Out-of-sample earnings forecasting for OLS and Theil–Sen models relative to a na^.ı^.ve no-change model

Abstract

Purpose

The purpose of this paper is to enlarge the exposure of the Theil–Sen (TS) methodology to the academic, analyst and practitioner communities using an earnings forecast setting. The study includes an appendix that describes the TS model in very basic terms and SAS code to assist readers in the implementation of the TS model. The study also presents an alternative approach to deflating or scaling variables.

Design/methodology/approach

Archival in nature using a combination of regression analysis and binomial tests.

Findings

The binomial test results support the hypothesis that the forecasting performance of the naïve no-change model is at least equal to or better than the ordinary least squares (OLS) model when earnings volatility is low. However, the results do not support the same hypothesis for the TS model nor do the results support the hypothesis that the OLS and TS models will outperform the naïve no-change model when cash flow volatility is high. Nevertheless, the study makes notable contributions to the literature, as the results indicate that the performance of the naïve model is at least as good as the OLS and TS models across 18 of the 20 binomial tests. Moreover, the results indicate that the performance of the TS model is always superior to the OLS model.

Research limitations/implications

The results are generalizable to US firms and may not extend to non-US firms.

Practical implications

The TS methodology is advantageous to OLS in that the results are robust to outlier observations, and there is no heteroscedasticity. Researchers will find this study to be useful given the use of a model (i.e. TS) which has to date received little attention, and the provision of the details for the mechanics of the model. A bonus for researchers is that the study includes SAS code for implementing the procedure.

Social implications

Awareness of alternative forecast methodologies could lead to improved forecasting results in certain contexts. The study also helps the financial community in general, as improved forecasting abilities are important for all capital market participants as they improve market efficiency.

Originality/value

Although a healthy literature exists for examining out-of-sample forecasts for earnings, the literature lacks an answer for a simple question before pursuing additional analyses: Are the results any better than those from a naive no-change forecast? The current study emphasizes the idea that the naïve no-change forecast is the most elementary model possible, and the researcher must first establish the superiority of a more complex model before conducting further analyses.

Citation

Francis, R.N. (2022), "Out-of-sample earnings forecasting for OLS and Theil–Sen models relative to a na^.ı^.ve no-change model", Journal of Applied Accounting Research, Vol. 23 No. 2, pp. 321-339. https://doi.org/10.1108/JAAR-10-2020-0206