STATS = PLEASE BID ONLY IF YOU CAN = FORECASTING

The Water Department of the city of Fort Worth, Texas, has to purchase untreated lake water from several administrative entities around the city in order to fulfill the water requirements of its population. Most of the water is treated and pumped at one of two plants – The Holly Water Treatment Complex and the Rolling Hills Plant. The rolling Hills Plant is located on the southeast side of Fort Worth and is on a higher plain than the west-side Holly Treatment Plant. Both plants are required to operate in order to meet the city’s demand; however, the electrical cost of pumping water out of the Holly Treatment Plant is approximately 15% higher than for the Rolling Hills Plant because of its lower elevation. Because of the cost differential, the water pumped from the tow plants has been slowly approaching a 60-40 split in favor of the Rolling Hills Plant.

For budgetary reasons, the City Manager would like you to forecast the water processed and pumped at the Holly Treatment Plant. He will use your forecasts as a basis for estimating the associated electrical cost. You are informed that water consumption varies from fall to spring and summer to winter. There is also a gradual increase in the water demand at the Holly Treatment Plant because the total demand made by the population has slowly increased.

Month	2001-2002	2002-2003	2003-2004	2004-2005	2005-2006
OCT	365.5	361.3	429.7	354.6	312.9
NOV	319.9	307.7	331.2	292.2	368.3
DEC	309.6	312.8	291.3	279.2	316.3
JAN	327.0	294.0	296.4	268.5	316.3
FEB	285.6	258.2	267.4	251.8	275.2
MAR	358.9	300.2	319.4	287.8	283.3
APR	326.5	402.3	350.2	336.4	286.2
MAY	324.6	367.3	447.4	350.6	352.7
JUNE	352.5	349.5	476.0	371.5	512.6
JULY	616.4	469.5	540.3	479.2	529.2
AUG	531.2	628.7	617.5	462.5	488.6
SEPT	403.6	428.7	429.9	421.0	461.4

1. Using the Data in the table, compute the centered moving averages.What is the benefit derivedfrom obtaining these moving averages?

2. Compute the seasonal indexes for each month.When does the Water Department experience the larges seasonal effect?Does this seem reasonable?Does there seem to be a seasonal pattern?

3.Deseasonalize the data and use the deseasonalized time series to determine the linear trend equation.What is the average increase in water use per month?How far into the future do you think the trend could be projected?

4.Assuming a multiplicative model, obtain the cyclical components.Does there

seem to be a cyclical pattern?

5.Prepare a forecast of water use in Fort Worth for the last three months of 2006

and the first month of 2007 using only the trend equation.Use the seasonal

indexes to adjust the deseasonalized forecasts.

6.In January 2007, the actual water use turned out to be 325.6.Discuss the

forecasting error encountered here.