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3X3 forecasting model,

The 33 forecasting model divides the stock market into three groups: overpriced, underpriced, and fairly priced. Each category leads to a different investment choice. An overpriced stock signals a sell, an underpriced stock suggests a buy, and a fairly priced stock means the best option is to hold.

To measure how well an analyst predicts these categories, we use a 33 table. The rows represent the actual condition of the stock, while the columns show the analyst's forecast. Correct predictions fall on the diagonal of the table, while mistakes fall off the diagonal. From this table, we can calculate three measures of performance.

• Accuracy tells us the percentage of correct predictions.
• Sensitivity shows how well the analyst identifies a specific type of stock, such as overpriced.
• Specificity shows how well the analyst avoids labeling the wrong stocks as belonging to that type.

In the example from the article, the analyst correctly classified about 72% of stocks in the market. Meaning, If you gave the analyst 100 random stocks, about 72 of those predictions would match reality, while about 28 would be wrong.

Actual \ Predicted	Overpriced	Underpriced	Fairly Priced	Total
Overpriced	150	20	30	200
Underpriced	30	130	50	210
Fairly Priced	20	40	200	260
Total	200	190	280	670

AC= Number of correct predictions/Total number of predictions

AC=480/670=72%

2X2 forecasting model, and

The 22 model simplifies the problem. Instead of three categories, it reduces the question to two: is the stock mispriced or fairly priced?

The table for this model has four outcomes.

A true positive occurs when a mispriced stock is correctly identified.

A false positive occurs when a fairly priced stock is incorrectly flagged as mispriced.

A false negative occurs when the analyst fails to detect a mispriced stock.

A true negative occurs when a fairly priced stock is correctly recognized.

This structure makes performance easier to evaluate. For example, in a case in the article with 100 stocks, the analyst identified 80 percent of mispriced stocks correctly but also mislabeled 20 percent of fair stocks . across all 100 predictions, 80 were right and 20 were wrong.

Actual \ Predicted	Mispriced	Fairly Priced	Total
Mispriced	40	10	50
Fairly Priced	10	40	50
Total	50	50	100
TP (true positives) = mispriced correctly flagged as mispriced.
TN (true negatives) = fair correctly called fair Accuracy=(TP+TN)/100=80%

Receiver Operator Characteristic (ROC) curve.

The ROC curve transforms these results into a visual picture of prediction quality. On the vertical axis, it plots the true positive rate (sensitivity). On the horizontal axis, it plots the false positive rate (1 - specificity).

The position of the curve carries important meaning.

A curve that bends toward the top-left corner reflects strong forecasting.

A curve that lies on the diagonal line shows performance no better than random guessing.

The area under the curve (AUC) provides a single score of overall accuracy. A value close to 1 reflects excellent forecasting, while a value near 0.5 reflects chance.

In practice, the ROC curve helps us see not only whether predictions are correct, but also how reliable they are across different conditions. It is a reminder that forecasting always involves trade-offs between identifying opportunities and avoiding mistakes

Bayesian method, Delphi model, Bottom-up, Top-down, correlation-based, statistical models, time-series model, and the basic forecasting model by Wallace Davidson III in Financial Forecasting and Decision Making (O'Reilly playlist)

Bayesian method

The Bayesian method starts with an initial belief, called a prior, and then updates that belief when new data becomes available. The result is a posterior forecast that reflects both the old belief and the new information. This method gives forecasts in terms of probabilities, which makes it easier to see uncertainty. The challenge is that results depend on how good the prior is, and the calculations can be very demanding, especially in finance, where models often need complex tools like MCMC or structural time-series analysis.(West, 1996)

Delphi Model

The Delphi method uses expert opinion gathered anonymously over several rounds. Each round gives feedback from the group and lets participants revise their predictions. The method works well when hard data is limited and expert judgment matters. The technique helps reduce groupthink by keeping inputs anonymous but can still converge too quickly toward consensus or suppress dissenting ideas.(Jae K. Shim, 2008)

Bottom-Up vs. Top-Down

Forecasting can start from granular details or big-picture variables. The bottom-up approach builds forecasts from units like regions or products and then aggregates them upward. The top-down approach starts with market-level figures and allocates them down to units. The bottom-up method offers precision but demands substantial coordination. The top-down method operates quickly but may miss important localized trends.(Chad W. Autry, 2013)

Statistical models, time-series model

Forecasting models often rely on historical patternsusing methods like moving averages, trend analysis, regression, or ARIMA. These techniques work well when historical behavior repeats. They also help capture seasonality and trend components. Their limitations surface when data patterns shift abruptly or when markets face shocks, structural breaks, or unprecedented events.(III, 2018)

Traditional forecasting models share several weaknesses that limit their reliability. Most of these models assume that the future will mirror the past. This assumption works in stable environments but breaks down when unexpected events or structural shifts occur. Many of these models also struggle with uncertainty. For example, they may give a single-point prediction without showing the confidence level or range of possible outcomes.

Some methods depend too heavily on human judgment. The Delphi model, while valuable, can embed biases if the expert panel lacks diversity or if consensus overshadows minority opinions. Structural approaches like bottom-up and top-down have their own challenges. Bottom-up forecasting can be slow and complicated because it requires detailed inputs from many sources, while top-down forecasting risks oversimplification by ignoring local variation. Advanced models such as Bayesian and time-series techniques provide sophistication but demand statistical expertise and high computing power. These requirements make them less accessible for organizations with limited resources.

Machine learning has gained momentum because it directly addresses many of these constraints. Unlike traditional models, ML can recognize complex, non-linear patterns that humans and basic statistics might miss. ML also works well with large and messy datasets, which are common in modern finance. Another advantage is adaptability. ML models can update quickly as new data arrives, which makes them useful in fast-changing markets. They also automate tasks like feature selection, which reduces the amount of manual modeling effort.

ML methods can provide richer measures of uncertainty by generating probability distributions rather than single numbers. This capability improves decision-making because managers can weigh risks more explicitly. Still, machine learning is not flawless. It introduces new challenges such as overfitting, black-box complexity, and the need for strong validation practices. The best results come when ML is used thoughtfully, supported by financial expertise, and checked against practical realities.