Empirical Testing of the EMH
(1). Anomalies or regularities.
An anomaly or regularity is where empirical evidence contradicts the EMH. For example, it may be the case that if a share price rises Alternating Series Test one day, it is more likely to rise the nest day and if it falls one day it is more likely to fall the nest day. This knowledge would enable us to predict future price movements with some accuracy it would contrabandist the EMH and as a result would be referred to as an anomaly.
(2). Tests of the weak form of the EMH.
Statistical tests of independence.
the weak form argues that there should be no correlation of price movements over time. This can be tested statistically.
One form of statistical test would look for auto -(or serial ) correlation. Autocorrelation describes the situation where the stock price movement for one period of time is related to the price movements in a previous period. For example, are stock price movements today linked to price movements yesterday or the day before?
Tests have found that usually there is not significant level of autocorrelation, except in the case of some portfolios of small shares. Even this may be due to measurement problems when collating stock price information. It is difficult to rely on prices for small stocks since they are often infrequently traded (the problem of non-synchronous trading).
Alternatively, a run test can look at the changes in price through time and compare the actual changes to what would be expected for a random series. For example, it is possible to look at whether the price has risen (+) or fallen (-) each day and look at the results.
A series such as the following would indicate that a rise is likely to be followed by a fall.
+ – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – +
A series such as the following would indicate that a rise is likely to be followed by a rise and a fall is likely to day followed by a fall.
+ + + + + + + + + – – – – – – – – – – – – – – – – – + + + + + + + + + + +
A series such as the following would indicate that there is no link in price movements from day to be and the movements are random.
+ – – – + + – + + – + + + – – + + – + – – – + + + – + – + + – + +
Tests have shown that price changes fall within the range for a random series. Supporting the idea of weak form efficiency. This relates to testing for both the public market and the OTC market.
Both of the above types of statistical test support the view that price movements are a random series, with no correlation from one period to the next. A small doubt may be present for small stocks, but even this may be explained by infrequent trading, as noted above.