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I have all the data for my US coinciding index for August except one, which I've estimated. In contrast to the weak employment data, the index is surprisingly robust. I've plotted the 3 month rate of change in the index against a weighted average of the ISM industry and ISM services surveys. Both series have been extreme-adjusted to remove statistical aberrations. On the face of it, these data do not yet point towards a double dip.
The correlation between these two indicators is very close. Of course, the 3 month rate of change would tend to lead the underlying series, which account for the absence of any leading relationship in the ISM surveys.
As always, clicking on the chart will give it you in the original size.
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