CHAPTER 12: FORECASTING TECHNIQUES

Question 1

what types of forecasts are often prepared

Answer 1

Budgets are based on forecasts. Forecasts might be prepared for:
the volume of output and sales
sales revenue (sales volume and sales prices)
costs.

Question 2

what are the purposes for forecasts

Answer 2

The purpose of forecasting in the budgeting process is to establish realistic assumptions for planning.

A forecast might be based on simple assumptions, such as a prediction of a 5% growth in sales volume or sales revenue. Similarly, budgeted expenditure might be forecast using a simple incremental budgeting approach, and adding a percentage amount for inflation on top of the previous year’s budget.

On the other hand, forecasts might be prepared using a number of forecasting models, methods or techniques that look to calculate trends and variations over previous years. The reason for using these models and techniques is that they might provide more reliable forecasts.

Question 3

what are possible forecasting techniques

Answer 3

Possible forecasting techniques:
the high-low method (see Chapter 2)
linear regression analysis
time series analysis
index numbers.

You may find that more than one technique will be used to forecast information for example index numbers can be used to adjust prices after regression analysis or the high low method has been applied to a set of data. It is also possible to use regression analysis rather than moving averages in time series analysis. This will be demonstrated later in this chapter.

Question 4

what is a regression analysis and what types are there

Answer 4

Regression analysis is concerned with establishing the relationship between a number of variables. We are only concerned here with linear relationships between 2 variables.
There are a variety of methods available for identifying the relationship:
1 Draw a scatter diagram and plot a line of best fit
2 The high-low method (see Chapter 2)
3 Least squares regression analysis

Question 5

how is least squares regression analysis conducted

Answer 5

Regression analysis finds the line of best fit computationally rather than by estimating the line on a scatter diagram. It seeks to minimise the distance between each point and the regression line.

where a is the y intercept of a straight line

a = (∑y/n) - (b∑x/n)

y = dependent variable
b = gradient
x = independent variable

Question 6

when is linear regression used in budgeting

Answer 6

Linear regression analysis can be used to make forecasts or estimates whenever a linear relationship is assumed between two variables, and historical data is available for analysis.

The regression equation can be used for predicting values of y from a given x value.
1If the value of x is within the range of our original data, the prediction is known as interpolation.
2If the value of x is outside the range of our original data, the prediction is known as extrapolation.

Question 7

what are other uses of linear regression analysis

Answer 7

Linear regression can also be used:
to establish a trend line from a time series. Time series is explained later in this chapter.
The independent variable (x) in a time series is time.
The dependent variable (y) is sales, production volume or cost etc.

as an alternative to using the high-low method in cost behaviour analysis. It should be more accurate than the high-low method, because it is based on more items of historical data, not just a ‘high’ and a ‘low’ value.
The independent variable (x) in total cost analysis is the volume of activity.
The dependent variable (y) is total cost.
The value of a is the amount of fixed costs.
The value of b is the variable cost per unit of activity.

the outcome of this analysis can produce

a sales budget or forecast can be prepared
costs can be estimated, for a budgeted level of activity.

Question 8

what are the benefits of simple linear regression

Answer 8

1Simple and easy to use.
2Looks at the basic relationship between two sets of data.
3Can be used to forecast and to produce budgets.
4Information required to complete the linear regression calculations should be readily available.
5Computer spreadsheet programmes often have a function that will calculate the relationship between two sets of data.
6Simplifies the budgeting process.

Question 9

what are the limitations of simple linear regression

Answer 9

1Assumes a linear relationship between the variables.
2Only measures the relationship between two variables. In reality the dependent variable is affected by many independent variables.
3Only interpolated forecasts tend to be reliable. The equation should not be used for extrapolation.
4Regression assumes that the historical behaviour of the data continues into the foreseeable future.
5Interpolated predictions are only reliable if there is a significant correlation between the data (see next section).

Question 10

what is positive and negative correlation

Answer 10

Correlation can be positive or negative.
Positive correlation means that high values of one variable are associated with high values of the other and that low values of one are associated with low values of the other.
Negative correlation means that low values of one variable are associated with high values of the other and vice versa.

Question 11

what are the degrees of correlation

Answer 11

Two variables might be:
(a)perfectly correlated
The graph on the left shows perfect positive correlation and the graph on the right show perfect negative correlation. All the pairs of values lie on a straight line. There is an exact linear relationship between the two variables.

(b)partly correlated
In the first diagram there is not an exact relationship, but low values of x tend to be associated with low values of y, and high values of x tend to be associated with high values of y.
In the second diagram again there is not an exact relationship, but low values of x tend to be associated with high values of y and vice versa.

(c)uncorrelated.
The values of the two variables seem to be completely unconnected.

