25

Resource: Ch. 9 in the text Read Exercises 9.1 on p. 130 & 9.3 on p. 131. Forecast personnel expenses and total revenues respectively, using weighted moving averages and moving averages. Explain how financial trends affect forecasting. Post your final answers as a Microsoft® Word attachment |
Day 5 (Friday) |

C H A P T E

R

9 Forecasting

As part of the planning and budgeting processes that precede each new fiscal year,

human service agencies are confronted with a series of questions: What will the

agency caseload be? Will the caseload go up, go down, or remain the same? Wha

t

does the revenue situation look like? Will revenues increase, stay the same, or

decline? What about expenses? In light of changes in caseload and revenues, can

the current pattern of expenses be maintained? Should expenses be reduced

?

Without some estimate of how many clients a human service agency will serve in

the coming fiscal year and what the revenue and expense picture will look like, it

is difficult to prepare a realistic line-item operating budget for a human service

agency.

There are essentially two ways human service administrators can estimate

future case loads, revenues, and expenses: by educated guessing or by one or more

of a variety of generally accepted forecasting techniques. As a general rule, the use

of one or more generally recognized forecasting techniques is preferable to simply

guessing. While an educated guess can sometimes turn out to be quite accurate, it

is hard to defend during the budget process.

Forecasting can be defined as techniques that predict the future based on his-

torical data (Lee & Shim, 1990:442). One of the interesting discoveries that

researchers have made about forecasting is that simple techniques perform (pro-

duce estimates) that are frequently just as accurate as complex forecasting tech-

niques (Cirincione, Gurrieri, & Van de Sande, 1999). Consequently, one doesn’t

have to be an expert in math or statistics to use many of the commonly recognized

forecasting techniques. This chapter presents four commonly recognized time

series forecasting techniques: (1) simple moving averages, (2) weighted moving

averages, (3) exponential smoothing, and (4) time series regression. The first three

of these forecasting techniques are relatively simple and the calculations can be

done by hand. Time series regression is a more complex forecasting technique that

requires the use of a computer and a basic understanding of some statistical con-

cepts. Today, a variety of low-cost computer programs can perform not only time

series forecasting, but moving averages, weighted moving averages, exponential

smoothing, and assorted other techniques that are not covered in this chapter.

Before proceeding directly to the discussion of the four forecasting tech-

niques, a few basic forecasting rules of thumb are presented.

118

Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.

ISBN

: 0-536

-1

2114-1

Some Basic Forecasting Rules of Thumb

Several rules of thumb can be used as guides in conducting forecasts and inter-

preting the results.

Rule 1. Examine the data for the presence or absence of a trend. Revenues and expenses

and, to a lesser extent, caseload, tend to change incrementally. Consequently, either

an upward or downward trend may be present in the data. Looking at Table 9.1, an

upward trend is clearly evident in the caseload data. The caseload has been trend-

ing upward for the past four fiscal years. On the other hand, the donation data do

not demonstrate a trend, but rather vary (increase and decrease) from year to year.

In the absence of any other data or any other contextual information about the

nature of the human service agency, the type of service involved, the client popu-

lation, the community, the local economy, and so on, we would expect that the

trend in the caseload data would continue for fiscal year 20X5. We are less sure

about the forecast for donations because of the absence of a trend.

Rule 2. The farther out the forecast, the less reliable the forecast. A forecast that looks

ahead one fiscal year will generally be more reliable (more accurate) than a forecast

that looks ahead three fiscal years. The reason is simple: Things change! A good

example of the problem with forecasts that look too far ahead is provided by the

U.S. space program. When the United States put a man on the moon in 1969, all

kinds of forecasts about the future of space exploration were made based on how

long it took us to reach the moon. According to many of these forecasts, we should

already have a space colony on Mars. But we don’t. Why? Because things change!

In the case of the space program, government funding for space exploration was

cut back and our space exploration policy changed from using manned spacecraft

to using unmanned spacecraft.

Rule 3. Older data are less important than more recent data. Table 9.1 could include

donation data for fiscal years 1999, 1998, 1997, and so on. But we know that a prob-

lem in forecasting is that things change. So, the older the data included in a fore-

cast, the more opportunity for things to change and, consequently, the less reliable

the forecast is likely to be.

