$1.$ Consider the following time series data,

a$.$ fill in the table below using the na$$ve method $($most recent value$)$ as the forecast for the next year, $(10$pts$)$

$8$

$9$

$10$

$11$

$12$

$13$

$14$

$15$

$16$

$17$

$18$

$19$

$20$

$21$

$22$

$23$

$24$

$25$

$26$

$27$

$28$

$29$

$30$

$31$

$32$

$33$

$34$

$35$

$36$

$37$

$38$

$39$

$40$

$41$

Year

Value

Forecast

Forecast

Error

Absolute Value of Forecast

Error

Squared Forecast

Error

Percentag Value of

Absolute

e Error Percentag e Error

$1$

$234$

$2$

$287$

$3$

$255$

$4$

$310$

$5$

$298$

$6$

$250$

$7$

$456$

$8$

$412$

$9$

$525$

$10$

$436$

Total

b$.$ Compute the following measures of forecast accuracy: $(5$ pts$)$

Mean absolute error

Mean squared error

Mean absolute percentage error

What is the forecast for year $11?$

Consider the following time series data,

a$.$ fill in the table belowthe average of all the historical data as a forecast for the next year, $(10$pts$)$

Year

Value

Forecast

Forecast

Error

Absolute Value of Forecast

Error

Squared

Error

Forecast Percenta Value of e Error

Absolute

Percentag e Error

$1$

$234$

$2$

$287$

$3$

$255$

$4$

$310$

$298$

$250$

$456$

$412$

$9$

$525$

$10$

$436$

Total

b$.$ Compute the following measures of forecast accuracy: $(5$ pts$)$

Mean absolute error

Mean squared error

Mean absolute percentage error

What is the forecast for year $11?$

c$.$ Which method appears to provide the better forecast comparing the na$$ve method to the average of past values forecasting?

$1.$ Consider the following time series data:

Year

Value

$1$

$234$

$2$

$287$

$3$

$255$

$4$

$310$

$5$

$6$

$298$

$250$

$7$

$302$

$8$

$267$

$9$

$225$

$10$

$336$

a$.$

b$.$

Construct a time series plot. What type of pattern exists in the data? $(5$pts$)$

Develop a three$-$year moving average for this time series by filling in the following table. $(10$pts$)$

Year

Value

Forecast

Forecast

Error

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

squared

Forecast

Error

$234$

$287$

$255$

$310$

$298$

$250$

$302$

$267$

$225$

$336$

c$.$ Compute MSE and a forecast for the year $11.$

a$.$

Use a $=0\mathrm{.}2$ to compute the exponential smoothing values for the time series by filling in the following table. Compute MSE and a forecast for year $11.(10$pts$)$

Year

$1$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

Value

Forecast

Forecast

Error

$234$

$287$

$255$

$310$

$298$

$250$

$302$

$267$

$225$

$336$

Squared Forecast

Error

b$.$ Compute MSE and a forecast for the year $11.(5$pts$)$

R

S

c$.$ Which method appears to provide the better forecast comparing the moving average and the exponential smooting?