Rongsheng (Royce) Zhang

Rongsheng (Royce) Zhang

He/Him

Undergraduate double major in Mathematics & Statistics (UIUC) | Minor in Computer Science & Data Science | Research & Industry Experience in AI/ML, Applied Optimization and Data Science

Forecasting Used Cars & Trucks CPI: Regression vs. ARIMA

Published in STAT 429 Final Project (UIUC), 2025

Abstract

This project analyzes the CPI of used cars and trucks in the U.S. to identify the most accurate model for short-term forecasting. We compared four modeling approaches: OLS regression with a COVID-19 breakpoint, Weighted Least Squares (WLS) to address heteroscedasticity, Lagged-Predictor Regression based on CCF analysis, and an ARIMA model. While macroeconomic predictors like New Vehicle CPI, Motor Fuel CPI, and the Federal Funds Rate showed significant relationships, linear models failed to fully resolve residual autocorrelation. The study concluded that an ARIMA(0,1,2) model provided the best stability and predictive accuracy (MAPE ≈ 0.67%) for 5-month-ahead forecasts.

Data

We utilized monthly U.S. time-series data from FRED spanning January 2000 to April 2025:

  • Used Cars & Trucks CPI (Response, CUSR0000SETA02)
  • New Vehicles CPI (Predictor, CUSR0000SETA01)
  • Motor Fuel CPI (Predictor, CUSR0000SETB)
  • Federal Funds Effective Rate (Predictor, FEDFUNDS)

A COVID-19 dummy variable was introduced for the post-January 2020 period to capture structural market shifts.

Methodology

  1. Exploratory Analysis: Confirmed non-stationarity in all series; applied differencing ($d=1$) to achieve stationarity.
  2. Regression Modeling:
    • Model 1 (OLS): Baseline with contemporaneous predictors and COVID dummy ($R^2 \approx 0.75$).
    • Model 2 (WLS): Applied to fix non-constant variance found in OLS.
    • Model 3 (Lagged): Incorporated specific lags (New CPI $t-1$, Fuel $t-3$, Fed Funds $t-12$) identified via Cross-Correlation Function (CCF) analysis ($R^2 \approx 0.79$).
  3. Time Series Modeling (ARIMA): Fitted an ARIMA(0,1,2) model based on ACF/PACF plots and AIC/BIC minimization.
  4. Evaluation: Models were compared using residual diagnostics (Ljung-Box, Normality) and out-of-sample forecast accuracy. The ARIMA model successfully eliminated autocorrelation artifacts present in the regression approaches.

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