Rule 4. The last actual value of the forecast variable is the single most important piece of

information. In Table 9.1, the caseload and donation forecasts are to be made for fis-

cal year 20X5; the last actual value for the caseload is 1,450 and the last actual value

for donations is $25,000. In the absence of any other data, the single best predictor of

the future is the last value of the forecast variable. The reason is that the last actual

value is the single piece of datum that is temporarily closest to the forecast. For

example, if the only datum we had in Table 9.1 was the last actual value for caseload

(1,450) for fiscal year 20X4, our best forecast for 20X5 would be 1,450. The last actual

Forecasting 119

Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.

IS

BN

: 0

-5

3

6

–

1

21

14

-1

value also provides a reality check for a forecast. For any forecast, the question

should be asked, Does the forecast seem reasonable given the last actual data?

Rule 5. The more one knows about the data, the better one can interpret the forecast. One

can forecast anything. The real gut issue is how to interpret the results of the fore-

cast. In Table 9.1, any one of a number of forecasting techniques could be used to

forecast the caseload for fiscal year 20X5. But the critical issue is, What are the data

trying to tell us? A trend in the caseload data is clearly evident over the past four

fiscal years. The caseload was 1,200 in FY 20X1 and increased 100 cases per year for

fiscal year 20X2 and 20X3. But then something happened to the trend. In FY 20X4,

the caseload increased by only 50. Why? What is going on? Unfortunately, we

don’t know anything about the Palmdale Human Service Agency, the type of ser-

vice involved, the client population, the community, the local economy, and

numerous other factors that could help provide us with a context in which to inter-

pret the forecast. If we had contextual information, we would be better able to

understand what the data are trying to tell us and we would be better able to inter-

pret the forecast. Something may be occurring with the agency, the service, or the

community that might explain the caseload data for fiscal year 20X4 and thus help

to interpret the forecast for 20X5.

With this brief discussion of some forecasting rules of thumb completed, we

can proceed to a discussion of our four forecasting techniques.

Simple Moving Averages

The forecasting technique called simple moving averages involves taking historical

data on the forecast variable for a series of time periods and computing a simple

arithmetic (mean) average. The forecaster must decide how many time periods of

the forecast variable to include in the moving average. For example, in Table 9.1,

we have historical values of the forecast variables of caseload and donations for

four fiscal years. Rule 3 comes into play here: Older data are less important than

more recent data. Following this guideline, we might decide to use only three years

of historical data on the caseload and donations to make our forecasts. Table 9.

2

takes this approach to forecasting caseload and donation data for fiscal year

20X5

using simple moving averages.

120 C H A P T E R 9

TABLE 9.1 The Palmdale Human Service Agency

Fiscal Year

20X1

20X2

20X

3

20X4

20X5

Caseload

1,200

1,300

1,400

1,450

?

Donations

$

25,000

22,000

27,000

25,000

?

Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.

ISBN

: 0-536 -12114-1

Using simple moving averages, the caseload forecast for fiscal year 20X5 is

1,383, whereas the donations forecast is $24,667. The caseload forecast is derived

by adding the caseload data for the three time periods and dividing by the num-

ber of time periods. The same procedure is used to forecast donations. At this

point we are reminded of Rule 1 relating to the presence or absence of a trend. We

know that an upward trend exists in the caseload data, but that no trend appears

to exist in the donations data. Thus, we should anticipate that the caseload fore-

cast will show a continuation of the trend, whereas the donations forecast will

continue to fluctuate.

Our expectations are satisfied with respect to the donations forecast, but not

for the caseload forecast. The donations forecast for fiscal year 20X5 is 24,667,

which is less than the last actual data for fiscal year 20X4. The donations forecast

continues to jump around. Our expectation is not satisfied for the caseload fore-

cast. The caseload forecast for fiscal year 20X5 is 1,383, which is again less than the

actual data for fiscal year 20X4. But we should expect, based on the observed trend

in the caseload data, a forecast that is greater than the actual caseload for fiscal year

20X4.

