STATISTICAL METHODS
Statistical Methods
• Trend projection • Regression technique
• Moving average method • Leading indicators method
Trend projection or mechanical exploration method
When time series data is available rdating to the sales of a product, trend projection method is
applied. Time series data of sales includcs cyclic changes in sales (c), seasonal variations(s),
trend (t) and irregular movemcnts (I).
sales = f (T, C, S, I)
Trend shows the long time tendency of the data. It is the result of changes in population.
Level of income, competitive conditions, changes in capital technology etc.
Cyclic changes in sales arise due to the periodical swings in the level of economic
activity such as prosperity or recessionary forces operating in the economy. These changes
are longer in duration and studying these variables is necessary for identifying the turning
points. Understanding cyclical changes is rather difficult, as these fluctuations do not follow a
regular course.
Seasonal variations in sales occur at particular points of time in a year. The seasonal
changes may take the form of climatic variations, festival seasons, holidays, marriage season
etc. Seasonal indices help in estimating seasonal fluctuations.
Irregular variations are non-measurable. Who can predict when an ealihquake, cyclone,
war, or an epidemic breaks out? A fter deducting the estimated sales attributable to the other
three variables, the residue is irregular changes.
Year Sales in '000 units
1995 25
1996 23
1997 30
1998 35
1999 43
2000 54
2001 49
2002 58
By fitting a trend line to the time series data demand forecast are obtained. Several
methods are available to analyze the time series data. The simplest method is assumed that the
four components of the time series data are related in an additive or mUltiplicative function.
In an additive function
Sales = T 1- C + S + I
In a multiplicative function
Sales = T x Cx Sx
[
Nole that in a multiplicative function if the value of any one variable is zero the sum of
the product would be zero. Therefore, it is assumed that the value of each variable is greater
than zero.
By using logarithms the multiplicative function is converted into an additive function
Log of sales = Log T + Log C t Log S + Log I
Whether one uses the additive or multiplicative function the trend value will be the same
but the seasonal and irregular variable values of sales data varies in both the functions.
Free hand method of trend projection
This is the easiest way of forecasting the demand. In this method, Time series data is plotted
on a diagram and a free hand trend line will be fitted in such a way that it passes through the
closest points on the scatter diagram as illustrated through the Table
The yearly sales data is represented on a graph and then by simple observation a trend
line fitted. By extending the trend line to 2003 or 200--l the sales fiJrecasts for the two subsequent
years can be obtained. Though, this method is easy and simple to forecast the sales yet it lacks
scientific approach.
The scientific approach of forecasting sales is to adopt the method of least squares or a
simple to regression approach.
• Trend projection • Regression technique
• Moving average method • Leading indicators method
Trend projection or mechanical exploration method
When time series data is available rdating to the sales of a product, trend projection method is
applied. Time series data of sales includcs cyclic changes in sales (c), seasonal variations(s),
trend (t) and irregular movemcnts (I).
sales = f (T, C, S, I)
Trend shows the long time tendency of the data. It is the result of changes in population.
Level of income, competitive conditions, changes in capital technology etc.
Cyclic changes in sales arise due to the periodical swings in the level of economic
activity such as prosperity or recessionary forces operating in the economy. These changes
are longer in duration and studying these variables is necessary for identifying the turning
points. Understanding cyclical changes is rather difficult, as these fluctuations do not follow a
regular course.
Seasonal variations in sales occur at particular points of time in a year. The seasonal
changes may take the form of climatic variations, festival seasons, holidays, marriage season
etc. Seasonal indices help in estimating seasonal fluctuations.
Irregular variations are non-measurable. Who can predict when an ealihquake, cyclone,
war, or an epidemic breaks out? A fter deducting the estimated sales attributable to the other
three variables, the residue is irregular changes.
Table 2.1 Trend projection
Year Sales in '000 units
1995 25
1996 23
1997 30
1998 35
1999 43
2000 54
2001 49
2002 58
By fitting a trend line to the time series data demand forecast are obtained. Several
methods are available to analyze the time series data. The simplest method is assumed that the
four components of the time series data are related in an additive or mUltiplicative function.
In an additive function
Sales = T 1- C + S + I
In a multiplicative function
Sales = T x Cx Sx
[
Nole that in a multiplicative function if the value of any one variable is zero the sum of
the product would be zero. Therefore, it is assumed that the value of each variable is greater
than zero.
By using logarithms the multiplicative function is converted into an additive function
Log of sales = Log T + Log C t Log S + Log I
Whether one uses the additive or multiplicative function the trend value will be the same
but the seasonal and irregular variable values of sales data varies in both the functions.
Free hand method of trend projection
This is the easiest way of forecasting the demand. In this method, Time series data is plotted
on a diagram and a free hand trend line will be fitted in such a way that it passes through the
closest points on the scatter diagram as illustrated through the Table
The yearly sales data is represented on a graph and then by simple observation a trend
line fitted. By extending the trend line to 2003 or 200--l the sales fiJrecasts for the two subsequent
years can be obtained. Though, this method is easy and simple to forecast the sales yet it lacks
scientific approach.
The scientific approach of forecasting sales is to adopt the method of least squares or a
simple to regression approach.
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