statisticstime forecasting
Project Description:
que 1:
the following data shows the selling price of threemonthold calves at a livestock auction for a period of 22 weeks.
week price week price
1 176 12 172
2 172 13 174
3 174 14 177
4 177 15 180
5 173 16 178
6 171 17 176
7 172 18 179
8 173 19 175
9 174 20 176
10 173 21 174
11 171 22 175
a. prepare a line graph of these data. do the data appear to be stationary or non stationary?
b. compute the twoperiod (k = 2) and fourperiod (k = 4) moving average predictions for the data set. i. compute the mse for each of the two moving averages. which appears to provide a better fit for this data set? ii. compute forecasts for weeks 23 and 24 using the twoperiod and four period moving average techniques.
c. use excel solver to determine the weights for a fourperiod weighted moving average on the data set that minimizes the mse.
i. what are the optimal values for the weights?
ii. what are the forecasts for weeks 23 and 24 using the fourperiod weighted moving average technique?
d. create an exponential smoothing model that minimizes the mse for the data set. use excel solver to estimate the optimal value of . i. what is the optimal value of ? ii. what are the forecasts for weeks 23 and 24 using the exponential smoothing technique?
e. which method appears to provide the best fit for this data set? explain.
que 2
the following data shows actual average prices of existing singlefamily homes in the u.s. for 19892001.
year average price($1000)
1989 114.4
1990 115.3
1991 124.7
1992 126.6
1993 129.3
1994 133.5
1995 135.8
1996 141.8
1997 150.5
1998 159.1
1999 168.3
2000 176.2
2001 185.3
a. prepare a line graph for these data. do the data seem to be stationary or nonstationary?
b. fit a linear trend model to the data. what is the estimated regression equation?
c. interpret the r2 value for your model.
d. prepare a line graph comparing the linear trend predictions against the original data. e. what are the forecasts for 2002 and 2003 using the linear trend model?
f. fit a quadratic trend model to the data. what is the estimated regression equation? g. compare the adjusted r2 value for the quadratic model in part
(f) to that of the linear trend model in part (b). what is implied by this comparison?
h. prepare a line graph comparing the quadratic trend predictions against the original data.
i. what are the forecasts for 2002 and 2003 using the quadratic trend model?
j. if you had to choose between the linear and quadratic trend models, which one would you use? why?
k. if you had chosen either a moving average or an exponential smoothing technique instead of a trend model, what implications would it have on your forecasts?
the following data shows the selling price of threemonthold calves at a livestock auction for a period of 22 weeks.
week price week price
1 176 12 172
2 172 13 174
3 174 14 177
4 177 15 180
5 173 16 178
6 171 17 176
7 172 18 179
8 173 19 175
9 174 20 176
10 173 21 174
11 171 22 175
a. prepare a line graph of these data. do the data appear to be stationary or non stationary?
b. compute the twoperiod (k = 2) and fourperiod (k = 4) moving average predictions for the data set. i. compute the mse for each of the two moving averages. which appears to provide a better fit for this data set? ii. compute forecasts for weeks 23 and 24 using the twoperiod and four period moving average techniques.
c. use excel solver to determine the weights for a fourperiod weighted moving average on the data set that minimizes the mse.
i. what are the optimal values for the weights?
ii. what are the forecasts for weeks 23 and 24 using the fourperiod weighted moving average technique?
d. create an exponential smoothing model that minimizes the mse for the data set. use excel solver to estimate the optimal value of . i. what is the optimal value of ? ii. what are the forecasts for weeks 23 and 24 using the exponential smoothing technique?
e. which method appears to provide the best fit for this data set? explain.
que 2
the following data shows actual average prices of existing singlefamily homes in the u.s. for 19892001.
year average price($1000)
1989 114.4
1990 115.3
1991 124.7
1992 126.6
1993 129.3
1994 133.5
1995 135.8
1996 141.8
1997 150.5
1998 159.1
1999 168.3
2000 176.2
2001 185.3
a. prepare a line graph for these data. do the data seem to be stationary or nonstationary?
b. fit a linear trend model to the data. what is the estimated regression equation?
c. interpret the r2 value for your model.
d. prepare a line graph comparing the linear trend predictions against the original data. e. what are the forecasts for 2002 and 2003 using the linear trend model?
f. fit a quadratic trend model to the data. what is the estimated regression equation? g. compare the adjusted r2 value for the quadratic model in part
(f) to that of the linear trend model in part (b). what is implied by this comparison?
h. prepare a line graph comparing the quadratic trend predictions against the original data.
i. what are the forecasts for 2002 and 2003 using the quadratic trend model?
j. if you had to choose between the linear and quadratic trend models, which one would you use? why?
k. if you had chosen either a moving average or an exponential smoothing technique instead of a trend model, what implications would it have on your forecasts?
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