What is the problem with the simple moving averages forecast of caseload for

fiscal year 20X5? Rules 3 and 4 provide some guidance. Rule 3 tells us that older

data are less important than more recent data. All the data in the two simple mov-

ing averages forecasts are weighted the same. Actually, no weights are used, which

has the effect of treating all data as though they were weighted equally. Rule 4 sug-

gests that the last actual value of the forecast variable is more important than the

other data and should perhaps be given greater weight in the forecast.

The point needs to be made that the moving in simple moving averages means

that for fiscal year 20X6, the forecast would be comprised of the actual caseload

and donations data for fiscal years 20X3, 20X4, and 20X5. The actual caseload and

donations data for 20X5 would be added to the moving averages and the caseload

and donations data for 20X2 would be deleted. This process keeps the simple mov-

ing average’s base of three fiscal years.

Forecasting 121

TABLE 9.2 Palmdale Human Service Agency

Caseload and Donations Forecasts

Using Simple Moving Averages

Fiscal Year

20X2

20X3

20X4

20X2–X4

20X5

Caseload

1,300

1,400

1,450

4,150

4,150

= 1,383

3

Donations

$22,000

27,000

25,000

74,000

74,000

= $24,667

3

Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.

IS

BN

: 0

-5

36

-1

21

14

-1

Weighted Moving Averages

The second of our four forecasting techniques, weighted moving averages, attempts

to improve on simple moving averages by assigning weights to the data that com-

prise the forecast. In keeping with Rules 3 and 4, the idea is to place more weight

on the last actual value of the forecast variable and decreasing weights on the older

data. For example, a common practice in weighted moving averages is to assign a

weight of “1” to the oldest datum to be used in the forecast and then assign increas-

ing weights to more recent data so that the last actual value receives the greatest

weight. Following this approach, Table 9.3 shows the results of a weighted moving

average forecast for caseload and donations for fiscal year 20X5.

Using weighted moving averages, the caseload forecast for fiscal year 20X5 is

1,408 and the donations forecast is $25,167. The caseload forecast is arrived at by

multiplying the caseload data for each year by its weight, adding the results

together, and dividing by the total number of weights. The forecast for donations

is obtained using the same approach. The caseload forecast of 1,408 appears more

realistic than the simple moving averages forecast of 1,383, but it is still less than

the last actual caseload data of 1,450 for fiscal year 20X4. Again, we are confronted

with the problem that we cannot put a lot of confidence in a forecast of 1,408 unless

we have some contextual information that explains why we should accept a case-

load forecast that does not demonstrate a continuation of the identified trend. The

122 C H A P T E R 9

TABLE 9.3 Palmdale Human Service Agency

Forecasts Using Weighted Moving Averages

Caseload

Fiscal Year

20X2

20X3

20X4

20X5

Caseload

1,300

1,400

1,450

8,450/6 = 1,408

Weight

1

2

3

6

Weighted Score

1,300

2,800

4,350

8,450

Donations

Fiscal Year

20X2

20X3

20X4

20X5

Donations

$22,000

27,000

25,000

$151,000/6 = $25,167

Weight

1

2

3

6

Weighted Score

$ 22,000

54,000

75,000

151,000

Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.

ISBN

: 0-536 -12114-1

donations forecast of $25,167 appears reasonable given the historical way in which

donations have tended to fluctuate.

Exponential Smoothing

In order to perform a forecast using either simple moving averages or weighted

moving averages, the forecaster must collect and save data for several historical

time periods. Exponential smoothing is a forecasting technique that requires only

two pieces of information: (a) the last actual value of the forecast variable and

(b) the last actual forecast. With these two pieces of information and the use of a

simple formula, we can forecast caseload, revenues, expenses, or any other vari-

able. One might say that exponential smoothing takes to heart Rule 4 that the last

actual value of the forecast variable is the single most important piece of informa-

tion. The forecasting formula used in exponential smoothing is

NF = LF + α (LD – LF) where NF = New forecast

LF = Last forecast

α = 0 to 1

LD = Last data

The formula is relatively straightforward with the exception of the alpha (α).

