Autocorrelation

A fundamental property of a time series where its statistical characteristics—mean, variance, and autocorrelation structure—remain constant over time. Most classical forecasting models, including ARIMA, require stationarity to produce reliable predictions.

• Dickey-Fuller test is the standard statistical test for stationarity
• Non-stationary series often exhibit strong autocorrelations that decay slowly
• Differencing is the primary technique to transform a non-stationary series into a stationary one

A classical statistical model that explicitly leverages autocorrelation patterns to forecast future values. ARIMA models describe a time series using three components:

• AR (Autoregressive): Uses the dependency between an observation and a specified number of lagged observations
• I (Integrated): Applies differencing to make the series stationary
• MA (Moving Average): Uses the dependency between an observation and residual errors from lagged observations

The ACF and PACF plots are the primary diagnostic tools for determining the appropriate AR and MA orders.

A diagnostic tool that measures the correlation between an observation and a lagged observation after removing the effects of intermediate lags. The PACF is critical for identifying the order of autoregressive models.

• A sharp cutoff after lag p in the PACF suggests an AR(p) model
• Unlike the ACF, the PACF isolates the direct relationship at each lag
• Used alongside the ACF to distinguish between AR and MA processes

A statistical technique that deconstructs a time series into its constituent components: trend, seasonality, and residual noise. Autocorrelation is the mathematical signature that reveals these underlying patterns.

• Strong autocorrelation at lag s (e.g., 7 for daily data with weekly patterns) indicates seasonality
• The residual component should ideally exhibit no autocorrelation (white noise)
• Decomposition methods include classical multiplicative/additive and STL (Seasonal-Trend decomposition using LOESS)

The process of creating informative input variables from raw temporal data to improve model accuracy. Autocorrelation analysis directly informs which features to construct.

• Lag features: Create variables for observations at t-1, t-2, t-7 based on significant ACF spikes
• Rolling window statistics: Compute moving averages and standard deviations over windows identified by autocorrelation patterns
• Date-time decompositions: Extract cyclical features like day-of-week or month to capture seasonal autocorrelation structure

A robust model evaluation technique for time series that respects the temporal order of observations. Unlike random cross-validation, walk-forward validation preserves the autocorrelation structure inherent in sequential data.

• The model is retrained on an expanding or rolling window of historical data
• Each forecast horizon is evaluated against actuals before moving forward
• Prevents data leakage where future autocorrelated observations would contaminate training
• Essential for simulating how a forecasting model will perform in production