Time Series and Trend Analysis

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

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. Y is the given data X is the year value in relation to the middle year Yt = 18.3 + 1.03x 2001 Yt = 18.3 + 1.03(6) = 18.3 + 6.18 = 22.48 Expected sales for 2001 = $22,480,000 Least-Squares Method Example • Annual soft drink sales • Find the expected sales for 2001

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