Time Series Forecasting (ARIMA & Stationarity)

Model autoregressive moving averages, verify stationarity with the ADF test, and analyze autocorrelation plots.

1. Stationarity & The Augmented Dickey-Fuller (ADF) Test

A time series is **weakly stationary** if its mean, variance, and autocovariance are invariant over time \(t\). The ADF test tests \(H_0\): presence of a unit root (non-stationary). If \(p < 0.05\), we reject \(H_0\) and confirm stationarity.

2. The \(\text{ARIMA}(p, d, q)\) Formulation

\[ Y_t = c + \sum_{i=1}^p \phi_i Y_{t-i} + \sum_{j=1}^q \theta_j \epsilon_{t-j} + \epsilon_t \]

Where \(p\) is the Autoregressive order (ACF/PACF), \(d\) is the differencing order, and \(q\) is the Moving Average error lag order.

🎯 Module Mastery Certification Quiz

+100 XP

What is the role of the differencing parameter (d) in an ARIMA(p, d, q) model?

To transform a non-stationary time series with a trend into a stationary series by computing consecutive step differences (Y_t - Y_{t-1}).

To divide the time series by 100.

To delete weekend trading days.

To remove all noise from the dataset.