Alpha is a value between 1 and 0 that is selected by the forecaster. The alpha deter-

mines how much weight in the new forecast will be placed on the last data (the last

value of the forecast variable) and, conversely, how much weight will be placed on

the last forecast. An alpha of 1 means that 100 percent of the new forecast will be

based on the last data and 0 per cent on the last forecast. An exponential smooth-

ing forecast using an alpha of 1 would result in a number that would be exactly the

same as the last actual value of the forecast variable. An alpha of zero means that 0

percent of the new forecast will be based on the last data and 100 percent on the last

forecast. An exponential smoothing forecast using an alpha of 0 would result in a

number that is exactly the same as the last forecast. An alpha of .5 means that 50

percent of the new forecast will be based on the last actual data and 50 percent on

the last forecast.

When using exponential smoothing, the alpha selected is determined by the

accuracy of the last forecast. For example, if the caseload forecast for fiscal year

20X4 was 1,700 and the actual caseload was 1,450, then the forecast was not very

accurate. In such a situation, the forecaster would want to select for the next fore-

cast (fiscal year 20X5) a high alpha (.7 to .9) that places more weight on the last

data and less weight on the last forecast. If, however, the caseload forecast for fis-

cal year 20X4 was 1,460 and the actual caseload for fiscal year 20X4 was 1,450,

then the forecast was quite accurate. In such a situation, the forecaster would

want to select for the next forecast (fiscal year 20X5) a low alpha (.2 to .3) that

places more weight on the last forecast and less weight on the last data. A small

alpha (.2 to .4) has the same effect as if data for several time periods were included

Forecasting 123

Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.

IS

BN

: 0

-5

36

-1

21

14

-1

in the forecast. In other words, a small alpha “smooths” the forecast, hence the

name exponential smoothing.

Let’s assume that the caseload forecast for fiscal year 20X4 was 1,500 and that

the donations forecast was $26,000. We know that the actual caseload and dona-

tions data for fiscal year 20X4 were, respectively, 1,450 and $25,000. Because the

caseload forecast was quite accurate, we will select an alpha of .2 for use in our

forecast of caseload for 20X5. Because the forecast for donations was somewhat

less accurate, we will select a higher alpha (.5) that will place equal emphasis on

both the last forecast and the last data. This information can now be entered into

the exponential smoothing formula (Table 9.4) and a fiscal year 20X5 forecast can

be made for both caseload and donations.

The exponential smoothing caseload forecast is 1,490 for 20X5. This forecast

appears to be realistic because the upward trend evidenced over the last four fiscal

years is continued and because the new forecast is greater than the actual caseload

data of 1,450 for fiscal year 20X4. Similarly, the exponential smoothing forecast for

donations of $25,500 for fiscal year 20X5 appears reasonable, but we are less sure of

this forecast because of the tendency of the donations data to fluctuate.

Time Series Regression

Time series regression is the last of the four generally recognized forecasting tech-

niques to be discussed in this chapter and the only one that requires the use of a

computer. Time series regression is more sophisticated than the other forecasting

124 C H A P T E R 9

TABLE 9.4 Palmdale Human Service Agency

Caseload and Donations Forecasts

Using Exponential Smoothing

Caseload

NF = LF + α(LD – LF)

= 1,500 + .2(1,450 – 1,500)

= 1,500 + .2(–50)

= 1,500 + (–10)

= 1,490

Donations

NF = LF + α (LD – LF)

= $26,000 + .5($25,000 – $26,000)

= $26,000 + .5(–$1,000)

= $26,000 + (–$500)

= $25,500

Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.

ISBN

: 0-536 -12114-1

techniques considered, but it also more powerful and provides more insights into

the data and the forecast. Time series regression forecasting also yields an estimate

of how much confidence one should have in the forecast. These features make it

one of the most commonly used forecasting techniques (Forester, 1993). Time series

regression forecasting can be performed using any computer software package

that contains a simple linear regression program.

Time series regression is an application of what is called the ordinary least

squares regression model. Time series regression forecasting attempts to find a

linear relationship between time (the independent variable) and the forecast vari-

able (the dependent variable). A linear relationship can be thought of as a trend.

