Time Series and Trend Analysis

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

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

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

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

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

Semi-Averages Example Annual soft drink sales

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

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

Moving Average Example Annual soft drink sales

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

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 =

Least-Squares Method Example Annual soft drink sales Find the expected sales for 2001 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 Y is the given data X is the year value in relation to the middle year

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

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

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