Investors who buy stocks to beat the Street should ask themselves if beating the Street is really a big deal. A close statistical examination of Wall Street's consensus earnings estimates suggests that analysts' estimates are very frequently too low-much more frequently than could happen by chance.

Take IBM (NYSE:IBM), a stock that is closely followed by 23 analysts in the last quarter. Their consensus has underestimated IBM's earnings in every one of the last 24 quarters. Another example is Apple (NASDAQ:AAPL). In the last 24 quarters, analysts underestimated the earnings 23 times and only for the fourth quarter of 2011 did they overestimate the earnings.

An analysis of the earnings estimates of 2850 companies during the period 2011-2012 indicated that the bias (underestimates of the earnings) is statistically significant at the 99% confidence level. The bias indicates that Wall Street analysts underestimated the earnings by an average of 5.7 cents per share (calculated as the average difference between the actual earnings reported and the Wall Street consensus estimate). About 62.3% of earnings reported during the period 2011-2012 were able to beat the consensus estimate calculated no earlier than five days prior to the earnings announcement.

In a research paper titled "Self-Fulfilling Stock Recommendations," scholars from Purdue and the London School of Economics criticized analysts because they have a vested interest to report low or high earning forecasts with a view to enhance their own recommendations for buying or selling stocks. The lower the earnings estimate, the more likely the stock will increase in price due to "earnings surprise" or, similarly, the higher the earnings estimate, the more likely the stock will decline because of "missing" Wall Street estimates.

From a statistical point of view, one should realize that the consensus estimate is an average that will be affected by the number of analysts who cover a given stock and their diversity of opinion. Many Wall Street stocks are covered by only one or two analysts: Using their consensus value could be like putting one leg in hot water and the other in cold water and concluding that you feel fine.

Given these findings indicating a potential opportunity, the next step in the research was to explore if this bias could be reduced by using statistical methods. The objective was to predict the future using data in hand. Using advanced statistical methods combining regression analysis of earnings per share and moving averages of past errors produced less error than the analysts. We have developed the adjusted earning model using 2/3 of the database as a test and 1/3 of the data as a validation sample. The results indicate that when our adjusted forecast was greater than Wall Street's estimate by 0.04, 0.05 and 0.06 cents, the respective returns were 1.8%, 2% and 2.6% return. These returns were for a short term obtained for a 3 day investment where a stock was purchased a day prior to the earnings announcement and sold a day after the earnings were announced and if annualized would be a large number. This was necessary since some stocks report the earnings before the market opens and others during or after hours.

In evaluating the above return, one should be aware that market reaction to earning results depends on other factors as well, such as meeting revenue estimates and corporate guidance.

The above results make it possible to forecast earnings "surprises," which are Wall Street's favorite explanation for sudden moves in prices of individual stocks.

Interestingly, Wall Street bias is larger when the stocks being considered are higher in price. A statistical analysis revealed that there is interaction between the Wall Street's estimate and the price of the stock. Examples: For the second quarter of 2011, the consensus estimate for Apple was $5.37. The forecasting model suggested $6.11; the actual was $6.40. The consensus estimate for Google for the third quarter 2011 was $8.74; the forecasting model estimated $9.13. The actual earnings were $9.72.

Even if stocks priced at $250 a share and higher are excluded from the analysis, the Wall Street bias still remained pronounced. Wall Street analysts underestimated quarterly earnings by an average of more than 3.9 cents.

Forecasting models are not restricted to a single quarter and can provide forecasts for periods farther in the future. Given that a forecasting model does a better job than Wall Street estimates, one can make the assumption that the yearly estimate will be more accurate than Wall Street. This estimate is important in forecasting future values of stocks. Using Apple as an example, Wall Street is expecting an annual EPS of $34.95. The new model suggests a higher estimate of $38.47, which will be adjusted each quarter when new data will become available.

We were able to tweak the model for better accuracy by using a weighted average of the Wall Street estimate and the statistical forecast. This increases the accuracy of the final forecast and reduces significantly the bias inherent in the Wall Street forecast. In each case, the final model we selected and the adjusted EPS was the result of identifying the model which produced the smallest error in forecasts between the actual and what we forecasted for the last 4 quarters.

The new models have advantages over accounting forecasts because the models can identify correctly seasonal business variations and profit trends and incorporate them into future forecasts.

Here are a few examples so the reader can see the benefit of using advanced forecasting models. Google (NASDAQ:GOOG) reported earnings on October 17, 2013. Wall Street's consensus estimate was $10.36. The model forecasted $10.80. The actual forecast came as $10.74 and the price per share increased by 13%. If you purchased the stock one day prior to the earnings announcement and sold it a day after the announcement, your profit for holding the stock 2 days would have been 13%. The forecasting model also provides the low and high range for the forecast. In this case, the low was $10.18 and the high was $11.50. This range gives us 95% confidence that the earnings per share will be in this range. Wall Street's forecast for the coming quarter is $12.21 and my forecast is $13.29 with a range of $12.40 to $13.80. It is interesting to note that our low forecast is higher than Wall Street's forecast.

Another example is ManPowerGroup (NYSE:MAN). On October 21, 2013, Wall Street expected earnings per share to be $1.08; our forecast was $1.10 with a range of $0.79 to $1.32. The actual earnings was $1.18. The stock appreciated by $4.80 which is 6.4% (again if purchased one day prior to earnings and sold after the announcement).

Our models provide further evidence for the relevance of using statistical models in the financial markets, as was previously demonstrated by the work of Robert Engle (Nobel Prize winner in Economics) in time series analysis. The problems with using such models are the complexity, the statistical knowledge necessary and the time required to validate competing models.

Stock earnings are a critical factor for future stock price direction and the models discussed here could optimize investors' decisions in terms of hedging or increasing one's position with anticipation of better earnings to come.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.