In other words, time series regression analyzes the data looking for a trend. The

time series regression model looks for (a) a positive linear relationship (or trend)

between time and the forecast variable, (b) a negative linear relationship (or

trend) between time and the value of the forecast variable, or (c) no linear rela-

tionship (or trend). A positive linear relationship (or trend) means that over time

the values of the forecast variable are increasing. A negative linear relationship (or

trend) means that over time the values of the forecast variable are decreasing. If

the time series regression model finds a moderate to strong positive or negative

linear relationship (or trend), the computer output can be used to make a forecast

using the formula

Y = A + BX where Y is the forecast (an unknown quantity)

A is the base or constant

B is the unit value change in the forecast variable

X is the increment of time to be forecasted

The use of an example should help make the discussion of time series regres-

sion forecasting more understandable. Table 9.5 demonstrates how time series

regression can be used to conduct a caseload forecast using the caseload data we

have used in the other forecasts. In conducting a caseload forecast using time series

regression, we are going to use all four years of available caseload data. Using

older data here does not violate Rule 3, because (a) a time series regression forecast

needs at least four (some would say five) data points to function properly and

(b) the analysis is able to differentiate between changes attributable to time (the

trend) and changes attributable to other factors.

The first part of Table 9.5 shows how the data for a time series regression fore-

cast are entered into a computer program. Time is always treated as the indepen-

dent variable (IV), whereas the forecast variable (e.g., caseload or donations) is

always treated as the dependent variable (DV). When the data are inputted into the

computer program, it is important not to reverse these variables. Time must

always be the independent variable or the computer output will be meaningless.

When inputting data into a time series regression, the time periods are trans-

formed into consecutive numbers. For example, we have four years of caseload

data (the time period) so fiscal year 20X1 = 1, 20X2 = 2, 20X3 = 3, and 20X4 = 4. The

oldest time period is always designated 1.

Forecasting 125

Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.

IS

BN

: 0

-5

36

-1

21

14

-1

The second part of Table 9.5 shows the resulting computer output, specifi-

cally the “coefficients” and the “model summary” sections. Computer programs

such as Statistical Packages for the Social Sciences (SPSS) provide a lot of output

that is not essential to the purposes of conducting and interpreting the results of a

time series regression forecast. For forecasting purposes, one needs to know the

value of R-square, the value of A (the constant), and the value of B (Var1). In SPSS,

the value of R-square is usually found as part of the model summary output, while

values of the A (constant) and the B (Var1) are usually found as part of the coeffi-

cients output.

The R-square tells us how much confidence we should have in the forecast.

R-square can vary between 0 and 1. R-square can also be thought of as a measure

of the strength of a trend (either positive or negative) in the values of the forecast

variable over time. If the R-square is greater than .7, a strong trend exists. An R-

square between .5 and .7 indicates a moderate trend; R-square less than .5 indicates

a weak trend. Looking at the model summary portion of the computer output

(Table 9.5), we can see that the R-square for the time series regression is .980, which

is significantly greater than .7. In terms of interpretation, we can say that we can

126 C H A P T E R 9

TABLE 9.5 Caseload Forecast Using Time Series Regression

Computer Input

Time Caseload

(IV) (DV)

1 1,200

2 1,300

3 1,400

4 1,450

Computer Output

Coefficients

Model

Constant

Var 1

Unstandardized Coefficients

B

1125

85

Std. Error

23.717

8.660

BETA

.990

t

47.434

9.815

Sig.

.000

.010

Model

Summary

Model

1

R

.990

R-Square

.980

Adjusted

R-Square

.969

Standard Error

of the Estimate

19.3649

Standardized Coefficients

Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.

ISBN

: 0-536 -12114-1

have a high degree of confidence in the result of a time series regression forecast.

Another interpretation is that the time series regression analysis has found a strong

trend in the caseload data. This strong trend can be used for forecasting purposes.

In order to perform a time series regression forecast, we must substitute the

relevant values into the formula Y = A + BX (Table 9.6). To the base value of A (a

constant), we add B (Var1) multiplied by X (the time period to be forecasted). Since

we are using four years of caseload data in the time series regression and we are

performing a forecast for the next fiscal year, X = 5. The result is a caseload forecast

of 1,550. This caseload forecast looks good because it is a continuation of the

observed trend in the caseload data and because it is greater than the last actual

caseload data for fiscal year 20X4.

