## Introduction

The research was carried out on Macy’s department stores. Because of the seasonal market, it was necessary to use a series of seasonal trend tests. Data was gathered from the first quarter, April 30, 2005 and was concluded on a third quarter, which was November 1, 2008. Altogether, there were 15 quarters. The first test we started with was the Decomposition test. This test demonstrated a seasonal pattern of revenues. It also shows any irregular movement of revenues. We decided to use the third quarter as our reference class. The reason we chose the third quarter is because it is the closest to the quarterly average. The quarterly average is $6,976,000,000. We then used another test called Winter’s Exponential Smoothing, which adds another equation to incorporate seasonality. The last test used was the Regression test, which helps us to forecast future revenues. The objective of this project is to find the most suitable test and to make predictions of future revenues of Macy’s Inc.

## Background information

Macy’s opened its doors on March 6, 1929 in New York City. Macy’s was named Federated Department Stores. Even though most of us know the name Macy’s, it wasn’t the official name until June 2007. The department store was a merge of several different department stores. These stores were Abraham & Straus of Brooklyn, Filene’s of Boston, F & R Lazarus & Co. of Columbus, OH, and Bloomingdale’s of New York. These retailers were a prominent presence with rich histories, so the news of these stores merging was phenomenal. As Federated emerged during WW 2 and the Great Depression, it was obvious the department store was very resilient and flexible. It was adapting by using plans such as the “pay when you can” credit policies. Mr. Fred Lazarus was so concerned about Thanksgiving falling on the last Thursday of the month, that he proposed that Thanksgiving be on the third Thursday of the month. President Roosevelt supported the proposition, and within the next couple of years the holiday was changed to the third Thursday of the month.

Macy’s has been a very profitable business in its entire history. We gathered data from 15 quarters and the revenues made range from $3,605,000,000 to a one-time record sale of $17,719,000,000. The average revenues are $6,976,000,000, with a $14 billion range. The descriptive statistics are shown on exhibit #1.

## Time Series Plot

The Time series plot, on exhibit #7, shows the best revenues were made in the fourth, eighth, and twelfth quarters, (with an exception of the eleventh quarter). This makes sense because the fourth quarters fall on the Christmas, Hanukkah and New Year’s holidays. The eleventh quarter (third quarter in 2007) shows a major rise in sales of $17 billion. Since no data shows the reason for this incline, we will assume that Macy’s might have had some close-out sales.

## Identifying components

For the reference variable, we used the third quarter. The third quarters are the ones that are closest to the average revenues. We gathered data in sets of four quarters. The first quarters were spring months, the second quarters were mainly summer months, the third quarters are fall months and of course the fourth quarter is made up of winter months. We used the first, second and fourth quarters as our response variables for our predictions and statistics.

## Summary of models / best model

The first test we used to summarize a seasonal pattern and find the response variable was the Decomposition test, which you will find on exhibit # 2. This also defines the trend of sales. The test also gave us a mean error of 1687 which was pretty low compared to one other test. The predicted sales from the Decomposition test are as follows. The forecast for quarter four of 2008 is 12,647,500,000. The first quarter of 2009 is predicted to be $6,900,700,000, the second quarter of 2009 is estimated to be $7,271,500,000, and quarter three of 2009 is predicted to have sales of $9,683,000,000.

The second test, we used, is the winter’s Exponential Smoothing test, exhibit # 3. The mean error was very high. It was 4118. And the estimated forecasts are as follows: For quarter four of 2008, the predicted sales are very close to that of the Decomposition test which is $11,673,900,000. The first quarter of 2009 is predicted to be $7,448,400,000; the second quarter of 2009 has a forecast of $6,852,500,000. The third quarter has a pretty high sales prediction of $10,633,500,000.

The Regression test, which is exhibit #4, has a mean error of 1647, which is lowest, and also the fourth quarter of 2008 has predicted sales of $10,381,000,000, which is less than the other predictions and the first quarter of 2009 has the lowest also of $6,892,000,000. The second quarter of 2009 is reasonably close to the other test predictions with sales of $6,898,000,000 and the third quarter has sales predicted to be $10,312,000,000.

By comparing all three testing methods we thought the Decomposition method was the most accurate, except, we found the data for the actual sales of the fourth quarter of 2009 and all three methods were far off. The actual revenues were $7,934,000,000. With that in mind, the Regression test might be the best choice. The Regression test was the closest with the revenues of the fourth quarter as $10,381,000,000. Therefore, we choose the Regression model to be the best. The forecast equation is shown on exhibit #6. The comparison table is on exhibit #5.

## Limitations

One of the problems we ran into was the amount of sales in the third quarter of 2007. The amount of revenues for that quarter was $ 17,719.00. We were unable to find the reason behind this. We just assumed that Macy’s might have had some store close out sales.

Another interesting thing discovered was that the actual amount of sales for the fourth quarter of 2008 was $7,934,000,000, and our predicted value for that very same quarter, on our chosen regression test, was $10,381,000,000. Since this was the lowest and had a reasonably low mean error, we decided to choose the regression model, but the revenues were a little off.

## Conclusion

After we gathered the data from 15 quarters, starting from April 30, 2005 and ending on a third quarter, which was November 1, 2008. We used the seasonal series model to predict the next four quarters. The predicted quarters started with the fourth quarter of 2008 and ended with the third quarter in 2009.

The first of the seasonal series tests was the Decomposition test. This was important in the identification of the seasonal pattern, which was the fourth quarter. The test also identifies the response variable which was the third quarter. We then performed the Winter’s Exponential Smoothing test which incorporates seasonality into the model. This test had a very high mean error, which was 4118, so we didn’t select that model as being the best one. The Regression model was the best model because we found that the actual revenues were closer to the Regression model and because the mean error was pretty low (1647).