How regular are directional movements in commodity and asset prices? A Wald test

• Up and down movements in commodity prices has symmetric momentum in both directions
• No strong evidence for random walk behavior in commodity prices
• Asset indices have momentum only in up movements
• Positive returns in the asset indices due to more frequent up movements
• Asset indices cannot reject weak-form efficiency in directional movements

This paper derives a Wald test to evaluate whether up/down movements in prices follow a two-state first-order time-homogenous Markov chain. Probabilities that prices, separated by up to k periods, move in the same direction are derived and compared to empirical probabilities using a Wald statistic. The hypothesis is evaluated for 48 monthly commodity prices and five major stock price indices. Nominal commodity prices show evidence of symmetric momentum in up and down movements. Stock indices have momentum in up movements, with a positive trend due to more frequent up movements. The testing reveals fundamental differences between commodity and asset prices. Several commodities show evidence against the null hypothesis, while none of the stock indices reject the hypothesis.