There exists theoretical and empirical evidence on the efficiency and robustness of Nonnegativity Restricted Least Squares combinations of forecasts. However, the computational complexity of the method hinders its widespread use in practice. We examine various optimizing and heuristic computational algorithms for estimating NRLS combination models and provide certain CPU-time reducing implementations. We empirically compare the combination weights identified by the alternative algorithms and their computational demands based on a total of more than 66,000 models estimated to combine the forecasts of thirty seven firm specific accounting earnings series. The ex ante prediction accuracies of combined forecasts from the optimizing versus heuristic algorithms are compared. The effects of fit sample size, model specification, multicollinearity, correlations of forecast errors, and series and forecast variances on the relative accuracy of the optimizing versus heuristic algorithms are analyzed. The results reveal that, in general, the computationally simple heuristic algorithms perform as well as the optimizing algorithms. No generalizable conclusions could be reached, however, about which algorithm should be used based on series and forecast characteristics.

This paper investigates the time-series properties and adjustment processes of a group of financial ratios for the purpose of finding accurate forecasting models. The ratios selected represent profitability, liquidity, cash position, turnover, and capital structure. Our investigation of financial ratios included two deflated earnings measures that have been the subject of considerable research. These are the return on assets and return on owners' equity ratios. Past research has focused on describing the movement of the income series over time, primarily to develop earnings forecasting models. Methods were sought to identify and disentangle the permanent and transitory components of income in an effort to improve forecasting accuracy, and hence equity pricing. To achieve this, researchers used models such as ARIMA, which removed a portion of transitory error from past earnings changes. Using a Kalman filter, Lieber et al. [1983] reported that by extracting the permanent component they could improve predictive ability. Disaggregating data in different ways has also been employed to improve forecast accuracy. Hopwood et al. [1982a] examined quarterly versus annual data and Kinney [1971] investigated segment as opposed to aggregated consolidated data. Manegold [1981] modelled the infrastructure of accounting variables using components of net income. Although not significantly superior to the univariate time-series models, Manegold`s component model was favored by the security-price-association tests. Lipe [1986] concluded that the decomposition of earnings provided a small but statistically significant amount of information above that provided by earnings alone. In this paper we disaggregate the return on assets and return on equity ratios into their component ratios for the purpose of obtaining improved forecasts of deflated earnings. To our knowledge this has not appeared in the literature. The Box-Jenkins method of identification, estimation, and diagnostic checking of autoregressive integrated moving-average models was used in the time-series analysis, and the method of instrumental variables was used for the partial-adjustment models. The hypothesis that firms adjust their ratios towards an industry mean could not be rejected. The analysis included the chemical, computer, food, and paper industries. Significant differences in the adjustment process of financial ratios across industries were found. The adjustment processes and the time-series patterns of the ratios were also found to vary across ratio categories. We find that global and firm-specific ARIMA models outperform the partial-adjustment models for all ratios and industries analyzed. We also find that predictive accuracy is improved when the sample is stratified by industry. Significant differences across industries were obscured when the analysis was performed with all industries combined. These results highlight the importance of analyzing industries separately. Finally, we observe that the prediction of return on assets and return on equity is significantly improved by disaggregating the component ratios. The mean absolute percentage errors for forecasts of return on investment and return on owner's equity derived by disaggregating the rates of return were predominantly smaller for all industries.