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In finance, forecasting is often conducted using financial modeling processes. Which is described as the task of building an abstract representation (a model) of a financial decision-making situation (Boundless Finance, n.d.). Assumptions play a key role in financial forecasts and can affect the way the forecasts predict the outcomes of decisions made on the corporate level. In this article, Harel and Harper (2021) suggest a unique method for forecasting stock prices based on concepts from machine learning and which differs from traditional stock prices forecasting methods. In the authors' hypothetical stock market, three types of stocks are traded: Overpriced Stocks (OP), Underpriced Stocks (UV), and Fairly Priced Stocks (FA). In total, there are N stocks traded in the market, and the financial analyst is attempting to predict whether a stock is OP, UP, or FA. By producing a 3 by 3 forecasting matrix, a 2 by 2 prediction matrix, and discussion on the ROC, the main idea was to investigate an analyst's forecasting ability to correctly predict the pricing of the stocks, and to assess the accuracy of predictions.

Within the purview of Harel and Harpaz (2021), the 3 by 3 model has columns that show the analyst's stock predictions, and rows that show the actual stock prices, while holding the number of stocks to be constant (N). Then, they show a prediction matrix. Where, A; B; C; D; E; F; G; H and I, represent specific set of observations for all stock predictions and their corresponding actual pricings. By an elimination process, the authors derived the True Negative Rate for Overpriced Stocks, the True Negative Rate for Underpriced Stocks, and the True Negative Rate for Fairly-Priced Stocks.

Next, the authors determined the accuracy of the analyst's prediction as the ratio of the number of correct hits, to the total number of stocks in the financial market.

Using the example in the table below:

It was possibly to determine the True Negative Rate for each category as:

The analyst's Prediction Accuracy is calculated as the ratio of the sum of the true positive predictions.

The interpretation here is that the stock analyst has 72% correct predictions for the 670 stocks in the financial market.

In general, the 2 by 2 model is widely used in strategic foresight and scenario planning. It helps organizations prepare for uncertainty by exploring multiple plausible futures. It can be structured as a quadrant with two key uncertainties on each axis and two extremes, creating four quadrants representing specific scenarios. The 2 by 2 model encourages creative thinking and strategic agility. It helps to identify risks and opportunities and is useful for long term planning and policy development.

Within the purview of Harel and Harpaz (2021), the 2 by 2 prediction matrix is similar to the 3 by 3 matrix but has only two columns.

The authors calculated sensitivity as:

This means 80% of the fairly priced stocks were correctly predicted to be so by the analyst

In general, the Receiver Operator Characteristic (ROC) curve is a graphical plot used to show the diagnostic ability of binary classifiers. It was first used in signal detection theory (see Wixted, 2020) but is now used in many other areas such as medicine, radiology, natural hazards and machine learning (Chan, 2025). Within the purview of financial management, the ROC curve is a plot of the True Positive Rate (on the y-axis) versus the False Positive Rate (on the x-axis) for every possible partition of data, holding (constant) the number of stocks (N) in the financial market (Harel & Harpaz, 2021). Operationally, it plots true positive rate (Sensitivity) vs. False Positive Rate (1 - Specificity) at various threshold settings, each point on the curve represents a different decision threshold. Key metrics include areas under the curve which range from 0.5 (random guessing) to 1.0 (perfect classification). Its applications include fraud detection and risk modelling.

Within the purview of Harel and Harpaz (2021), the ROC curve demonstrates the ability of the analyst to correctly predict the mispriced stocks. It also shows the tradeoff between the False Positive Rate and the True Positive Rate. The ROC looks like this:

The closer the curve approaches the 45- diagonal, the less accurate is the prediction, as the 45-degrees diagonal-line represents a random prediction. The area under the ROC curve, is a measure of comparing the forecasting performance, for all data combinations, holding the number of stock constant. The larger, (smaller) is the area under the ROC curve, the worse (better) is the analyst's (trader's or investor's) predictive ability, whereas, a prefect prediction should have an area of 1.

Research the UMGC library and O'Reilly for information on traditional financial forecasting models, i.e. those that do not rely on machine learning.