Question 12

what is the correlation coefficient

Answer 12

The degree of correlation can be measured by the Pearsonian correlation coefficient, r (also known as the product moment correlation coefficient).
r must always be between –1 and +1.
If r = +1, there is perfect positive correlation
If r = 0, there is no correlation
If r = –1, there is perfect negative correlation
For other values of r, the meaning is not so clear. It is generally taken that if r > 0.8, then there is strong positive correlation and if r < – 0.8, there is strong negative correlation.

formula for r will be given in exam

Question 13

what is the coefficient of determination

Answer 13

The coefficient of determination, r2 measures the proportion of changes in y that can be explained by changes in x when a straight line relationship has been established.

Question 14

what is a time series analysis technique

Answer 14

A time series is a series of figures recorded over time, e.g. unemployment over the last 5 years, output over the last 12 months.

Question 15

what is time series analysis used for

Answer 15

Time series analysis is a technique used to:
identify whether there is any underlying historical trend
use this analysis of the historical trend to forecast the trend into the future
identify whether there are any seasonal variations around the trend
apply estimated seasonal variations to a trend line forecast in order to prepare a forecast season by season.
A time series has 4 components:
Trend
Seasonal variations
Cyclical variations
Residual or random variations.

Question 16

in time series analysis what 3 ways is the trend measured

Answer 16

Most time series follow some sort of long term movement. In time series analysis the trend is measured by:
1Inspection. A graph of the data is produced and the trend line is drawn by eye with the aim of plotting the line so that it lies in the middle of the data points.
2Least squares regression analysis. x represents time (each month would be given a number e.g. January =1, February =2 etc) and y is the data.
3Moving averages. This method attempts to remove seasonal or cyclical variations by a process of averaging.

Question 17

how are seasonal variations analysed in time series analysis

Answer 17

Once the trend has been found, the seasonal variation can be determined. Seasonal variations are short-term fluctuations in value due to different circumstances which occur at different times of the year, on different days of the week, different times of day, for example traffic is greatest in the morning and evening rush hours.
If there is a straight-line trend in the time series, seasonal variations must cancel each other out. The total of the seasonal variations over each cycle should be zero. Seasonal variations can be measured:
in units or in monetary values
as a percentage value or index value in relation to the underlying trend.

Question 18

what are the 2 main models of seasonal variation

Answer 18

Seasonal variations are used to forecast future figures by amending the trend. There are two main models:
1The additive model. Here the seasonal variation is expressed as an absolute amount to be added on to the trend to find the actual result, e.g. ice cream sales in summer are expected to be $200,000 above the trend.
Forecast = Trend + Seasonal variation
2The multiplicative model. Here the seasonal variation is expressed as a ratio/proportion/percentage to be multiplied by the trend to arrive at the actual figure, e.g. ice cream sales are expected to be 50% more than the trend.
Forecast = Trend × Seasonal variation

Question 19

what are cyclical variations

Answer 19

Cyclical variations are medium-term to long term influences usually associated with the economy. These cycles are rarely of consistent length and we would need 6 or 7 full cycles of data to be sure that the cycle was there.

Question 20

what are residual or random variations

Answer 20

Residual or random variations are caused by irregular items, which cannot be predicted, such as a fire or flood.

Question 21

how can you forecast with the use of time series analysis

Answer 21

We are only really interested in the first two components of time series, the trend and any seasonal variations, when we are looking to forecast for a budget as the cyclical variations are too long term and residual variations are too unpredictable.
A trend over time, established from historical data, and adjusted for seasonal variations, can then be used to make predictions for the future.

Question 22

what is a moving average

Answer 22

A moving average is a series of averages calculated from historical time series data.

By using moving averages, the variations in a time series can be eliminated leaving a ‘smoothed’ set of figures which is taken as the trend.

Question 23

advantages of time series analysis

Answer 23

The advantages of forecasting using time series analysis are that:
forecasts are based on clearly-understood assumptions
trend lines can be reviewed after each successive time period, when the most recent historical data is added to the analysis; consequently, the reliability of the forecasts can be assessed
forecasting accuracy can possibly be improved with experience.

Question 24

disadvantages of time series analysis

Answer 24

The disadvantages of forecasting with time series analysis are that:
there is an assumption that what has happened in the past is a reliable guide to the future
there is an assumption that a straight-line trend exists
there is an assumption that seasonal variations are constant, either in actual values using the additive model (such as dollars of sales) or as a proportion of the trend line value using the multiplicative model.
None of these assumptions might be valid.

Question 25

what is an index number

Answer 25

An index number is a technique for comparing, over time, changes in some feature of a group of items (e.g. price, quantity consumed, etc) by expressing the property each year as a percentage of some earlier year.

