Assessing Point Forecast Bias Across Multiple Time Series: Measures and Visual Tools

Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well known and well researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy to implement metrics and visualization tools that are likely to be applicable in practice. To study the statistical properties of alternative measures we use theoretical concepts and simulation experiments based on artificial data with predetermined features. We describe the difference between mean and median bias, describe the connection between metrics for accuracy and bias, provide suitable bias measures depending on the loss function used to optimise forecasts, and suggest which measures for accuracy should be used to accompany bias indicators. We propose several new measures and provide our recommendations on how to evaluate forecast bias across multiple series. /// Note: This is the final version of the paper, which appeared in the International Journal of Statistics and Probability. The first draft of this paper was uploaded to Preprints.org on 11 May, 2021: https://doi.org/10.20944/preprints202105.0261.v1 /// Copyrights: This is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

Assessing Point Forecast Bias Across Multiple Time Series: Measures and Visual Tools

Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under-represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well-known and well-researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling-origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy-to-implement metrics and visualization tools that are likely to be applicable in practice. To study the statistical properties of alternative measures we use theoretical concepts and simulation experiments based on artificial data with predetermined features. We describe the difference between mean and median bias, describe the connection between metrics for accuracy and bias, provide suitable bias measures depending on the loss function used to optimise forecasts, and suggest which measures for accuracy should be used to accompany bias indicators. We propose several new measures and provide our recommendations on how to evaluate forecast bias across multiple series.

Asymmetry in Subseasonal Surface Air Temperature Forecast Error with Respect to Soil Moisture Initialization

Soil moisture (W) helps control evapotranspiration (ET), and ET variations can in turn have a distinct impact on 2-m air temperature (T2M), given that increases in evaporative cooling encourage reduced temperatures. Soil moisture is accordingly linked to T2M, and realistic soil moisture initialization has, in previous studies, been shown to improve the skill of subseasonal T2M forecasts. The relationship between soil moisture and evapotranspiration, however, is distinctly nonlinear, with ET tending to increase with soil moisture in drier conditions and to be insensitive to soil moisture variations in wetter conditions. Here, through an extensive analysis of subseasonal forecasts produced with a state-of-the-art seasonal forecast system, this nonlinearity is shown to imprint itself on T2M forecast error in the conterminous United States in two unique ways: (i) the T2M forecast bias (relative to independent observations) induced by a negative precipitation bias tends to be larger for dry initializations, and (ii) on average, the unbiased root-mean-square error (ubRMSE) tends to be larger for dry initializations. Such findings can aid in the identification of forecasts of opportunity; taken a step further, they suggest a pathway for improving bias correction and uncertainty estimation in subseasonal T2M forecasts by conditioning each on initial soil moisture state.

The information content of managerial insider trading: evidence from analyst forecasts

PurposeThis paper examines the effect of managerial insider trading on analyst forecast accuracy, dispersion and bias. Specifically, the authors test whether insider-trading information is positively associated with the precision of earnings forecasts. In addition, this relationship between Regulation Fair Disclosure (FD) and the Galleon insider trading case is examined.Design/methodology/approachPooled ordinary least squares (Pooled OLS) rregressions with year-fixed effects, firm-fixed effects, and firm-level clustered standard errors are used. Our proxies for forecast precision are regressed on alternative measures of insider trading activities and a vector of control variables.FindingsInsider-trading information is positively associated with the precision of earnings forecasts. Analysts provide better forecast accuracy, less forecast dispersion and lower forecast bias among firms with insider trading in the six months leading to the forecast issues. In addition, bullish (bearish) insider trades are associated with increased (decreased) forecast bias. Insider trading information complements analysts' independent opinion and increases the precision of their forecast.Practical implicationsRegulators may pursue rules that promote the rapid disclosure of managerial insider trades, particularly given the increasing availability of Internet tools. Securities regulators may attempt to increase transparency and enhance the reporting procedures of corporate insiders, for example, using Internet sources with direct release to the public to ensure more timely information dissemination.Originality/valueThe authors document a positive association between earnings forecast precision and managerial insider trading up to six months prior to the forecast issue. This relationship is stronger after the Securities and Exchange Commission (SEC) prohibited the selective disclosure of material nonpublic information through Regulation FD. In addition, the association between insider trading and forecast accuracy has weakened after the Galleon insider trading case.

Assessing Point Forecast Bias Across Multiple Time Series: Measures and Visual Tools

Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under-represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well-known and well-researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling-origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy-to-implement metrics and visualization tools that are likely to be applicable in practice. To study the statistical properties of alternative measures we use theoretical concepts and simulation experiments based on artificial data with predetermined features. We describe the difference between mean and median bias, describe the connection between metrics for accuracy and bias, provide suitable bias measures depending on the loss function used to optimise forecasts, and suggest which measures for accuracy should be used to accompany bias indicators. We propose several new measures and provide our recommendations on how to evaluate forecast bias across multiple series.