The value of the U.S. dollar relative to other currencies can partially explain speculative influence on cotton prices. As the U.S. dollar weakens, it can encourage flows of money into alternative financial markets like commodity futures. In addition, a weakening U.S. dollar in theory would stimulate more U.S. exports of physical cotton since it would be cheaper relative to competing foreign cotton. So there is a double reason for cotton markets to get stronger when the U.S. dollar weakens, and vice versa.
The weak dollar/stronger cotton price relationship has generally been the case except during very specific situations like a sustained weakening euro currency (e.g., late 2009/early 2010, and again in late 2011).
For the week ending Friday, January 27, the U.S. dollar index (DXH23) gyrated sideways across the week (see chart below courtesy of Barchart.com). Longer term, the dollar index has been in a downtrend from the late September highs.