The year that is used as the initial year for comparison is known as the base year. The base year for an index should be chosen with some care. As far as possible it should be a ‘typical year’ therefore being as free as possible from abnormal occurrences. The base year should also be fairly recent and revised on a regular basis.

Question 26

what are the 3 types of index numbers

Answer 26

Index numbers are used in a variety of situations and to measure changes in all sorts of items. As the uses of index numbers are so diverse a number of different types of indices have been developed.
We shall deal below with the following:
simple indices
chain based indices
multi-item (or weighted) indices.

Question 27

what are simple index numbers

Answer 27

A simple index is one that measures the changes in either price or quantity of a single item.

There are therefore two types of simple indices:
a price index
a quantity index.

The formulae for calculating simple indices are:

simple price index = (p1/p0) x 100

simple quantity index = (q1/q0) x 100

Where:
p0 is the price at time 0
p1 is the price at time 1
q0 is the quantity at time 0
q1 is the quantity at time 1

Question 28

what are chain base index numbers

Answer 28

A chain base index number expresses each year’s value as a percentage of the value for the previous year.
If a series of index numbers are required for different years, showing the rate of change of the variable from one year to the next, the chain base method is used.
This simply means that each index number is calculated using the previous year as base. If the rate of change is increasing, then the index numbers will be rising; if it is constant, the numbers will remain the same and if it is decreasing the numbers will be falling.

Question 29

what are multi-item (weighted) index numbers and how can it be measured for a price index

Answer 29

A weighted index measures the change in overall price or overall quantity of a number of different items compared to the base year.
For example, an organisation might produce three different products and an index is to be constructed to measure the selling price changes of all three products. In order to do this the percentage change in each of the three selling price must first be calculated individually and the results must then be weighted to reflect the relative importance of each of the three products.
For a price index:
Step 1 Calculate the simple price index for each of the items.
Step 2 These price indices must then be weighted in some suitable manner in order to produce an overall price index.
Similarly if a quantity index is to be calculated:
Step 1 Calculate the simple quantity index for each of the items.
Step 2 These quantity indices must then be weighted in some suitable manner in order to produce an overall quantity index.

Question 30

what are Laspeyre index numbers

Answer 30

Laspeyre index numbers use the base year quantity or base year price to weight the index.

formula given in exam

Question 31

what are advantages and disadvantages of Laspeyre indices

Answer 31

Advantages of Laspeyre indices
Cheaper, as the obtaining of new quantities each year, which may be a costly exercise, is avoided.
Easier to calculate where a series of years are being compared, since the denominator remains the same for all years.
Disadvantages of Laspeyre indices
An out-of-date consumption pattern may be used, so that trends become unrealistic.
As prices rise, quantities purchased tend to fall if there are alternative goods available. This decrease is not reflected in the Laspeyre index which tends therefore to overestimate the effect of rising prices.

Question 32

what are Paasche index numbers

Answer 32

Paasche index numbers use the current year quantity or current year price to weight the index.

Question 33

what are advantages and disadvantages of Paasche indices

Answer 33

Advantage of Paasche indices
Since current year weights are used, this results in an index based on the current pattern of consumption so that a less frequent revision of base year is needed.
Disadvantages of Paasche indices
Where a series of years is involved, the amount of calculation is greater as both the numerator and the denominator need to be recalculated each year.
Can only be constructed if up-to-date quantity information is available.
Rising prices have the opposite effect on the weights, so a Paasche price index tends to underestimate the effect of inflation.

Question 34

advantages and disadvantages of index numbers

Answer 34

Advantages of index numbers
They aid management to understanding the information presented to them.
Indices present changes in data or information over time in percentage terms.
They make comparison between items of data easier and more meaningful – it is relatively easy to make comparisons and draw conclusions from figures when you are starting from a base of 100.
The ability to calculate separate price and quantity indices allows management to identify the relative importance of changes in each of two variables.
Disadvantages of index numbers
There may be no single correct way of calculating an index, especially the more sophisticated index numbers. The user of the information should bear in mind the basis on which the index is calculated.
The overall result obtained from multi-item index numbers are averages.
They should only be applied to the items which are included in the index calculation.
They are relative values, not absolute figures and may not give the whole picture.

Question 35

how can index numbers affect the accuracy of forecasting

Answer 35

The accuracy of forecasting is affected by the need to adjust historical data and future forecasts to allow for price or cost inflation.
When historical data is used to calculate a trend line or line of best fit, it should ideally be adjusted to the same index level for prices or costs. If the actual cost or revenue data is used, without adjustments for inflation, the resulting line of best fit will include the inflationary differences.
When a forecast is made from a line of best fit, an adjustment to the forecast should be made for anticipated inflation in the forecast period.