• • Bayesian method, Delphi model, Bottom-up, Top-down, correlation-based, statistical models, time-series model, and the basic forecasting model by Wallace Davidson III inFinancial Forecasting and Decision Making(O'Reilly playlist)
• Examples include:
  • What limitations and/or constraints do traditional financial forecasting models possess?
  • What was the impetus for integrating machine learning into financial forecasting models?
• Bayesian Method-A probabilistic forecasting approach that updates predictions as new data becomes available. It incorporates prior beliefs (or distributions) and revises them using observed evidence, making it ideal for dynamic environments with uncertainty.
• Delphi Model-A structured qualitative method that gathers expert opinions through multiple rounds of anonymous surveys. The goal is to reach a consensus forecast, especially useful when quantitative data is limited or future conditions are highly uncertain.
• Bottom-Up Forecasting-This method allows for client input (Davidson, 2018), it starts at the operational or departmental level, aggregating individual forecasts (e.g., unit sales, costs) to build a company-wide projection. It's detailed and grounded in micro-level insights, often used when granular data is available.
• Correlation-Based Models-These models identify relationships between variables (e.g., sales and advertising spend) and use statistical correlation to forecast outcomes. While useful, they assume past relationships will persist, which may not hold in volatile markets.
• Statistical Models-Include techniques like regression analysis, moving averages, and exponential smoothing. Davidson emphasizes regression for projecting financial statements, using historical data to estimate future values based on trends and relationships.
• Time-Series Models- Focus on patterns over timesuch as seasonality, trends, and cycles. These models use historical data points to predict future values, often employing techniques like ARIMA or exponential smoothing.
• Basic Forecasting Model (Davidson)-Davidson's foundational model uses the percent-of-sales method to project financial statements. Key features include:
• • Identifying spontaneous and non-spontaneous accounts
  • Estimating external financing needs (EFN)
  • Sensitivity analysis to test assumptions
  • Integration of income statement and balance sheet forecasts

This model is especially useful for planning sustainable growth and evaluating capital structure decisions.

Limitations:

• Dependence on Historical Data-Most models rely heavily on past performance to predict future outcomes.
• Static Assumptions- Although assumptions are a necessary part of the forecasting process (Davidson, 2018), forecasts often use fixed assumptions (e.g., constant growth rates, stable costs).
• Limited Flexibility-Traditional models may struggle to incorporate qualitative factors like consumer sentiment, geopolitical risks, or emerging technologies.
• Garbage In, Garbage Out-The accuracy of forecasts is only as good as the input data.
• Overfitting or Oversimplification-Some models are too complex, capturing noise rather than signal.
• Time Horizon Challenges- Forecasts become less reliable the further out they go.
• Human Bias and Judgment- Subjective inputslike management expectations or analyst adjustmentscan introduce bias. Cognitive biases such as anchoring bias may skew results.
• Failure to Capture Tail Risks-Many models underestimate the likelihood of extreme events (e.g., financial crises, pandemics).

Key triggers of machine learning:

• Explosion of Big Data- Financial institutions began generating and accessing massive volumes of structured and unstructured datafrom transactions and market feeds to social media and news sentiment.
• Demand for Greater Accuracy- Forecasting errors can be costly. ML models, especially deep learning and ensemble methods, offer improved predictive accuracy by capturing nonlinear relationships and subtle interactions that classical models often miss.
• Real-Time Decision Making- Markets move fast. ML enables real-time analytics, allowing firms to adjust forecasts and strategies instantly based on new data inputs.
• Automation and Efficiency- ML automates data preprocessing, feature selection, and model tuningreducing manual effort and speeding up forecasting cycles. This also minimizes human bias and error in model construction.
• Complexity of Financial Systems- Financial markets are influenced by countless variableseconomic indicators, geopolitical events, consumer behavior, etc. ML can model these complex, dynamic systems more effectively than traditional linear models.
• Competitive Advantage- Early adopters of ML gained an edge in areas like algorithmic trading, credit scoring, fraud detection, and portfolio optimization.
• Advancements in Computing Power- The rise of cloud computing, GPUs, and parallel processing made it feasible to train and deploy ML models at scalesomething that was previously too resource-intensive.