Why does the time series caseload forecast perform so much better than the

other forecasting techniques? The answer is that time series regression is particu-

larly sensitive to, and performs best, when a strong trend is present. The three

other forecasting techniques discussed in this chapter are not as sensitive to trends.

At this point it is probably advisable to pause for a moment and explain

exactly what the values of the A (constant) and the B (Var1 or variable 1) mean in a

time series regression. When conducting a time series regression, many computer

programs provide for the optional generation of a graph of the linear relationship

between time and the forecast variable. Figure 9.1 is such a graph. The indepen-

dent variable (time) is shown on the x-axis and the dependent variable (caseload)

is shown on the y-axis. In the middle of the graph are four data points. The first

data point represents the caseload data (1,200) for fiscal year 20X1 (year 1). The sec-

ond data point represents the caseload data (1,300) for fiscal year 20X2 (year 2). The

third data point represents the caseload data (1,400) for fiscal year 20X3 (year 3).

And finally, the fourth data point represents the caseload data (1,450) for 20X4

(year 4).

The line in the center of the graph is the regression line. The regression line can

be thought of as “the best line” that expresses the linear relationship (the trend)

between time and the forecast variable. The line begins at 1,125. This point is called

A (constant) because it is the fixed point at which the regression line begins. This

point is also called the y-intercept because it is the point at which the regression line

crosses the y-axis. The slope of the regression line then goes up 85 (B or Var1) for

each time period (year). In performing the actual time series regression forecast,

the regression line is simply extended out to the time period being forecasted. In

Forecasting 127

TABLE 9.6 Caseload Forecast Using Time

Series Regression

Y = A + BX

= 1125 + 85(5)

= 1125 + 425

= 1550

Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.

IS

BN

: 0

-5

36

-1

21

14

-1

this example, caseload is being forecasted for the fifth year. The mathematics of the

forecast are simply to begin with the value of A (constant) and then to add the

value of B (Var1) for each time period (year) up to the forecast time period (year):

1,125 + 85 (year 1) + 85 (year 2) + 85 (year 3) + 85 (year 4) + 85 (year 5) = 1,550

Now let’s do a time series regression forecast for donations. The top portion of

Table 9.7 shows how the data are entered into the computer program; the lower por-

tion shows the computer output. In the “coefficients” section of the output, we see

that the value of A (constant) is 23,500 and the value of B (Var1) is 500. In the model

summary section, we see that the R-square is .098. The R-square is extremely low,

which means that we can have little confidence in any forecast made using time

series regression. Another way of interpreting the low R-Square is that the com-

puter could not find a trend in the data. Knowing that we can have no confidence in

the results, let’s go ahead anyway and do a time series regression forecast using the

formula Y = A + BX (see Table 9.8) The resulting forecast for donations is $27,000 in

fiscal year 20X5, but we know that we can have absolutely no confidence in this

forecast.

The two time series regression forecasts for caseload and for donations

demonstrate the strengths and limitations of this forecasting technique. Time series

regression forecasting works well when a strong (R-square = .7 or greater) trend

exists, works less well when a moderate (R-square = .4 to .7) trend exist, and does

not work well at all when a weak (R-square = less than .4) exists.

128 C H A P T E R 9

FIGURE 9.1 Graph of Time and Caseload

with Regression Line

1600

1500

1400

1300

1200

1100

1000

1 2 3 4 5

x -axis

y

-a

xi

s

ISBN

: 0-536 -12114-1

When to Use Which Forecasting Technique

The preceding discussion of the four generally recognized forecasting techniques

(in particular, the discussion of time series regression) allows three more rules of

thumb to be offered:

Rule 6. When a strong trend (R-square = .7 or greater) is present in the data, use

time series regression.

