.) YOUR TASK: a) Plot SRG. b) Produce a histogram of returns of SRG and superimpose a normal curve. c) Interpret your results in a) and b). d) Fit GARCH(1,1) model to the SRG data and provide a model diagnostics (Jarque-Bera test, Ljung-Box test, scatter plots, QQ plots and histograms of returns and residuals and acf of squared returns and squared residuals). Interpret your result. Date SRG 1 19980710 0.148437500 2 19980713 -0.027210884 3 19980714 0.020979021 4 19980715 -0.003397260 5 19980716 -0.085935782 6 19980717 0.060150376 7 19980720 -0.053163121 8 19980721 -0.104865772 9 19980722 0.020886330 10 19980723 -0.127016393
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11 19980724 -0.032900173 12 19980727 -0.111611650 13 19980728 -0.131141808 14 19980729 0.000000000 15 19980730 0.009358020 16 19980731 -0.009271259 17 19980803 -0.069229221 18 19980804 0.060864865 19 19980805 -0.006420055 20 19980806 0.006461538 21 19980807 -0.006420055 22 19980810 -0.012820513 23 19980811 -0.116883117 24 19980812 0.183882353 25 19980813 -0.006260558 26 19980814 -0.012500000 27 19980817 -0.075949367 28 19980818 -0.047890411 29 19980819 0.021523941 30 19980820 -0.070422535 31 19980821 -0.045454545 32 19980824 -0.118984127 33 19980825 -0.009080427 34 19980826 0.009163636 35 19980827 -0.045113866 36 19980828 -0.056603774 37 19980831 -0.169920000 38 19980901 0.228797224 39 19980902 0.088313725 40 19980903 -0.054050159 41 19980904 -0.066737772 42 19980908 0.000000000 43 19980909 -0.102040816 44 19980910 -0.124909091 45 19980911 -0.013089549 46 19980914 0.013263158 47 19980915 0.025971328 48 19980916 0.000000000 49 19980917 -0.012758202 50 19980918 0.038564103 51 19980921 -0.111198894 52 19980922 -0.013777778 53 19980923 0.056331681 54 19980924 -0.040102389 55 19980925 0.000000000 56 19980928 0.027777778 57 19980929 -0.135135135 58 19980930 0.031250000 59 19981001 -0.030303030 60 19981002 0.109500000 61 19981005 0.028165840 62 19981006 0.068376068 63 19981007 -0.038358974 64 19981008 -0.013438567 65 19981009 0.027027027 66 19981012 0.052631579 67 19981013 -0.037400000
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68 19981014 0.032412217 69 19981015 0.006238680 70 19981016 -0.056200000 71 19981019 0.059546514 72 19981020 -0.025000000
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Assignment_4_S07 - Bonus Homework 4(optional STAT 443...

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