Forecasting Inflation with Machine Learning and Traditional Time-Series Models: A Multi-Horizon Rolling-Origin Assessment

1. INTRODUCTION

Inflation forecasting is a central problem in applied macroeconomics because expected inflation influences monetary policy decisions, financial market valuation, wage bargaining, contract design and household planning [1, 2]. Forecasting inflation is nevertheless difficult because inflation combines persistent serial dependence with episodes of rapid change. Recent inflation values often contain useful information for short-horizon forecasts, but supply disturbances, changes in demand, monetary-policy responses and shifts in expectations can alter the inflation path over longer horizons [3].

One of the most important empirical properties of inflation is persistence. Sticky price adjustment, wage-setting arrangements, adaptive expectations and delayed policy transmission can cause inflation to respond gradually to disturbances [4–6]. This persistence allows autoregressive and naive forecasts to remain competitive, particularly at short horizons. However, a stable autoregressive relationship cannot represent every inflation episode. The post-2020 increase in US inflation combined supply constraints, relative-price changes, labour-market pressures and demand-related influences that were difficult to anticipate using lagged inflation alone [7–10].

These properties have different approaches to them across classical time-series and machine-learning models. SARIMA accounts for linear auto-regression, moving-average and seasonal relationship in an economical model or stochastic model [11–13]. XGBoost has the ability to model nonlinear decision-tree partitions, and can model conditional relationships between lagged values and rolling statistics [14–17]. More flexibility could be of benefit in case the relation turns out to be nonlinear, but also adds sensitivity to the choice of the hyper-parameters and can make overfitting more likely when samples are relatively small, as is common with macro-economic data.

The prediction horizon also affects the accuracy of forecasts. The forecast for one month of inflation is sensitive to the most recent inflation figure, and a 12 months forecast would have higher levels of accumulated uncertainty. Measures of how well one-step-ahead forecasts are realized may therefore be misleading if used to assess comparative performance. The leakages were studied at 1-, 3-, 6- and 12-month time horizons for some common target dates in a leakage-controlled rolling-origin design.

RQ1: How do SARIMA, XGBoost, naive and seasonal-naive forecasts compare at 1-, 3-, 6- and 12-month horizons?

RQ2: Does relative performance differ between predefined pre-2020 and post-2020 target periods?

RQ3: Are pairwise loss differences statistically significant after accounting for overlapping multi-step errors and multiple testing?

RQ4: Which XGBoost feature groups contribute to their forecast performance?

RQ5: How well calibrated and sharp are the models’ 80% and 95% prediction intervals?

H1: The relative predictive performance of SARIMA and XGBoost is horizon dependent, with SARIMA expected to perform strongly at shorter horizons and XGBoost potentially improving relative to SARIMA at the 12-month horizon.

H1 is evaluated using changing error rankings and horizon-specific pairwise comparisons. It is not treated as though one omnibus test directly establishes horizon dependence. The reproduced evidence ultimately does not support the hypothesised ranking reversal because SARIMA records the lowest RMSE on every horizon.

The contribution is not the first one that uses XGBoost for inflation forecasting (which is already established). Rather, in this study the univariate re-evaluation is done under the controlled setting of SARIMA and the XGBoost model share the same Sticky CPI history. It blends the advantages of pre-specified models, of separating and directly specifying the recursive and direct strategies, of common dates of forecast, of naive benchmarks, of forecast accuracy tests, of prediction intervals, of a predetermined period comparison, of feature ablation and of prediction combination. The design thus focuses on the replicability of the findings, and minimizes the risk that differences are caused by differential access to external macroeconomic predictors.

2. LITERATURE REVIEW

2.1. General Forecasting and Economic Time-Series Evaluation

A forecasting experiment is reliable if it maintains the order of the information as it arrives. Later observations can be used for model development for earlier forecasts by random cross validation. Instead, the rolling-origin and expanding-window procedures sequentially step the origin and use only information up to the current origin to form each prediction [18]. This results in repeating out-of-sample errors and is not reliant on any one arbitrary hold out date.

Multi-step forecasts can be recursive or non-recursive. A recursive strategy estimates one model and then extends it out to longer time horizons, and may build up errors. A direct strategy is the estimation of a distinct model for each horizon, with no attempt to use shorter-horizon predictions in the following steps, at the cost of having more models. The differences in the performance can thus be attributed to both the model family and multi-step strategy [19, 20].

Clear standards are a must. A naive forecast is used to check if the sophisticated model is better than the persistence model; a seasonal-naive model is used to check annual repetition. The consensus evidence is the lower value of RMSE or MAE, but formal comparison of forecasts needs a loss-differential test. The errors in multi-step forecasts may be serially correlated, which can justify the use of HAC variance estimation and finite-sample [21, 22].

Forecasts of point values are also inadequate when considering policy applications. Empirical coverage, width and proper scoring rules need to be used to evaluate prediction intervals [23, 24]. Model selection risk can be minimized by forecasting combinations, though the importance of assessing combinations out of sample is not emphasized [25].

