Scott Monaco

Economics & Finance2 min read

Retail Trade Time Series Forecasting

Code

Retail Trade Time Series Forecasting

Problem Statement

Retail trade volumes are deeply seasonal and trend-driven - making them a natural fit for time series forecasting. This project builds SARIMA models for two structurally different metro areas to predict monthly retail trade employment, using data from the St. Louis Fed (FRED).

The two regions - Seattle-Tacoma-Bellevue and Dallas-Fort Worth-Arlington - were chosen for their contrasting economic profiles: tech-heavy Pacific Northwest vs. diversified Sun Belt.

Methodology

Seasonality Detection

Examining the retail trade data reveals a clear repeating pattern every 12 months, as indicated by the vertical lines. Additionally, there is an upward trend, suggesting the series is non-stationary.

Retail trade time series showing clear 12-month seasonal pattern
Time series plot revealing clear 12-month seasonality and upward trend in Seattle retail trade data.

Achieving Stationarity

To use a SARIMA model, stationarity is required. The first difference was applied, yielding an ADF test p-value of 0.033. To achieve 99% confidence, a second difference was taken.

Differencing analysis to achieve stationarity
Differencing analysis confirms d=2 is required to achieve stationarity (ADF p-value = 0.00).

ACF and PACF Analysis

The PACF plot shows the 11th lag is significant (p=11, P=0). The ACF plot shows the 12th lag is significant (Q=1, q=0). This gives a SARIMA order of (11, 2, 0)(0, 0, 1, 12).

ACF and PACF plots for determining SARIMA model parameters
ACF and PACF plots used to determine the SARIMA model order parameters.

Results

SARIMA Predictions

SARIMA predictions vs actual values for Seattle and Dallas
SARIMA model predictions vs. actual values for both metro areas. Seattle MAPE: 2.6%, Dallas MAPE: 1.82%.

Model Comparison

Model performance comparison between Seattle and Dallas
Model performance metrics comparison between Seattle and Dallas regions.

Next Steps

  • Incorporate exogenous variables to enhance predictive power
  • Explore Facebook Prophet as an alternative algorithm, well-suited for handling seasonality
  • Analyze error plots to identify any systematic patterns the model may be missing

Tools and technologies

  • Python
  • statsmodels
  • SARIMA
  • Pandas

Data source: U.S. Census BureauStatus: Completed

  • Time Series
  • SARIMA
  • Forecasting