27 Machine-Learning Models Tried to Forecast US Inflation — a Classical One Won

Data and preprocessing

The study uses monthly CPI-U data (base period 1982-84 = 100) sourced from the U.S. Bureau of Labor Statistics, spanning more than two decades through December 2023. Before modeling, the authors ran three standard diagnostic tests. A Shapiro-Wilk test rejected normality (the data does not follow a bell-curve distribution). A Ljung-Box test rejected the hypothesis that the series is white noise, with a p-value far below conventional significance thresholds — confirming the series has genuine, statistically significant autocorrelation rather than being random. An Augmented Dickey-Fuller (ADF) test for stationarity returned a p-value of 0.98, far above the threshold needed to reject non-stationarity, confirming the raw series is non-stationary: its mean and variance shift over time rather than staying constant, which most forecasting models assume they won't. To address this, the authors applied a first-order (non-seasonal) difference, transforming the raw level series into a differenced series that behaves as stationary. A boxplot check found no significant outliers in the data.

Modeling pipeline

Twenty-seven models were fit using the PyCaret time-series module (version 3.4) in Python, following a standard supervised-learning workflow: data cleaning (handling missing values, feature scaling, outlier checks), an 80/20 train-test split, model fitting on the training set, and evaluation on the held-out test set using three metrics — Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) — plus R-squared. The model roster spanned simple baselines (naive and seasonal-naive forecasters, a grand-means forecaster), classical statistical methods (ARIMA, Auto-ARIMA, exponential smoothing, ETS, Theta forecaster), and machine-learning regressors adapted for time series with deseasonalizing and detrending preprocessing (random forest, gradient boosting, extreme gradient boosting, light gradient boosting, AdaBoost, ridge, lasso, elastic net, Bayesian ridge, k-nearest neighbors, extra trees, decision tree, and several others).

The winning model: ETS

ETS stands for Error, Trend, Seasonality — a classical state-space formulation of exponential smoothing, distinct from most of the machine-learning models it was tested against. Rather than learning flexible, potentially non-linear patterns from data the way a tree-based or gradient-boosted model does, ETS explicitly decomposes a time series into three components it models directly: an error term (additive or multiplicative), a trend term (none, additive, multiplicative, or damped), and a seasonal term (none, additive, or multiplicative). The general form of the model, following the standard formulation used in the forecasting literature, can be written as:

Of the 27 models tested, ETS achieved the lowest RMSE, narrowly ahead of plain exponential smoothing and meaningfully ahead of ARIMA and every tree-based or boosting method in the comparison. Every one of the simple naive-style baselines (naive forecaster, seasonal naive, Croston's method, grand means forecaster) scored worst by a wide margin, confirming the more structured models were capturing real signal rather than just trend momentum.

The two-year forecast

Applying the winning ETS model, the study forecasts CPI-U monthly from January 2024 through December 2025. The annual averages move from roughly 304.7 (2023, actual) to about 314.1 (2024, forecast) to about 323.6 (2025, forecast) — increases of approximately 3.1% and 3.0% year-over-year respectively. Within each forecast year, the model projects a consistent intra-year shape: CPI-U rises fairly steadily from January through July, then levels off or moves only slightly for the remainder of the year, in both 2024 and 2025.

The study offers several candidate explanations for the January-to-July pattern, presented as plausible contributing factors rather than a single isolated cause: a rebound in consumer spending after the holiday season, tax-refund-driven spending concentrated in February through April, seasonal demand for travel, clothing, and outdoor goods through the spring and early summer, seasonally higher energy demand as travel picks up, planting-season agricultural supply constraints ahead of harvest, a general post-winter pickup in economic activity and employment, and seasonal supply-chain dynamics. The paper does not attempt to isolate which of these mechanisms dominates, and readers should treat them as a menu of plausible contributing factors rather than an econometrically isolated causal decomposition.

A companion result: the same method applied to India

One of the two authors, B. S. Kambo, is a former Deputy Director (Statistics) at India's Ministry of Labour & Employment, and has previously modeled India's own consumer price data — including a 2019 study fitting an ARIMA model to India's CPI for industrial workers, and a 2020 study forecasting the trajectory of COVID-19 case counts in India using similar time-series methods. In the same journal issue as this paper, the same author team (Kambo, together with Gurinder Singh and Jassimar Singh) ran a directly comparable exercise on India's Consumer Price Index for Industrial Workers (CPI-IW), testing 28 models rather than 27. There, a different model won: a Long Short-Term Memory (LSTM) neural network — not ETS — was found to be the best fit, and the resulting forecast projected India's CPI-IW rising by roughly 3.4 points during the summer/monsoon months (April to September) before staying comparatively stable over winter (October to March). The fact that a different model won on India's series than on the U.S. series is itself informative: it suggests there is no universally best forecasting method for consumer price indices, and that model choice should be validated separately for each country's data rather than assumed to transfer.

Limitations

The comparison covers one country's inflation series over one historical window, using models and preprocessing choices (differencing, deseasonalizing, the specific PyCaret defaults) that the authors selected; a different preprocessing pipeline or a longer/shorter data window could plausibly favor a different model. The forecast itself is a two-year statistical projection based on historical patterns, not an economic model incorporating policy decisions, external shocks, or structural breaks — the kind of event (a new tariff regime, a recession, an energy-price shock) that historically has moved CPI-U in ways a purely statistical time-series model, however well-fitted to the past, would not have anticipated in advance.

Why RMSE, specifically, was the deciding metric

The study reported three accuracy measures for every model rather than just one: Mean Absolute Error, Root Mean Square Error, and Mean Absolute Percentage Error. These don't always agree on a winner, since RMSE penalizes large individual errors more heavily than MAE does, while MAPE expresses error as a percentage rather than in the index's own units. In this case the picture was consistent across measures -- ETS and plain exponential smoothing occupied the top two spots on all three metrics, with a similar gap over the rest of the field each time -- which is a stronger result than a model that only wins on one metric and looks mediocre on the others. That consistency across three different ways of scoring error is part of why the result reads as a genuine finding about this series rather than an artifact of which single metric happened to be reported.