Consider the following time series data

$$\begin{array}{l|rrrrrr} \text { Week } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Value } & 18 & 13 & 16 & 11 & 17 & 14 \end{array}$$

Use $\alpha=0.2$ to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7.

Consider the following time series data:

$$\begin{array}{c|rrrrrr} \text { Week } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Value } & 18 & 13 & 16 & 11 & 17 & 14 \end{array}$$

Using the naive method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy:

What is the forecast for week 7?

Consider the following time series data:

$$\begin{array}{c|rrrrrr} \text { Week } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Value } & 18 & 13 & 16 & 11 & 17 & 14 \end{array}$$

Using the naive method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy:

Mean absolute error

Consider the following time series data

$$\begin{array}{l|rrrrrrr} \text { Month } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text { Value } & 24 & 13 & 20 & 12 & 19 & 23 & 15 \end{array}$$

Develop a three-week moving average for this time series. Compute MSE and a forecast for week 8.

Consider the following time series data

$$\begin{array}{l|rrrrrrr} \text { Month } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text { Value } & 24 & 13 & 20 & 12 & 19 & 23 & 15 \end{array}$$

Construct a time series plot. What type of pattern exists in the data?

Consider the following time series data.

$$\begin{matrix} \text{Week} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6}\\ \hline \text{Value} & \text{18} & \text{13} & \text{16} & \text{11} & \text{17} & \text{14}\\ \end{matrix}$$

Using the naive method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy. a. Mean absolute error. b. Mean squared error. c. Mean absolute percentage error. d. What is the forecast for week 7?

Consider the following time series data.

$$\begin{matrix} \text{Month} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7}\\ \text{Value} & \text{24} & \text{13} & \text{20} & \text{12} & \text{19} & \text{23} & \text{15}\\ \end{matrix}$$

a. Compute MSE using the most recent value as the forecast for the next period. What is the forecast for month 8? b. Compute MSE using the average of all the data available as the forecast for the next period. What is the forecast for month 8? c. Which method appears to provide the better forecast?

For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83. a. Construct a time series plot. What type of pattern exists in the data? b. Compare the three-month moving average approach with the exponential smoothing approach for $\alpha =$ .2. Which provides more accurate forecasts using MSE as the measure of forecast accuracy? c. What is the forecast for next month?

Investment advisors estimated the stock market returns for four market segments: computers, financial, manufacturing, and pharmaceuticals. Annual return projections vary depending on whether the general economic conditions are improving, stable, or declining. The anticipated annual return percentages for each market segment under each economic condition are as follows:

Assume that an individual investor wants to select one market segment for a new investment. A forecast shows improving to declining economic conditions with the following probabilities: improving (0.2), stable (0.5), and declining (0.3). What is the preferred market segment for the investor, and what is the expected return percentage?

"Investment advisors estimated the stock market returns for four market segments: computers, financial, manufacturing, and pharmaceuticals. Annual return projections vary depending on whether the general economic conditions are improving, stable, or declining. The anticipated annual return percentages for each market segment under each economic condition are as follows:

$$\begin{aligned} &\text { Economic Condition }\\ &\begin{array}{lccc} \text { Market Segment } & \text { Improving } & \text { Stable } & \text { Declining } \\ \text { Computers } & 10 & 2 & -4 \\ \text { Financial } & 8 & 5 & -3 \\ \text { Manufacturing } & 6 & 4 & -2 \\ \text { Pharmaceuticals } & 6 & 5 & -1 \end{array} \end{aligned}$$

Assume that an individual investor wants to select one market segment for a new investment. A forecast shows improving to declining economic conditions with the following probabilities: improving (0.2), stable (0.5), and declining (0.3). What is the preferred market segment for the investor, and what is the expected return percentage?"

Consider the following time series data

$$\begin{array}{l|rrrrrrr} \text { Month } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text { Value } & 24 & 13 & 20 & 12 & 19 & 23 & 15 \end{array}$$

Which method appears to provide the better forecast?

Consider the following time series data

$$\begin{array}{l|rrrrrr} \text { Week } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Value } & 18 & 13 & 16 & 11 & 17 & 14 \end{array}$$

Use trial and error to find a value of the exponential smoothing coefficient $\alpha$ that results in a smaller MSE than what you calculated for $\alpha=0.2$.

For the following time series, compute the three-period moving averages.

Refer to the time series data in the previous problem. Using the average of all the historical data as a forecast for the next period, compute the following measures of forecast accuracy:

What is the forecast for week 7?