CHAPTER 12: FORECASTING TECHNIQUES Flashcards
what types of forecasts are often prepared
Budgets are based on forecasts. Forecasts might be prepared for:
the volume of output and sales
sales revenue (sales volume and sales prices)
costs.
what are the purposes for forecasts
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.
what are possible forecasting techniques
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.
what is a regression analysis and what types are there
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
how is least squares regression analysis conducted
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
when is linear regression used in budgeting
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.
what are other uses of linear regression analysis
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.
what are the benefits of simple linear regression
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.
what are the limitations of simple linear regression
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).
what is positive and negative correlation
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.
what are the degrees of correlation
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.
what is the correlation coefficient
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
what is the coefficient of determination
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.
what is a time series analysis technique
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.
what is time series analysis used for
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.
in time series analysis what 3 ways is the trend measured
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.
how are seasonal variations analysed in time series analysis
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.
what are the 2 main models of seasonal variation
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
what are cyclical variations
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.
what are residual or random variations
Residual or random variations are caused by irregular items, which cannot be predicted, such as a fire or flood.
how can you forecast with the use of time series analysis
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.
what is a moving average
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.
advantages of time series analysis
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.
disadvantages of time series analysis
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.
