Business Science Solutions

Autocorrelation in ASX Stock Indices

The Autocorrelation Function (ACF) in Stock Returns is a measure of the correlation between the returns of a stock and the returns of the same stock lagged by a certain number of periods.

ρ_{i} = \frac{\sum _{t = 1}^{T - i} ( r _{t} - r ˉ ) ( r _{t - i} - r ˉ )}{\sum _{t = 1}^{T} ( r _{t} - r ˉ ) ^{2}}

The Partial Autocorrelation Function (PACF) removes the effect of the intermediate lags, and is useful in identifying the order of an autoregressive model.

ϕ_{i} = \frac{ρ _{i} - \sum _{j = 1}^{i - 1} ϕ _{i - 1, j} ρ _{i - j}}{1 - \sum _{j = 1}^{i - 1} ϕ _{i - 1, j} ρ _{j}}

In efficient markets there should be very low autocorrelation as stocks should have low memory of past returns, this is satisfied in all sectors of the Australian market.