Purpose: To learn how to apply simple forecast evaluation metrics such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE). To apply the simple forecasting techniques naive forecast, seasonally naive forecast, and mean forecast to a forecasting problem and evaluate their performance. This exercise is due Tuesday, September 12.

Recall that the forecast error is given by \(e_{i}=y_{i}-\hat{y}_{i}\). During our in-class forecasting exercise all of you produced forecasts \(\hat{y}_i\) of the unemployment rate (from the Household Survey) and the additions to nonfarm payrolls (from the Establishment Survey) that was released in the August 2017 Employment Report produced by the Bureau of Labor Statistics (BLS) on September 1, 2017. The actual unemployment rate for August 2017 turned out to be 4.4 percent. Here’s a list of your forecasts \(\{\hat{y}_i\}_{i=1,\cdots,24}\)for the unemployment rate. Each forecast is indexed by \(i\):

Index Unemployment Forecast \(\hat{y}_i\) Nonfarm Payroll Forecast \(\hat{y}_i\)
1 3.0 160,000
2 5.7 208,000
3 5.2 190,000
4 4.8 215,000
5 4.4 202,000
6 4.1 200,000
7 4.3 224,000
8 4.5 147,000
9 4.4 195,000
10 4.3 148,000
11 4.2 146,830
12 4.2 150,000
13 4.0 147,000
14 5.3 200,000
15 4.2 220,000
16 4.4 180,000
17 4.2 237,500
18 4.2 176,000
19 4.4 250,000
20 4.8 146,850
21 4.7 190,000
22 4.3 182,000
23 4.3 220,000
24 4.1 220,000

Implement all the questions in R. In addition to submitting your homework via CANVAS, submit individual R files to my SMU e-mail address prior to the deadline.

  1. What is the mean of your unemployment forecasts? (0.25 points)

  2. What is the median of your nonfarm payroll forecasts? (0.25 points)

  3. What is the interquartile range of the nonfarm payroll forecast? (0.25 points)

  4. What is the interquintile range of the nonfarm payroll forecast? (0.25 points)

  5. What is the interdecile range of the nonfarm payroll forecast? (0.5 points)

  6. What is the maximum of the unemployment forecast? (0.25 points)

  7. What is the minimum of the nonfarm payroll forecast? (0.25 points)

  8. What is the mean of the nonfarm payroll forecasts that are stricly above the median? (1.0 points)

  9. What is the median of the unemployment forecasts that are strictly below the mean? (1.0 points)

Recall that the Mean Absolute Error (MAE) and the Root Mean Squared Error (RMSE) are given by \[ \begin{align*} \text{Mean Absolute Error: MAE} & = \text{mean}(|e_{i}|),\\ \text{Root Mean Squared Error: RMSE} & = \sqrt{\text{mean}(e_{i}^2)}. \end{align*} \]

  1. What is the MAE for the set of unemployment forecasts? (1.0 points)

  2. What is the RMSE for the set of unemployment forecasts? (1.0 points)

  3. What is the MAE for the set of nonfarm payroll forecasts? (1.0 points)

  4. What is the RMSE for the set of nonfarm payroll forecasts? (1.0 points)

The Mean Absolute Percentage Error is

\[\text{Mean Absolute Percentage Error: MAPE} = \text{mean}(|p_{i}|).\] where \[ p_{i} = 100 \cdot \frac{e_{i}}{y_{i}}\]

  1. What is the MAPE for your unemployment forecasts? (1.0 points)

  2. What is the MAPE for your nonfarm payroll forecasts? (1.0 points)

  3. [OPTIONAL] What is a more useful measure of forecast error when comparing the ECO5375 students’ performance on the forecasting exercises on unemployment and nonfarm payroll forecasts?