Trends, Forecasts and Patterns

Question 1

Business Strategy Issues

Answer 1

Long term trend - T
Seasonal variations - S
Cyclical variations - C
Random variations - R

Question 2

Time Series Analysis

Answer 2

Involves the analysis of past observations in order to forecast a variable into the future

Question 3

Steps of Time Series Analysis

Answer 3

Find the trend
Calculate the seasonal variation
Forecast the next year of numbers

Seasonal variation can be found through additive model or multiplicative model

Question 4

Additive Model

Answer 4

Used when seasonal variations are fixed amounts. On a graph, the gap above and below the trendline remains consistent over time

Question 5

Multiplicative Model

Answer 5

Used when seasonal variations are a percentage amount. On a graph, the gap above and below the trendline is always getting bigger over time

Question 6

Forecasting on a Graph

Answer 6

To forecast using a graph, simply extend the graph, using the same patterns found in previous periods

Question 7

Adjusting the Trend Line: Additive Model

Answer 7

Additive model assumes variations to be a consistent amount:

Y = T + S + C + R

Y is income
T is long term trend
S is seasonal variation
C is cyclical variation
R is random variation

Question 8

Adjusting the Trend Line: Multiplicative Model

Answer 8

Additive model assumes the seasonal variation to be a constant proportion:

Y = T x S x C x R

Y is income
T is long term trend
S is seasonal variation
C is cyclical variation
R is random variation

Question 9

Calculating the Adjusted Value Using the Multiplicative Model

Answer 9

Actual value
Adjusted value = ——————————-
Seasonal component

Can be rearranged to find seasonal comp or actual value

Question 10

Calculating the Adjusted Value Using the Additive Model

Answer 10

Adjusted value = trend + seasonal component

Question 11

Forecasting Future Sales Figures Using a Sales Equation

Answer 11

Step 1: calculate the trend
Step 2: calc seasonal variation using additive variation (units sold - trend)
Step 3: forecast sales using additive variation (the equation)
Step 4: Calculate the seasonal variations using multiplicative variation (% difference between actual figures and the trend)
Step 5: forecast sales using multiplicative variation (trend figures x by %)

Question 12

Calculating the Trend Given the Actual Sales and the Seasonal Variation

Answer 12

Step 1: express multiplicative variation as a decimal (e.g. 8% = 1.08)
Step 2: use the addictive model formula to calculate the trend:
Y = T + S, rearranged as
Y
T = —–
S

Question 13

Finding the Linear Trendline Using the Least Squares Method

Answer 13

T = a + bt

T = trend
a = where the trendline cuts the vertical axis at 0
b = increase or decrease in one time period
t = time period

Question 14

The Increase or Decrease in One Time Period in a Linear Trend

Answer 14

NΣxy - ΣxΣy
b = ——————-
NΣx² - (Σx)²

b = increase or decrease in one time period
x = the quarter number
y = the actual data
n = the number of items of data

Question 15

Where the Trendline Cuts the Vertical Axis at Time 0

Answer 15

a = ȳ - bx̄

b = increase or decrease in one time period
x̄ = average of x
ȳ = average of y

Question 16

Forecasting a Trendline Using Linear Regression

Answer 16

Step 1: find the trend line using the least squares method

Step 2: trend line forecasts

Question 17

Variances Around the Trendline: Seasonal Variation

Answer 17

 Trend

Question 18

Calculating Variances Around the Trendline

Answer 18

Step 1: work out the trend for previous periods
Step 2: calculate the seasonal variations
Step 3: work out the average (mean) seasonal variation
Step 4: make a prediction taking into account seasonal variations