8.2 Forecasting technique - Time series analysis

Question 1

A time series is a

Answer 1

• Series of values for a variable which changes over time
• Where the variable is subject to seasonal variations it will be measured at regular intervals
• It is often shown as a histogram showing a basic trend line and the actual data line

Question 2

Components of a time series

Answer 2

• The basic trend (T) - long term
• Seasonal variations (S) - short term
• Cyclical variations (C) - medium to long term
• Residual variations (R) - short term

Question 3

The basic trend refers to

Answer 3

The general direction of the graph of a time series over a long interval of time once the short term variations have been smoothed out

Question 4

Seasonal variations are

Answer 4

• Short term fluctuations in value due to different circumstances which occur at different times of the year, week, day, etc
• Some seasons are better than average (the trend) and some worse
• If there is a straight line trend in the time series then the seasonal variations must cancel each other out (total of seasonal variations over each cycle should be zero)

Question 5

Cyclical variations are

Answer 5

• Medium to long term fluctuations about the basic trend
• These cycles are rarely of consistent length and do not necessarily follow similar patterns
• They are usually associated with the economy, such as intervals of boom, decline, recession and recovery

Question 6

Time series analysis is a technique for analysing a time series in order to

Answer 6

• Identify whether there is an underlying historical trend (T) and if there is measure it
• Use this analysis of the historic trend to forecast the trend into the future
• Identify whether there are any seasonal variations (S) around the trend and if there are measure them
• Apply estimated seasonal variations to a trend line forecast in order to prepare a forecast season by season

Question 6

Residual or random variations are the

Answer 6

• Irregular items due to chance events such as pandemics, floods, strikes, etc
• They are unpredictable and therefore cannot play a large part in forecasting
• The residual is the difference between the actual value and the figure predicted using the trend, the cyclical variation and the seasonal variation
• It is important to extract any significant residual variations from the time series data before using them for forecasting

Question 7

Three main methods for calculating the underlying trend of the data

Answer 7

• Inspection - The trend line can be drawn by eye with the aim of plotting the line so that it lies in the middle of the data
• Least squares regression analysis (also high-low) - The x axis represents time and the periods of time are numbers
• Moving averages - Attempts to remove seasonal or cyclical variations by a process of averaging

Question 8

Models to predict future values for seasonal variation

Answer 8

• The additive model
• The multiplicative model

Question 9

The additive model formula

Answer 9

The four components of the time series are expressed as absolute values which are simply added together to produce the actual figures:
Actual / prediction = T + S (simplified version) + C +R
Therefore: S = Actual - T (difference between computed trend figure and original time series figure)

Question 10

The additive model results

Answer 10

• A seasonal variation can be calculated for each period in the trend line
• Seasonal variation is positive: actual value > trend value
• Seasonal variation is negative: actual value < trend value
• An average variation for each season is calculated and the sum of seasonal variations has to be zero
• If they do not add up to zero, the seasonal variations should be adjusted so that they do add up to zero

Question 11

The multiplicative model

Answer 11

• The seasonal variation is expressed as a ratio / proportion / percentage
• To find forecast figures multiply the trend figure by the seasonal variation percentage
  Actual / prediction = T x S (simplified version) x C x R