<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<!--[if !mso]><style>v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style><![endif]--><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:AdvEPSTIM;
panose-1:2 11 6 4 2 2 2 2 2 4;}
@font-face
{font-family:AdvPSMP10;
panose-1:2 11 6 4 2 2 2 2 2 4;}
@font-face
{font-family:AdvSPSMI;
panose-1:2 11 6 4 2 2 2 2 2 4;}
@font-face
{font-family:AdvP4C4E59;
panose-1:2 11 6 4 2 2 2 2 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
mso-fareast-language:EN-US;}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
{mso-style-priority:34;
margin-top:0cm;
margin-right:0cm;
margin-bottom:0cm;
margin-left:36.0pt;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
mso-fareast-language:EN-US;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri",sans-serif;
mso-fareast-language:EN-US;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:72.0pt 72.0pt 72.0pt 72.0pt;}
div.WordSection1
{page:WordSection1;}
/* List Definitions */
@list l0
{mso-list-id:198394794;
mso-list-type:hybrid;
mso-list-template-ids:694437840 134807567 134807577 134807579 134807567 134807577 134807579 134807567 134807577 134807579;}
@list l0:level1
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level2
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level3
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l0:level4
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level5
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level6
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l0:level7
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level8
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-18.0pt;}
@list l0:level9
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
ol
{margin-bottom:0cm;}
ul
{margin-bottom:0cm;}
--></style>
</head>
<body lang="en-BE" link="#0563C1" vlink="#954F72" style="word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal"><span lang="NL">Dear all, <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="NL"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">In the light of the research with two fellow colleagues, we are already making a lot of progress thanks to the last very detailed answer by Alex Garland. <o:p></o:p></span></p>
<ol style="margin-top:0cm" start="1" type="1">
<li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level1 lfo1"><span lang="EN-US">We did a brief analysis already with over 100 Garch models (8 volatility models, 5 conditional distributions: norm, sstd, std, ged, sged & various arma orders) estimated
via rugarch by Alexios Galanos and comparing them using AIC. <o:p></o:p></span></li><li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level1 lfo1"><span lang="EN-US">From visualizing the models we observed the general trend that for all models the skewed student’s t-distribution is the “best” conditional density (lowest AIC)
for all GARCH models tested. <o:p></o:p></span></li><li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level1 lfo1"><span lang="EN-US">We then did a moving window approach using the ugarchroll. Which works perfectly.<o:p></o:p></span></li><li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level1 lfo1"><span lang="EN-US">As an extension of our analysis we wanted to compare the garch models with time varying higher moments using the racd package. Although there is already a lot of
literature there in the past decades and I must say the documentation about this is already very helpful on unstarched and the vignette, but I cannot figure out why there is never convergence using the skewed student’s t (see indicated warning).
<o:p></o:p></span></li><ol style="margin-top:0cm" start="1" type="a">
<li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level2 lfo1"><span lang="EN-US">I followed Bali et al. (2008) “</span><span style="font-size:10.0pt;font-family:"AdvEPSTIM",serif">In this paper, we adopt the conditional density approach initiated
by <span style="color:#000066">Hansen (1994) </span>and extended by <span style="color:#000066">
Jondeau and Rockinger (2003) </span>to model the conditional high-order moment parameters of the SGT density as follows:
<br>
</span><img width="144" height="51" style="width:1.5in;height:.5312in" id="Picture_x0020_1" src="cid:image001.png@01D75219.D9E013C0"><span style="font-size:10.0pt;font-family:"AdvEPSTIM",serif"><br>
where </span><span lang="EN-US" style="font-size:10.0pt;font-family:"AdvPSMP10",serif">lambda</span><span style="font-size:6.0pt;font-family:"AdvSPSMI",serif;position:relative;top:2.0pt;mso-text-raise:-2.0pt">t
</span><span style="font-size:10.0pt;font-family:"AdvEPSTIM",serif">is the unrestricted skewness parameter</span><span lang="EN-US" style="font-size:10.0pt;font-family:"AdvEPSTIM",serif"> (sometimes referred to as “xi”)</span><span style="font-size:10.0pt;font-family:"AdvEPSTIM",serif">
and </span><span lang="EN-US" style="font-size:10.0pt;font-family:"AdvPSMP10",serif">eta</span><span style="font-size:6.0pt;font-family:"AdvSPSMI",serif;position:relative;top:2.0pt;mso-text-raise:-2.0pt">t
</span><span style="font-size:10.0pt;font-family:"AdvEPSTIM",serif">and </span><span lang="EN-US" style="font-size:10.0pt;font-family:"AdvPSMP10",serif">kappa<sub>t</sub></span><span lang="EN-US" style="font-size:10.0pt;font-family:"AdvP4C4E59",serif">
</span><span style="font-size:10.0pt;font-family:"AdvEPSTIM",serif">are the unrestricted kurtosis parameters.</span><span lang="EN-US"><o:p></o:p></span></li><li class="MsoListParagraph" style="margin-left:0cm;mso-list:l0 level2 lfo1"><span lang="EN-US">So I would think this is basically using the “pwl” for the skew and shape order as in the documentation of racd is stated: “</span><span style="mso-fareast-language:EN-GB">Jondeau
and Rockinger (2003) used, among other tested parameterizations, first order piecewise linear dynamic</span><span lang="EN-US" style="mso-fareast-language:EN-GB">”.</span><span lang="EN-US"><o:p></o:p></span></li></ol>
</ol>
<p class="MsoNormal"><span lang="EN-US">Below is my code<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-left:36.0pt"><span lang="EN-US" style="mso-fareast-language:EN-GB">spec = racd::acdspec(mean.model = list(armaOrder = c(1, 0)), variance.model = list(variance.targeting = FALSE),distribution.model = list(model = 'sstd', skewOrder
= c(1, 1, 1), shapeOrder = c(1,1,1), skewmodel = 'pwl', shapemodel = 'pwl'))<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:36.0pt"><span lang="EN-US" style="mso-fareast-language:EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-left:36.0pt"><span lang="EN-US" style="mso-fareast-language:EN-GB">cl = makePSOCKcluster(10)<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:36.0pt"><span lang="EN-US" style="mso-fareast-language:EN-GB">rollacd = racd::acdroll(sGARCH_ACDspec, data = R, n.start = 2500, refit.every = 500,refit.window = "moving", solver = "hybrid", calculate.VaR = TRUE, VaR.alpha
= 0.05, cluster = cl, fit.control = list(), solver.control = list())<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-left:36.0pt"><span lang="EN-US" style="mso-fareast-language:EN-GB">stopCluster(cl)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-GB">It might have something to do with the distribution “sstd” because “jsu” for example works very well and extremely fast. But still is there a way to solve this for the “sstd”? I always
get “<span style="color:red">non-converged estimation windows present...resubsmit object with different solver parameters...</span>” Tried the resume() command with another solver, change the tolerance inside of the solver.control list, change the window sizes,
other suggestions? <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-GB">Looking forward hearing from you,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-GB">Best, <o:p>
</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-GB">Enjo<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p></o:p></span></p>
</div>
</body>
</html>