Index Numbers and Time series

Concept:The weighted geometric mean of price relatives with fixed base period weights satisfies the time reversal test.Explanation:The weighted geometric mean index is given by $P_{01} = \prod \left( \frac{p_1}{p_0} \right)^{w / \sum w}$ where $w$ are base period values.For the time reversal test, we need $P_{01} \times P_{10} = 1$.Reversing the time gives $P_{10} = \prod \left( \frac{p_0}{p_1} \right)^{w / \sum w} = \frac{1}{P_{01}}$.Hence $P_{01} \times P_{10} = 1$, so the test is satisfied.It does not generally satisfy the circular test or factor reversal test (unless it is Fisher's ideal index).Answer:Time Reversal Test