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Movement Prediction-Adjusted Naive Forecast: Is the Naive Baseline Unbeatable in Financial Time Series Forecasting?

Cheng Zhang

TL;DR

The paper tackles the difficulty of beating the naive forecast in financial time series by introducing MPANF, a forecast-combination that injects movement direction into the naive forecast. MPANF forecasts follow \\hat{y}_t = y_{t-1} + \\hat{d}_t \\cdot \\alpha \\cdot \\bar{\\epsilon}, with an analytically derived in-sample coefficient \\hat{\\alpha}_{in}^* = 2 \\cdot ACC_{in} - 1 and a retrospective out-of-sample condition \\hat{\\alpha}_{out}^* \\cdot \\bar{\\epsilon}_{out} \ge \\frac{1}{2} \\hat{\\alpha}_{in}^* \\cdot \\bar{\\epsilon}_{in}. The approach is model-agnostic, validated on eight U.S. financial series using RMSE, MAE, MAPE, and sMAPE, and shows MPANF generally surpasses the naive baseline when movement predictions are reliable. The theoretical results link movement-prediction accuracy to out-of-sample gains and demonstrate the conditional nature of improvements, providing a practical pathway to leverage directional signals in forecasting. Overall, the work reframes the naive baseline as a conditional benchmark and offers a principled, low-overhead forecast-combination method with empirical support and clear diagnostic criteria.

Abstract

In financial time series forecasting, the naive forecast is a notoriously difficult benchmark to surpass because of the stochastic nature of the data. Motivated by this challenge, this study introduces the movement prediction-adjusted naive forecast (MPANF), a forecast combination method that systematically refines the naive forecast by incorporating directional information. In particular, MPANF adjusts the naive forecast with an increment formed by three components: the in-sample mean absolute increment as the base magnitude, the movement prediction as the sign, and a coefficient derived from the in-sample movement prediction accuracy as the scaling factor. The experimental results on eight financial time series, using the RMSE, MAE, MAPE, and sMAPE, show that with a movement prediction accuracy of approximately 0.55, MPANF generally outperforms common benchmarks, including the naive forecast, naive forecast with drift, IMA(1,1), and linear regression. These findings indicate that MPANF has the potential to outperform the naive baseline when reliable movement predictions are available.

Movement Prediction-Adjusted Naive Forecast: Is the Naive Baseline Unbeatable in Financial Time Series Forecasting?

TL;DR

The paper tackles the difficulty of beating the naive forecast in financial time series by introducing MPANF, a forecast-combination that injects movement direction into the naive forecast. MPANF forecasts follow \\hat{y}_t = y_{t-1} + \\hat{d}_t \\cdot \\alpha \\cdot \\bar{\\epsilon}, with an analytically derived in-sample coefficient \\hat{\\alpha}_{in}^* = 2 \\cdot ACC_{in} - 1 and a retrospective out-of-sample condition \\hat{\\alpha}_{out}^* \\cdot \\bar{\\epsilon}_{out} \ge \\frac{1}{2} \\hat{\\alpha}_{in}^* \\cdot \\bar{\\epsilon}_{in}. The approach is model-agnostic, validated on eight U.S. financial series using RMSE, MAE, MAPE, and sMAPE, and shows MPANF generally surpasses the naive baseline when movement predictions are reliable. The theoretical results link movement-prediction accuracy to out-of-sample gains and demonstrate the conditional nature of improvements, providing a practical pathway to leverage directional signals in forecasting. Overall, the work reframes the naive baseline as a conditional benchmark and offers a principled, low-overhead forecast-combination method with empirical support and clear diagnostic criteria.

Abstract

In financial time series forecasting, the naive forecast is a notoriously difficult benchmark to surpass because of the stochastic nature of the data. Motivated by this challenge, this study introduces the movement prediction-adjusted naive forecast (MPANF), a forecast combination method that systematically refines the naive forecast by incorporating directional information. In particular, MPANF adjusts the naive forecast with an increment formed by three components: the in-sample mean absolute increment as the base magnitude, the movement prediction as the sign, and a coefficient derived from the in-sample movement prediction accuracy as the scaling factor. The experimental results on eight financial time series, using the RMSE, MAE, MAPE, and sMAPE, show that with a movement prediction accuracy of approximately 0.55, MPANF generally outperforms common benchmarks, including the naive forecast, naive forecast with drift, IMA(1,1), and linear regression. These findings indicate that MPANF has the potential to outperform the naive baseline when reliable movement predictions are available.
Paper Structure (15 sections, 3 theorems, 29 equations, 8 figures, 6 tables, 1 algorithm)

This paper contains 15 sections, 3 theorems, 29 equations, 8 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. MPANF
  3. General Formulation
  4. Optimal Coefficient
  5. Retrospective Condition
  6. Algorithmic Implementation
  7. Experiments
  8. Experimental Setup
  9. Datasets and Preprocessing
  10. Baselines and Evaluation Metrics
  11. Experimental Results
  12. Out-of-Sample Performance
  13. Retrospective Validation
  14. Discussion
  15. Conclusions

Key Result

Proposition 1

The analytical estimate of the optimal in-sample coefficient, denoted by $\hat{\alpha}_{\text{in}}^{*}$, which is the optimal solution for a convex approximation of the in-sample MSE difference between the naive forecast and the MPANF, is given by:

Figures (8)

  • Figure 1: Forecasting framework incorporating naive forecast and movement prediction.
  • Figure 2: Time series of eight target variables.
  • Figure 3: Open price of FTSE.
  • Figure 4: Out-of-sample forecasts by different methods.
  • Figure 5: Comparison of the RMSEs of different methods.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Proposition 1: Coefficient Estimate
  • Proposition 2: In-sample MSE Improvement
  • Proposition 3: Retrospective Condition