Recently, I was assigned to teach forecasting to a special group of business students. The course concentrates entirely on forecasting the future based on past observations. As such, its contents fit perfectly with the equity markets. The course book, "Business Forecasting" by John E. Hanke and Dean W. Wicherin, offers several forecasting techniques, which can be easily applied to markets. The forecasting methods explained in the book range from exponential smoothing methods to autoregressive moving average methodology. One of the interesting approaches suggested in the book is forecasting through decomposition analysis.

According to the theory of decomposition analysis, the data consists of four components. The first component is the trend. According to the authors, trend is the component "that represents the underlying growth (or decline) in the series." Next is the cyclical portion of data. Cycles are wave-like patterns that happen due to cyclical nature of economic activities. The third portion is seasonality. Seasonality is usually observed on a monthly or quarterly basis. As the authors explain, "seasonal variation refers to a more or less stable patter of change that appears annually and repeats itself year after year." The last part is named irregularity. This component is the portion of data that reflects the unpredictable nature of data or just random fluctuations.

There are two types of decomposition models. First is the additive decomposition. Next comes the multiplicative decomposition. Both models suggest similar outcomes. Therefore, choosing one over the other depends on individual circumstances. In any case, our aim is to minimize the irregularity portion in the forecast data.

Here is the additive decomposition:

Y = T + S + C + I

Y = T x S x C x I

We could easily get more into the details, but this is enough for the moment. The computer software performs the rest of the work for us.

In this article, I will apply the decomposition model to **McDonald's (NYSE:MCD)**. Due to purely statistical reasons (lower estimation errors), I have chosen the additive decomposition over the multiplication decomposition. Applying the additive decomposition models to McDonald's earnings data suggest the following outcomes:

Additive Model

Data EPS

Length 40

NMissing 2

Fitted Trend Equation: Yt = 0.1661 + 0.0299*t

Seasonal Indices

Period Index

- 1 -0.088073
- 2 0.034844
- 3 0.103177
- 4 -0.049948

Accuracy Measures

- MAPE 18.1003
- MAD 0.0750
- MSD 0.0107

Forecasts

Period Forecast

- 2012 Q2 1.42598
- 2012 Q3 1.52419
- 2012 Q4 1.40094
- 2013 Q1 1.39270

*Source for all charts: author.*

I used the quarterly earnings data from the last 10 years, which offers a reasonable number of observations. There have been some periods when McDonald's reported negative earnings. Since these were special circumstances, the negative earnings data were removed from our analysis. The black line shows the actual quarterly earnings of McDonald's, whereas the red line shows the forecast earnings according to our model.

The model looks like a good fit for quarterly earnings. Forecast errors measured by mean average percentage error (MAPE), Mean Absolute Deviation (MAD), and Mean Square Deviation (MSD) are very low. The model also suggests a forecast EPS of $1.426 for the second quarter of 2012, and $1.524 for the third quarter of this year.

The component analysis shows an obvious positive trend in McDonald's earnings. The trend model suggests an earnings growth of 3% for each quarter. Another interesting observation is the strong seasonality in the company's earnings. The company reports its best earnings report in the third quarter, whereas the first-quarter earnings substantially underperform other seasons. Variation in the fourth quarter earnings is pretty high, so estimates might not hold well for the fourth-quarter earnings.

From a purely statistical point, the model is a very solid one where the residual terms are almost perfectly, normally distributed. The mean of the error terms is zero, and there is no obvious trend in the error terms. Thus, we have a strong and statistically validated model.

**Summary**

So what does all this mean for investors? Well, we just established a solid statistical model for estimating McDonald's quarterly earnings for future. Our model suggests an EPS of $1.426 for Q2 2012, $1.524 for Q3 2012, and $1.40 for Q4 2012. As we know, a positive earnings surprise usually triggers a positive momentum for the stock. Comparing my estimates with CNBC, I do not see much of a surprise for the next quarter. CNBC suggests a consensus estimate of $1.42 for Q2 2012, $1.58 for Q3 2012, and $1.46 for the last quarter of this year.

Basically, I am expecting McDonald's to report in line with consensus estimates for this quarter, and there is a likelihood of a slight earnings miss for the following two quarters. While I think McDonald's is a great company, it is still on the pricey side of the market. That is another reason to wait for a correction in McDonald's' stock price until it falls below my fair value range, which is about $85 per share at the moment.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.