Demand for a product and the forecasting department's forecast (naïve model) for a product are shown below. Compute the mean absolute error. ? ? \[\begin{array} { | c | c | c | } \hline \text { Period } & \text { Actual Demand } & \text { Forecasted Demand } \\ \hline 1 & 12 & - \\ \hline 2 & 15 & 12 \\ \hline 3 & 14 & 15 \\ \hline 4 & 18 & 16 \\ \hline \end{array}\]

A) 1 B) 1.5 C) 2 D) 2.5 A) 1 B) 1.5 C) 2 D) 2.5 C

The following times series shows the demand for a particular product over the past 10 months. \[\begin{array} { | c | c | } \hline \text { Month } & \text { Demand } \\ \hline 1 & 324 \\ \hline 2 & 311 \\ \hline 3 & 303 \\ \hline 4 & 314 \\ \hline 5 & 323 \\ \hline 6 & 313 \\ \hline 7 & 302 \\ \hline 8 & 315 \\ \hline 9 & 312 \\ \hline 10 & 326 \\ \hline \end{array}\] a. Construct a time series plot. What type of pattern exists in the data? b. Develop a three-month moving average for this time series. Compute MSE and a forecast for month 11.

a. @#IMG-DLM& The data appear to follow

The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years. \[\begin{array} { | c | c | c | } \hline \text { Year } & \text { Quarter } & \text { Profit (\$1000s) } \\ \hline 1 & 1 & 45 \\ \hline 1 & 2 & 51 \\ \hline 1 & 3 & 72 \\ \hline 1 & 4 & 50 \\ \hline 2 & 1 & 49 \\ \hline 2 & 2 & 45 \\ \hline 2 & 3 & 79 \\ \hline 2 & 4 & 54 \\ \hline 3 & 1 & 42 \\ \hline 3 & 2 & 58 \\ \hline 3 & 3 & 70 \\ \hline 3 & 4 & 56 \\ \hline \end{array}\] a. Construct a time series plot. What type of pattern exists in the data? b. Develop a three-period moving average for this time series. Compute MSE and a forecast of profit (in $1000s) for the next quarter.

Rewrite the data as below: @#IMG-DLM& a. @#IMG-DLM& The data

Consider the following time series. \[\begin{array} { | c | c | } \hline \boldsymbol { t } & \boldsymbol { y } \boldsymbol { t } \\ \hline 1 & 1,234 \\ \hline 2 & 1,201 \\ \hline 3 & 1,103 \\ \hline 4 & 987 \\ \hline 5 & 945 \\ \hline 6 & 891 \\ \hline 7 & 817 \\ \hline 8 & 734 \\ \hline \end{array}\] a. Construct a time series plot. What type of pattern exists in the data? b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. c. What is the forecast for t = 9?

a. @#IMG-DLM& The data appear to show a linear tre

Consider the following time series data: \[\begin{array} { | c | c | } \hline \boldsymbol { t } & \boldsymbol { y } \boldsymbol { t } \\ \hline 1 & 0.345 \\ \hline 2 & 0.366 \\ \hline 3 & 0.398 \\ \hline 4 & 0.356 \\ \hline 5 & 0.456 \\ \hline 6 & 0.478 \\ \hline 7 & 0.543 \\ \hline 8 & 0.596 \\ \hline 9 & 0.634 \\ \hline 10 & 0.698 \\ \hline \end{array}\] a. Construct a time series plot. What type of pattern exists in the data? b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. c. What is the forecast for t = 11?

a. @#IMG-DLM& This time series plot shows an upwar

Consider the following time series data. \[\begin{array} { | c | c | } \hline \text { Year } & \text { Value } \\ \hline 1 & 234 \\ \hline 2 & 287 \\ \hline 3 & 255 \\ \hline 4 & 310 \\ \hline 5 & 298 \\ \hline 6 & 250 \\ \hline 7 & 456 \\ \hline 8 & 412 \\ \hline 9 & 525 \\ \hline 10 & 436 \\ \hline \end{array}\] Using the average of all the historical data as a forecast for the next year, 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 year 11?

The following table shows the calculatio

A) the long-run shift or movement in the time series observable over several periods of time. B) the outcome of a random experiment. C) the recurring patterns observed over successive periods of time. D) the short-run shift or movement in the time series observable for some specific period of time. A) the long-run shift or movement in the time series observable over several periods of time. B) the outcome of a random experiment. C) the recurring patterns observed over successive periods of time. D) the short-run shift or movement in the time series observable for some specific period of time.

Exam 8: Time Series Analysis and Forecasting

Demand for a product and the forecasting department's forecast (naïve model) for a product are shown below. Compute the mean absolute error. ? ? Period Actual Demand Forecasted Demand 1 12 - 2 15 12 3 14 15 4 18 16

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Question 1

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C

Consider the following time series data. Year Value 1 234 2 287 3 255 4 310 5 298 6 250 7 302 8 267 9 225 10 336 a. Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for year 11. b. Use trial and error to find a value of the exponential smoothing coefficient α (rounded to 2 decimal places) that results in a smaller MSE than what you calculated for α = 0.2. c. Compute the forecast for year 11 using the smoothing coefficient α selected using trial error.

