Index Numbers and Time series

Concept:Fisher's ideal index satisfies the time reversal and factor reversal tests but fails the circular test.Explanation:Fisher’s ideal index is given by $\sqrt{P_{01}^L \times P_{01}^P}$.It satisfies the time reversal test: $P_{01} \times P_{10} = 1$.It also satisfies the factor reversal test: price index × quantity index = value index.However, it does not satisfy the circular test, which requires that $P_{01} \times P_{12} \times P_{20} = 1$ for all periods.The unit test is not a standard property for index numbers; Fisher’s index is not designed to satisfy it.Answer:Circular test