Forecasting 129

TABLE 9.7 Donations Using Time Series Regression

Computer Input

Time Caseload

(IV) (DV)

1 $25,000

2 22,000

3 27,000

4 25,000

Computer Output

Coefficients

Model

Constant

Var 1

Unstandardized Coefficients

B

23,500

500

Std. Error

2936.835

1702.381

BETA

.313

t

8.002

.466

Sig.

.015

.687

Model Summary

Model

1

R

.313

R-Square

.098

Adjusted

R-Square

–.353

Standard Error

of the Estimate

2397.9165

Standardized Coefficients

TABLE 9.8 Donations Using Time

Series Regression

Y = A + BX

= $23,500 + $500(5)

= $23,500 + $2,500

= $27,000

IS

BN

: 0

-5

36

-1

21

14

-1

Rule 7. When a moderate trend (R-square = .4 to .7) is present in the data, use

moving averages or weighted moving averages.

Rule 8. When a weak trend (R-square = less than .4) or no trend is present in the

data, use exponential smoothing with the choice of alpha dependent upon the

accuracy of the last forecast.

Following Rule 6, for any given forecast, a forecaster should first use time

series regression and determine if a trend is present in the data and the strength of

any such trend.

Summary

This chapter presented four generally recognized forecasting techniques: (1) sim-

ple moving averages, (2) weighted moving averages, (3) exponential smoothing,

and (4) time series regression. The advantages and disadvantages of each forecast-

ing technique were identified and several rules of thumb were provided to guide

human services administrators in the selection of the most appropriate forecasting

technique and in interpreting the results of forecasts.

E X E R C I S E S

Exercise 9.1

The following data represent total personnel expenses for the Palmdale Human

Service Agency for past four fiscal years:

20X1 $5,250,000

20X2 $5,500,000

20X3 $6,000,000

20X4 $6,750,000

Forecast personnel expenses for fiscal year 20X5 using moving averages, weighted

moving averages, exponential smoothing, and time series regression. For moving

averages and weighted moving averages, use only the data for the past three fiscal

years. For weighted moving averages, assign a value of 1 to the data for 20X2, a

value of 2 to the data for 20X3, and a value of 3 to the data for 20X4. For exponen-

tial smoothing, assume that the last forecast for fiscal year 20X4 was $6,300,000.

You decide on the alpha to be used for exponential smoothing. For time series

regression, use the data for all four fiscal years. Which forecast will you use? Why?

130 C H A P T E R 9

ISBN

: 0-536 -12114-1

Exercise 9.2

The following data represent total “person trips” (service outputs or units of ser-

vice) provided by the Palmdale Human Service Agency’s specialized transporta-

tion program for the past four fiscal years:

20X1 12,000

20X2 15,000

20X3 13,500

20X4 14,250

Forecast person trips for fiscal year 20X5 using moving averages, weighted mov-

ing averages, exponential smoothing, and time series regression. For moving aver-

ages and weighted moving averages, use only the data for the past three fiscal

years. For weighted moving averages, assign a value of 1 to the data for 20X2, a

value of 2 to the data for 20X3, and a value of 3 to the data for 20X4. For exponen-

tial smoothing, assume that the last forecast for fiscal year 20X4 was 15,000. You

decide on the alpha to be used for exponential smoothing. For time series regres-

sion, use the data for all four fiscal years. Which forecast will you use? Why?

Exercise 9.3

The following data represent total revenues (from all sources) for the Palmdale

Human Service Agency for the past four fiscal years:

20X1 $15,000,000

20X2 $14,250,000

20X3 $14,000,000

20X4 $13,500,000

Forecast total revenues for fiscal year 20X5 using moving averages, weighted mov-

ing averages, exponential smoothing, and time series regression. For moving aver-

ages and weighted moving averages, use only the data for the past three fiscal

years. For weighted moving averages, assign a value of 1 to the data for 20X2, a

value of 2 to the data for 20X3, and a value of 3 to the data for 20X4. For exponen-

tial smoothing, assume that the last forecast for fiscal year 20X4 was $13,000,000.

You decide on the alpha to be used for exponential smoothing. For time series

regression, use the data for all four fiscal years. Which forecast will you use? Why?

Forecasting 131

IS

BN

: 0

-5

36

-1

21

14

-1