Chapter 5: Forecasting - statistical tehniques (Part 1) Flashcards
Quantitative techniques to improve the accuracy of a budget
-Time series analysis
-Linear Regression
-Index numbers
What is Time Series Analysis?
A time series analysis is a series of figures recorded over a period of time.
For example: Sales per month for the last 3 years
Most time series analysis are made up of patterns within the figures and if we can identify the patterns this can allow us to predict what will happen to the time series in the future.
Components of a time series analysis?
2 quantitative
2 theory
-Trend
-Seasonal variation
-Cyclical variation
-Random Variation
Time series analysis - Trend
The trend is the underlying long term movement in a constant direction, over a prolonged period of time.
For example - there is a probably an upward trend in sales of smart phones over the last five years
Time Series Analysis - Seasonal Variation
Seasonal Variation are predictable, recurring fluctuations over the short-term, typically of up to a year in duration.
For example - if we are an ice cream retailer there is likely to be a repeating pattern within our sales figures showing that sales in summer months are higher on average.
Seasonal Variations do not just have to occur over a year, there could be repeating pattern on a weekly basis.
Time Series Analysis - Cyclical variation
Cyclical variation are recurring patterns like seasonal variations but tend to occur over a longer period of time which is not usually of fixed length. An example would be the economic cycle.
Time Series Analysis - Random Variation
Random variations are unpredictable fluctuations caused by random events such as a natural disasters. An example of this may be the unusually high sales of umbrellas in June 2006 due to unusually wet weather conditions. This is not a pattern that is expected to repeat and is impossible to predict in advance.
Time Series Models - The additive model
The components are assumed to add together to give the time series:
TS = T + SV
Positive seasonal variation = normally above trend
Negative seasonal variation = normally below trend
Time Series Models - The multiplicative (or proportional) model
The components are assumed to add together to give the time series:
TS = Time * Seasonal variation
Expressed as a percentage or fraction of the trend
A seasonal variation above 100% implies that the period involved is normally above trend
A seasonal variation below 100% implies that the period involved is normally below trend
De-seasonalising data
De-seasonalising data is when the seasonal variation is removed to leave the trend.
Re-arrange the formula to get what Trend equalls
Using moving averages to find the trend within time series averages
Step 1 - Find the trend
(work out 3-period moving average for example)
Step 2 - Identify seasonal variation
(Compare actual time series to trend figures)
Step 3 - Forecasting future figures
Linear Regression (method of ‘least squares’) formula
y = a + bx
y = Total costs as measured by the upright y-axis on the graph
a= point that the line intercepts the y-axis which is the fixed cost
b = slope of the line which is the variable cost per unit
x = volume of production measured by the flat x-axis on the graph
Assumptions and limitations of forecasting the trend using past data
Observations may not be typical of normal behavior. It is always best to use as much past data as possible to improve accuracy of the calculations.
Using historic data may not be meaningful for forecasting future results as patterns can change over time.
Assumes linear relationship between two variables which is unlikely in the real world.
The reliability of the trend line depends on how closely the data fits the line of best fit. In some situations the line of best fit may not be a representative of the historic data.
Many other factors may affect variables, for example: Costs are not just affected by changes in volume
