Hands-On Machine Learning for Algorithmic Trading

How to identify the number of lags

In practice, the challenge consists in deciding on the appropriate order p of lagged terms. The time series analysis tools for serial correlation play a key role. The ACF estimates the autocorrelation between observations at different lags, which in turn results from both direct and indirect linear dependence.

Hence, for an AR model of order k, the ACF will show a significant serial correlation up to lag k and, due to the inertia caused by the indirect effects of the linear relationship, will extend to subsequent lags and eventually trail off as the effect was weakened. On the other hand, the PACF only measures the direct linear relationship between observations a given lag apart so that it will not reflect ...