CH21: Trends, Forecasts and Patterns

Question 1

What is one of the challenges of forecasting?

Answer 1

Variables rarely move in a perfectly uniform manner overtime. There are several causes of these variations over time.

Question 2

What are the causes of variations over time?

Answer 2

1) Long term trend -T - the underlying direction and quantity change over the long term e.g. UK HOUSE PRICES between 1995-2015.
2) Seasonal variations - S- short term trends and fluctuations e.g. higher sales of surfboards in SUMMER
3) Cyclical variations - C - happen over a longer period than seasonal variations (often over many years). e.g. periods of RECESSION in economies which tend to recur every few years.
4) Random variations - R - impossible to forecast. e.g. natural disasters.

Question 3

What is the definition of Time series analysis?

Answer 3

The analysis of PAST observations in order to forecast a variable into a FUTURE period

note. Time series analysis can be used to forecast a seasonal variation into the future

Question 4

What are the 3 steps in time series analysis?

Note. Time series analysis can be used to forecast a seasonal variation into the future

Answer 4

1) Find the trend
2) Calculate the seasonal variation’S’ (also the cyclical ‘C’ and random ‘R’ variations) - using the additive or multiplicative model
3) Forecast the next year of numbers

Question 5

In terms of Time series analysis - how do you find the trend?

Answer 5

Simplest way is to plot the graph and draw line of best fit

Question 6

In terms of time series analysis - how do you calculate the seasonal variation?

Answer 6

2 methods:

1) ADDITIVE model - assumes seasonal variation to be a fixed/constant amount
2) MULTIPLICATIVE model - assumes seasonal variation to be a constant proportion

Question 7

In terms of time series analysis - when do you use the Additive model? and what are the limitations?

Answer 7

Use: when seasonal variations are fixed amounts/stays the same each period (i.e. the gap above and below the trend line remains constant over time)

limitation: difficult to use when organisation grows as you sell more in different seasons

Question 8

In terms of time series analysis - when do you use the Multiplicative model? and what are the limitations?

Answer 8

Use: when seasonal variations are percentage amount (i.e. the gap above and below the trend line is always getting bigger and bigger over time)

limitation: difficult to predict future sales as it assumes that the % seasonal variation from the trend line will always be the same e.g. summer sales will always be 50% higher than winter sales

Question 9

In terms of time series analysis - how do you forecast the next period’s set of numbers graphically (e.g. future sales)?

Answer 9

extend the graph, using same patterns found in previous periods.

Question 10

Formula: Additive model for time series analysis

Answer 10

Y = T+S+C+R

Y= income
T= trend
S = seasonal variation
C = cyclical variation
R= random variation

Question 11

Formula: Multiplicative model for time series analysis

Answer 11

Y= T x S x C x R

Question 12

How do you find the seasonal component/variation using the multiplicative model?

Answer 12

Adjusted value = Actual value / Seasonal component

hence:

Seasonal component = actual value / adjusted value

note. adjusted value refers to revised figures after a seasonal adjustment

Question 13

How do you find the seasonal component/variation using the additive model?

Answer 13

Adjusted value = Trend + Seasonal component

hence

Seasonal component = Adjusted value - trend

Question 14

Assuming sales follow a trend represented by the equation: y = 100+25x

What does x represent?

Answer 14

x = the quarter number i.e. in Q1, x = 1, Q2 x=2 etc

for Q1, the trend would be calculated by

y= 100+ (25 x 1)
y= 125

Question 15

What are the steps to forecast future sales using the trend equation?

Answer 15

1) Calculate the trend
2) Calculate the seasonal variations using either and additive or multiplicative variation
3) Apply this seasonal variation to the trend for future period

To calculate forecasted sales via Additive model - you would do actual units sold minus trend to find the additive variation then add the difference (i.e. the seasonal additive variation) to the future quarters trend to

To calculate forecasted sales via Multiplicative model- calculate percentage difference between the actual sales and trend (i.e. the multiplicative seasonal variation) then apply this % change to the trend for future quarter trends
% difference = (Units sold/trend) -1 x 100

Question 16

Why is the multiplicative model seen as a better option vs. additive model?

Answer 16

Seasonal variations tend to increase/decrease in line with the movement of the trend

i.e. it is unlikely that sales will increase by exactly a fixed amount of units during a certain quarter in a year as suggested by the additive model

Question 17

What is the line of best fit trend line formula? and what does the line of best fit show?

Answer 17

y= a+bx

b= gradient
a= the point where the line cuts the y axis
y and x are variables (y axis and x axis variables)

Shows the trend of data over time, makes it easier to understand the correlation

Question 18

What is the most accurate way to find the LINEAR trendline?

Answer 18

Least squares method

T=a+bt

T=Trend
a=where the line cuts the y axis at time 0
b=increase or decrease in one time period
t=time period

Question 19

What is the formula for Seasonal variation?

Answer 19

Seasonal variation = Actual value/Trend

Question 20

What are the 4 steps to find the average variation?

i.e. calculating the variances around the trendline

Answer 20

1) Workout the trend for previous periods via T=a+bt
2) Calculate the seasonal variations: S= Actual value/Trend
3) Workout the average (mean) seasonal variation
4) Make a prediction taking into account average seasonal variations

Question 21

Why do we need to calculate average variations around the trendline?

Answer 21

Not all correlations are linear hence need to calculate variances around the trend line via average variations