2.2. Inflation Persistence and Forecasting

The persistence of inflation reflects the persistence of a relation with the inflation’s past and the gradual response to inflation changes. It may be due to delayed policy transmission, expectations, wage-setting mechanisms and price stickiness [3, 26]. Statistically, persistence appears through positive autocorrelation over several lags.

Although AR methods are increasingly employed for preventing this problem, ARIMA type models are still widely applied in this area because they make apparent serial dependence and provide uncertainty estimates of the model. Their limitations occur when there is change in linear relationships or when recycled errors occur [27]. Machine learning methods give regularisation and non-linear function approximation; however, some benefits from their use rely on the information content, on the number of samples and on the design of the validation [28, 29].

No literature supports universal machine-learning superiority. In data-rich settings, flexible models can be useful, while simpler autoregressive models can be easily outperformed by inflation’s high persistence [30]. A controlled univariate design is then useful to assess whether the addition of value to the series into nonlinear feature transformations is worth the added model complexity when the same series is used for both model families.

2.3. Predefined Period Analysis

The differences in inflation levels and volatility can be easily seen among the 70s, the Great Moderation, and the post-2020 episode [29, 30]. The post-2020 inflation episode is thus regarded as a helpful ad hoc stress scenario as it represented both supply-side restrictions, price shocks, labour-market pressures and inflation expectations. Recent studies on pandemic-era inflation have highlighted how these forces affected the short-run inflation environment, and the challenge of forecasting inflation. In the broader literature, formal methods of structural breaks are appropriate, but are not employed to pinpoint a break date in this research. The a priori target-date split for January-2020 is solely for showing performance for that point in time. In line with this, the analysis below considers only the specified periods, the pre-2020 inflation episode and episode of increased instability; it does not suggest that a breakpoint is actually found here, but simply background details and future extensions are mentioned.

2.4. Research Gap

Although inflation forecasting has been extensively examined using traditional econometric models and, more recently, machine-learning methods, several methodological gaps remain. First, many machine-learning studies use data-rich predictor sets containing labour-market, financial, monetary, commodity-price and expectations variables. Such studies demonstrate the potential value of flexible algorithms but do not isolate whether improvements arise from the nonlinear model itself or from access to a larger information set. There is, therefore a need for a controlled comparison in which classical and machine-learning models receive the same underlying historical information.

Second, existing studies frequently concentrate on one-step-ahead or a limited number of forecast horizons. This provides an incomplete assessment because the persistence, uncertainty and information requirements of inflation forecasting change as the horizon increases [31, 32]. Moreover, comparisons between statistical and machine-learning approaches do not always clarify whether multi-step predictions are generated recursively or through separate direct models. Since recursive and direct strategies have different bias–variance properties, failing to distinguish them can obscure the source of observed performance differences.

Third, the temporal validation procedures used in machine-learning forecasting are not always reported with sufficient precision. Studies can use a general reference of rolling or expanding validation, even if the actual training dates are not mentioned, the number of validation folds is not mentioned, the sample size is not mentioned for the different horizons and the hyperparameters are not re tuned during the final evaluation. This raises questions on how repeatable the results are and the chance of introducing look-ahead bias. Multi-step forecast errors have also to be treated appropriately for overlapping (finite-sample, treatment of multiple forecast comparisons) but the loss differential direction is not always reported.

The fourth, the comparative literature is focused on providing point forecast accuracy, and less on providing prediction-interval coverage, interval width, feature-group contribution and forecast combinations. As a result, it is difficult to distinguish between a model that has a low average error and one that has well-calibrated uncertainty estimates – and whether the success of a model is due to lagged or rolling predictors. Another typical type of interpretation of period-specific evaluations is as evidence of structural change, without making a formal breakpoint estimate.

This paper strives to fill these gaps by conducting a univariate and multi-horizon controlled comparison of SARIMA and XGBoost based on same history of the Sticky CPI. It uses an explicit model specified separately for the development set, a set of 5 validation folds of the expanding window choosing the target dates for each explicitly provided, deterministic model choices, recursive SARIMA models (may be used for the top level forecasting model), direct XGBoost models for the forecasts within a given window (expanding window across the folds) and a common set of target dates for the out-of-the-sample forecasts. The comparison also includes a number of naive benchmarks, tests of forecast error, prediction intervals, feature-group ablation and forecast combinations as well as a clearly defined pre-2020/post-2020 period analysis. The trick here is the transparency of the methodology, and the ability to reproduce and develop meaningful comparisons rather than ascribing the first use of machine learning to inflation forecasting.

3. METHODOLOGY

3.1. Empirical Pipeline

The design is summarised in Fig. (1). The pre-2008 sample is employed for diagnostic analysis, order selection with SARIMA model and tuning for XGBoost across horizons. The 200 target months used for the last pseudo out-of-choice test is the same for all the horizons. The difference lies in the orders for both the SARIMA and the four separately tuned direct horizon-specific models of XGBoost: the SARIMA has a fixed order and creates recursive multi-step forecasts, while XGBoost has four different orders and creates four independently tuned direct horizon-specific forecasts. Point accuracy, interval performance and pairwise forecast-accuracy tests or predefined-period comparisons, feature ablations and combinations of forecasts are subsequently assessed.

Fig. (4). Autocorrelation function of Sticky CPI.