Estimating intrinsic currency values

People talk about the strengthening and weakening of individual currencies all the time, even though the forex market trades currency pairs. The intuition behind such statements is the idea of intrinsic currency values, which means value can be associated with individual currencies in their own right.

One standard way to measure changes in an individual currency's value is by referencing changes in the value of the corresponding trade-weighted basket. However, when applied simultaneously to

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