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Financial Toolkit : Fitting a GARCH(1,1) model
Input
Garch(1,1) : \( \sigma_{t}^2 = \omega + \alpha X_{t-1}^2 + \beta \sigma_{t-1}^2\), \(X_{t} = \sigma_{t} Z_{t}\) where \( Z_{t} \sim N(0,1) \)
Calculation mode
Absolute
ln(X_{t+1} / X_{t})
ln(X_{t} / X_{t+1})
(X_{t+1} - X{t}) / X_{t}
(X_{t} -X_{t+1})/ X_{t+1}
Data set
0.007728 0.007779 0.007746 0.007816 0.007837 0.007924 0.007888 0.007657 0.007683 0.007746 0.007806 0.007839 0.007837 0.007826 0.007831 0.007838 0.007863 0.007832 0.007738 0.007797 0.007816 0.00777 0.007765 0.007774 0.007737 0.007755 0.007758 0.007631 0.007686 0.007678 0.007672 0.00771 0.007689 0.007734 0.00777 0.007775 0.007772 0.007797 0.007796 0.007791 0.007746 0.007739 0.007757 0.007798 0.007801 0.007809 0.007824 0.007859 0.007877 0.007872 0.007852 0.007809 0.007791 0.007893 0.007859 0.007888 0.007938 0.007971 0.008056 0.008026 0.007991 0.00806 0.00801 0.008002 0.007951 0.007957 0.007957 0.007957 0.007924 0.008071 0.008074 0.008055 0.008053 0.008072 0.008056 0.008017 0.008029 0.008032 0.0080 0.008024 0.008016 0.008012 0.007998 0.008032 0.008003 0.008024 0.00804 0.008042 0.008036 0.008024 0.008016 0.007955 0.007973 0.008013 0.008005 0.008019 0.00805 0.008043 0.008037 0.008012 0.007996 0.007992 0.007916 0.007943 0.007918 0.007955 0.007987 0.007994 0.008016 0.007991 0.007927 0.007929 0.007962 0.007949 0.00793 0.007911 0.007782 0.007779 0.007693 0.007652 0.007666 0.007522 0.007477 0.007463 0.0074 0.007436 0.007491 0.007584 0.00751 0.00753 0.007541 0.007524 0.007516 0.007407 0.007411 0.007471 0.007508 0.007537 0.007648 0.007582 0.007553 0.00759 0.007571 0.007533 0.007543 0.007539 0.007526 0.007524 0.007493 0.007479 0.007421 0.007428 0.00746 0.00753 0.007513 0.007561 0.007471 0.007509 0.007509 0.007468 0.007481 0.007452 0.007491 0.007472 0.007446 0.007321 0.007322 0.007315 0.007358 0.007384 0.007477 0.007475 0.007505 0.007485 0.007517 0.00744 0.007467 0.007454 0.007476 0.007468 0.007454 0.00744 0.00744 0.007452 0.007452 0.007452 0.007457 0.007434 0.007485 0.00751 0.007484 0.007499 0.007505 0.007567 0.00763 0.00775 0.007863 0.007837 0.007865 0.007875 0.00786 0.007878 0.007896 0.007896 0.007881 0.007926 0.007967 0.007927 0.007992 0.007968 0.008006 0.008042 0.008004 0.008012 0.007978 0.008032 0.008071 0.008142 0.008079 0.008096 0.008068 0.008193 0.008127 0.00818 0.008218 0.008236 0.008276 0.008258 0.008185 0.008224 0.008193 0.008247 0.008251 0.008247 0.008228 0.008147 0.008165 0.008178 0.008147 0.008125 0.008157 0.008123 0.008056 0.008063 0.00799 0.008042 0.008021 0.008026 0.007955 0.007962 0.008006 0.0081 0.008016 0.007969 0.0079 0.007905 0.007944 0.007944 0.007943 0.007908 0.007808 0.00784 0.007816 0.007723 0.007813 0.007797 0.007872 0.007831 0.007806 0.007781 0.007717 0.007719 0.007696 0.007719 0.007746 0.007716 0.007723 0.00772 0.007786 0.007828 0.007774 0.007865 0.007959 0.007913 0.007945 0.007911 0.007868 0.00791 0.007931 0.007899 0.00793 0.00789 0.007804 0.007814 0.007817 0.007781 0.007776 0.007775 0.007752 0.007721 0.007707 0.007701 0.00769 0.00765 0.007593 0.007576 0.007618 0.007618 0.007654 0.007533 0.00751 0.007553 0.007553 0.007579 0.007638 0.007598 0.007571 0.007565 0.007534 0.007541 0.00753 0.007555 0.007556 0.007571 0.007593 0.007583 0.007572 0.007613 0.007617 0.007619 0.007576 0.007563 0.007523 0.007467 0.007468 0.007473 0.007479 0.007438 0.007417 0.007439 0.00739 0.007359 0.007283 0.007302 0.007233 0.007189 0.007202 0.007047 0.007063 0.007021 0.007041 0.007131 0.006988 0.006993 0.007028 0.007056 0.00708 0.006985 0.00701 0.006982 0.00687 0.006717 0.00672 0.006724 0.006633 0.006884 0.006889 0.006889 0.006952 0.007105 0.007184 0.007101 0.007126 0.007008 0.007018 0.006971 0.007057 0.00707 0.007158 0.007199 0.007168 0.007184 0.007141 0.007138 0.007186 0.007148 0.007043 0.00706 0.007046 0.007063 0.00707 0.00703 0.007022 0.007102 0.007178 0.007181 0.007292 0.00731 0.007345 0.007319 0.007171 0.007168 0.007189 0.007178 0.007185 0.007092 0.007047 0.007047 0.007018 0.006964 0.0070 0.007009 0.006989 0.006988 0.006977 0.00697 0.006958 0.006983 0.006919 0.006882 0.006843 0.00681 0.00683 0.0068 0.006832 0.006832 0.006827 0.006816 0.006825 0.006734 0.006824 0.006854 0.006894 0.006888 0.006879 0.007001 0.007011 0.007149 0.007095 0.007179 0.0071736 0.00708466 0.00710227 0.00702741 0.00701262 0.00701262 0.00695169 0.00691563 0.00693241 0.00699056 0.00705716 0.00707714 0.00705965 0.0070497 0.0070373 0.00702988 0.00707214 0.00706464 0.00704722 0.00705965 0.0070373 0.00701508 0.00699399 0.00696379 0.00699545 0.00696864 0.00697837 0.00698812 0.0070028 0.0069808 0.00695749 0.00696379 0.00696621 0.00695894 0.00693722 0.00692761 0.00695894 0.00696621 0.00693963 0.00696864 0.00697593 0.00696136 0.00702494 0.00700771 0.00699301 0.00696961 0.00696233 0.00695265 0.00693241 0.00693963 0.00692521 0.0069541 0.00694686 0.00694686 0.0069541 0.006943 0.00695652 0.00694927 0.00696379 0.0070028 0.00704225 0.00699301 0.00696864 0.00684932 0.00686342 0.00699301 0.00694444 0.00694203 0.00689085 0.00689085 0.00688231 0.00688231 0.00687994 0.00687616 0.00687758 0.00685166 0.00687049 0.00683293 0.00685166 0.00688468 0.00691563 0.00691563 0.00698812 0.00694444 0.00692377 0.00690846 0.00687994 0.00688089 0.00689417 0.00687994 0.00688468 0.006892 0.00693722 0.00693241 0.00693626 0.00693001 0.00694203 0.00691802 0.00687994 0.00688373 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