1. Time Series and Trend Analysis

2. Time Series Time series examines a series of data over time
In studying the series, patterns become evident and these patterns are used to assist with future decision making
Time series relies on the following;
Identification of the underlying trend line
Measurement of past patterns and the assumption that these patterns will be repeated in the future
Forecast of future trends of data

3. Components of Time Series
The four main components of time series are;
Secular trend
Cyclical movement
Seasonal movement
Irregular movement

4. 1. Secular Movement
A secular trend identifies the underlying trend of the data
It is the long term direction of the data, usually described by the ‘line of best fit’
The secular trend is influenced by;
Population
Productivity improvement
Technological changes
Market changes
The most common methods for depicting the secular trends are;
Freehand drawing
Semi-average
Least-squares method
Exponential smoothing

5. 1a Freehand Drawing
Freehand drawing involves plotting the data on a scatter diagram
From the plots you should be able to get an idea of the trend

6. 1b Semi-Averages The semi-average technique is as follows;
Divide the data into two equal time ranges
Average each of the two time ranges
Draw a straight line through the two points

7. Semi-Averages Example
Annual soft drink sales

8. Class Exercise 2
Calculate the co-ordinates for the semi average trend line
Graph the data and draw the trend line
Estimate the value for year 12 using the line of best fit

9. 1c Moving Average
The technique for finding a moving average for a particular observation is to find the average of the m observations before the observation, the observation itself and the m observations after the observation
Thus a total of (2m + 1) observations must be averaged each time a moving average is calculated

10. Moving Average Example
Annual soft drink sales

11. Class Exercise 1 Calculate the following;
The trend line for a three year moving average
The trend line for a five year moving average
Year
Data
3yr MT
3yr MA
5yr MT
5yr MA 1 2 3 4 5 6 7 8 9

12. 1d Least-Squares Method
This method uses the given series of data to develop a trend line for predictive purposes
The least-squares method establishes a trend line from;
Yt = a + bx where a =
b =

13. Least-Squares Method Example
Annual soft drink sales
Find the expected sales for 2001
Yt = x
2001 Yt = (6) =
= 22.48
Expected sales for 2001 = $22,480,000
Y is the given data
X is the year value in relation to the middle year

14. 2. Cyclical Variation
Cyclical variations have recurring patterns over a longer and more erratic time scale
There are a number of techniques for identifying cyclical variation in a time series
One method is the residual method

15. 3. Seasonal Variation
The seasonal variation of a time series is a pattern of change that recurs regularly over time
Seasonal variations are usually due to the differences between seasons and to festive occasions
Time series graphs may be prepared using an adjustment for seasonal variations
Such graphs are said to be seasonally adjusted

16. 4. Irregular Variation
Irregular variation in a time series occurs over varying (usually short) periods
It follows no regular pattern and is by nature unpredictable