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a. Smoothing constant α = 0.2 $\begin{array} { | c | c | r | r | r | } \hline \text { Year } & \text { Value } & \text { Forecast } & \begin{array} { c } \text { Forecast } \\\text { Error }\end{array} & \begin{array} { c } \text { Squared } \\\text { Forecast } \\\text { Error }\end{array} \\\hline 1 & 234 & & & \\\hline 2 & 287 & 234.00 & 53.00 & 2,809.00 \\\hline 3 & 255 & 244.60 & 10.40 & 108.16 \\\hline 4 & 310 & 246.68 & 63.32 & 4,009.42 \\\hline 5 & 298 & 259.34 & 38.66 & 1,494.29 \\\hline 6 & 250 & 267.08 & - 17.08 & 291.56 \\\hline 7 & 302 & 263.66 & 38.34 & 1,469.94 \\\hline 8 & 267 & 271.33 & - 4.33 & 18.73 \\\hline 9 & 225 & 270.46 & - 45.46 & 2,066.84 \\\hline 10 & 336 & 261.37 & 74.63 & 5,569.64 \\\hline & & & \text { Total } & \mathbf { 1 7 8 3 7 . 5 8 } \\\hline\end{array}$ MSE = 17,837.58/9 = 1,981.95
The forecast for year 11 is $\hat { y } _ { 11 }$ = αy₁₀ + (1- α) $\hat { y } _ { 10 }$ = (0.2)(336) + (1 - 0.2)(261.37) = 276.30.
b. Several values of α will yield an MSE smaller than the MSE associated with α = 0.2. The table below shows the resulting MSE from several different α. $\begin{array} { l l } \alpha & \text { MSE } \\\hline 0.1 & 2,285.29 \\0.2 & 1,981.95 \\0.3 & 1,928.71 \\0.4 & 1,978.37 \\0.5 & 2,081.20 \\0.6 & 2,219.57 \\0.7 & 2,387.01 \\0.8 & 2,580.70\end{array}$ The value of α that yields the minimum MSE is α = 0.29, which yields an MSE of 1928.08. $\alpha$ =0.29
$\begin{array}{|c|r|r|r|r|}\hline \text { Year } & \text { Value } & \text { Forecast} & \text { Forecast error} & \text { Squared Forecast Error } \\\hline 1 & 234 & & & \\\hline 2 & 287 & 234.00 & 53.00 & 2,809.00 \\\hline 3 & 255 & 249.37 & 5.63 & 31.70 \\\hline 4 & 310 & 251.00 & 59.00 & 3,480.68 \\\hline 5 & 298 & 268.11 & 29.89 & 893.30 \\\hline 6 & 250 & 276.78 & -26.78 & 717.14 \\\hline 7 & 302 & 269.01 & 32.99 & 1,088.11 \\\hline 8 & 267 & 278.58 & -11.58 & 134.09 \\\hline 9 & 225 & 275.22 & -50.22 & 2,522.20 \\\hline 10 & 336 & 260.66 & 75.34 & 5,676.53 \\\hline & && \text { Total } & \mathbf{1 7 , 3 5 2 . 7 4} \\\hline\end{array}$ MSE = 17,352.74/9 = 1,928.08
The forecast for year 11 is $\hat { y } _ { 11 }$ = αy₁₀ + (1- α) $\hat { y } _ { 10 }$ = (0.29)(336) + (1 - 0.29)260.66 = 282.51.

An exponential trend pattern occurs when

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B

The following times series shows the demand for a particular product over the past 10 months. Month Demand 1 324 2 311 3 303 4 314 5 323 6 313 7 302 8 315 9 312 10 326 a. Construct a time series plot. What type of pattern exists in the data? b. Develop a three-month moving average for this time series. Compute MSE and a forecast for month 11.

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Question 4

The monthly market shares of General Electric Company for 12 consecutive months follow. Develop three-month and four-month moving averages for this time series. Does the three-month or the four-month moving average provide the better forecasts based on MSE? Explain your reasoning. Month Market Shares 1 23.39 2 23.56 3 23.02 4 23.03 5 23.60 6 23.37 7 23.21 8 23.40 9 23.31 10 23.94 11 23.39 12 23.50

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Question 5

A time series plot of a period of time (in months) verses sales (in number of units) is shown below. Which of the following data patterns best describes the scenario shown?

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Question 6

The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years. Year Quarter Profit ( \1 000s) 1 1 45 1 2 51 1 3 72 1 4 50 2 1 49 2 2 45 2 3 79 2 4 54 3 1 42 3 2 58 3 3 70 3 4 56 a. Construct a time series plot. What type of pattern exists in the data? b. Develop a three-period moving average for this time series. Compute MSE and a forecast of profit (in $1000s) for the next quarter.

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Question 7

A time series with a seasonal pattern can be modeled by treating the season as a

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Question 8

Which is not true regarding trend patterns?

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Question 9

A time series plot of a period of time (in weeks) verses sales (in 1,000's of gallons) is shown below. Which of the following data patterns best describes the scenario shown?

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Question 20

Demand for a product and the forecasting department's forecast (naïve model) for a product are shown below. Compute the mean absolute error. ? ? Period Actual Demand Forecasted Demand 1 12 - 2 15 12 3 14 15 4 18 16

An exponential trend pattern occurs when

A time series plot of a period of time (in months) verses sales (in number of units) is shown below. Which of the following data patterns best describes the scenario shown?

A time series with a seasonal pattern can be modeled by treating the season as a

Which is not true regarding trend patterns?

A time series plot of a period of time (in weeks) verses sales (in 1,000's of gallons) is shown below. Which of the following data patterns best describes the scenario shown?

Which of the following states the objective of time series analysis?

The moving averages and exponential smoothing methods are appropriate for a time series exhibiting

If the forecasted value of the time series variable for period 2 is 22.5 and the actual value observed for period 2 is 25, what is the forecast error in period 2?

The exponential smoothing forecast for period t + 1 is a weighted average of the

Trend refers to

Which of the following measures of forecast accuracy is susceptible to the problem of positive and negative forecast errors offsetting one another?

A causal model provides evidence of ______________ between an independent variable and the variable to be forecast.

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