The Augmented Dickey-Fuller Test

Latest lecture I have attended on the topic was lead by Ishan Shah from QuantInsti

What is the ADF Test?
The Augmented Dickey-Fuller (ADF) test is a statistical tool used to check if a time series is non-stationary due to a unit root. It helps to understand whether the patterns in the data are reliable over time or if they’re caused by trends that don’t repeat in a predictable way. Essentially, it’s like a test that tells you if certain characteristics of your data (like the average value) stay the same or change as time goes on.
ADF expands on the Dickey-Fuller test by including higher-order regressive processes to account for serial correlation in the error terms. This is important because many time series exhibit some form of autocorrelation, which the basic Dickey-Fuller test does not account for.

How the ADF Test Works:

1. Model Specification: The ADF test starts with specifying a model that includes the term to be tested (typically the lagged level of the time series) along with lagged differences of the series. The number of lagged differences included is determined based on various criteria like the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC).

2. Regression and Coefficient Estimation: The specified model is estimated using ordinary least squares (OLS), and the key coefficient of interest is the one attached to the lagged level of the series.