<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<style type="text/css" style="display:none"><!-- p { margin-top: 0px; margin-bottom: 0px; }--></style>
</head>
<body dir="ltr">
<div id="OWAFontStyleDivID" style="font-size:12pt;color:#000000;background-color:#FFFFFF;font-family:Calibri,Arial,Helvetica,sans-serif;">
<p>Hello,</p>
<p> </p>
<p> I am trying to use non-parametric Granger spectral decomposition on a simple, artificial MVAR system:</p>
<p> </p>
<p>x(t) = 0.80*x(t-1) - 0.50*x(t-2) + 0.40*z(t-1)</p>
<p>y(t) = 0.53*y(t-1) - 0.80*y(t-2)</p>
<p>z(t) = 0.50*z(t-1) - 0.20*z(t-2) + 0.50*y(t-1)</p>
<p> </p>
<p> This example system is drawn from Dhamala, Rangarajan, & Ding, 2008, NeuroImage, where is it used to demonstrate "prima facie", or erroneous conclusions about causality when the conditional decomposition is not used (i.e. in the system itself y->z->x,
but an additional link y->x is seen when the non-conditional granger calculation is used).</p>
<p> </p>
<p> In my code and output included below, the Fourier power and non-conditional Granger output are as expected, but the conditional Granger output appears to be uniformly near zero.</p>
<p> </p>
<p> The only difference between the two cases in my code is the setting of a single parameter passed to ft_connectivityanalsysis, cfg.granger.conditional being 'no' and 'yes' in the respective cases.</p>
<p> </p>
<p> My apologies if I have missed an archived post addressing this issue, as this is quite likely to be an error on my part. Alternatively, I do not recognize the calculation being performed in blockwise_conditionalgranger.m. If someone has a reference to
this, I may be able to figure this out myself (I am working from Chen, Bressler, & Ding, 2006, "Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data", Journal of Neuroscience Methods).</p>
<p> </p>
<p> Thank you for your help,</p>
<p> </p>
<p>Per A. Lysne</p>
<p>University of New Mexico</p>
<p><a href="mailto:lysne@unm.edu">lysne@unm.edu</a></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p>The first image is the Fourier power spectra of the system (abs applied to complex-valued cross-power). The second image is the non-conditional Granger decomposition, and the third image the conditional Granger. My convention for plotting is "row-causes-column".
Results are generated using 100 trials of 300 samples apiece with an assumed sampling frequency of 200 Hz. Software is Matlab R2012a, Student Edition, and my Fieldtrip download is dated 6/3/2014. The code which generated these images is attached.</p>
<p> </p>
<p> </p>
<p><img title="MVAR2.Spectra.jpg" style="width: 559px;" originalWidth="560" originalHeight="420" rszImgCmd="100" setHeight="419" setWidth="559" hasHeight="false" src="cid:898dbd0d-1330-430a-8327-bd9a95f2b7fe"></p>
<p><img title="MVAR2.NonCondGranger.jpg" originalWidth="560" originalHeight="420" rszImgCmd="100" setHeight="420" setWidth="560" hasHeight="false" src="cid:889457b8-d09d-4655-bac6-e3da92b8be20"><img title="MVAR2.CondGranger.jpg" originalWidth="32" originalHeight="32" rszImgCmd="100" src="cid:f640ae0e-d04f-451c-87ab-0f93aaa79870"></p>
</div>
</body>
</html>