BS6_Measurement of Trend.pptx

Business Statistics - II B.Com.

1. Measurement of Trend Dr. R. Muthu krishnaveni Assistant professor

2. Secular Trend It is a long term movement in Time series. The general tendency of the time series is to increase or decrease or stagnate during a long period of time is called the secular trend or simply trend. Population growth, improved technological progress, changes in consumers taste are the various factors of upward trend. We may notice downward trend relating to deaths, epidemics, due to improved medical facilities and sanitations. Thus a time series shows fluctuations in the upward or downward direction in the long run

3. Methods of Measuring Trend Trend is measured by the following mathematical methods. 1. Graphical method ( F reehand Method) 2 . Method of Semi-averages 3 . Method of moving averages 4 . Method of Least Squares

4. Graphical Method This is the easiest and simplest method of measuring trend. In this method, given data must be plotted on the graph, taking time on the horizontal axis and values on the vertical axis. Draw a smooth curve which will show the direction of the trend. While fitting a trend line the following important points should be noted to get a perfect trend line. ( i ) The curve should be smooth. (ii) As far as possible there must be equal number of points above and below the trend line. (iii) The sum of the squares of the vertical deviations from the trend should be as small as possible. (iv) If there are cycles, equal number of cycles should be above or below the trend line. (v) In case of cyclical data, the area of the cycles above and below should be nearly equal.

5. Example Measure the trend using the method of the freehand curve from the given data of production of wheat in a particular area of the world . Years 1981 1982 1983 1984 1985 1986 1987 1988 1989 Production Million Metric Tons 6.6 6.9 5.6 6.3 8.4 7.2 7.2 8.5 8.5

6. Solution

7. Merits 1. It is the simplest and easiest method. It saves time and labour. 2. It can be used to describe all kinds of trends. 3. This can be used widely in application. 4. It helps to understand the character of time series and to select appropriate trend .

8. Demerits 1. It is highly subjective. Different trend curves will be obtained by different persons for the same set of data. 2. It is dangerous to use freehand trend for forecasting purposes. 3. It does not enable us to measure trend in precise quantitative terms.

9. Method of semi averages In this method, the given data is divided into two parts, preferably with the same number of years. For example, if we are given data from 1981 to 1998 i.e., over a period of 18 years, the two equal parts will be first nine years, i.e., 1981 to 1989 and from 1990 to 1998. In case of odd number of years like 5,7,9,11 etc , two equal parts can be made simply by omitting the middle year. For example, if the data are given for 7 years from 1991 to 1997, the two equal parts would be from 1991 to 1993 and from 1995 to 1997, the middle year 1994 will be omitted. After the data have been divided into two parts, an average of each parts is obtained. Thus we get two points. Each point is plotted at the mid-point of the class interval covered by respective part and then the two points are joined by a straight line which gives us the required trend line. The line can be extended downwards and upwards to get intermediate values or to predict future values.

10. Odd number of years Year: 2000 2001 2002 2003 2004 2005 2006 Data: a b c d e f g Semi average   SA1=       SA2=   Year: 2000 2001 2002 2003 2004 2005 2006 Data: a b c d e f g Semi average           Difference in middle periods (DMP)= 2005 –2001 = 4 years Difference in semi averages =SA2 – SA1 =DSA Annual increase in trend = Trend of 2000 = Trend of 2001 - AIT Trend of 2002 = Trend of2001+AIT   d is ignored

11. Even number of years Year: 2000 2001 2002 2003 2004 2005 2006 2007 Data: a b c d e f g h Semi average:         Year: 2000 2001 2002 2003 2004 2005 2006 2007 Data: a b c d e f g h Semi average: Difference in middle periods (DMP)= 2005.5 – 2001.5= 4 years Difference in semi averages =SA2 – SA1 =DSA Annual increase in trend = 𝐷𝑆𝐴/𝐷𝑀𝑃 Trend of 2000 = Trend of 2001 - AIT Trend of 2002 = Trend of2001+AIT

12. Merits and Demerits Merits: 1 . It is simple and easy to calculate 2. By this method every one getting same trend line. 3. Since the line can be extended in both ways, we can find the later and earlier estimates. Demerits : 1. This method assumes the presence of linear trend to the values of time series which may not exist. 2. The trend values and the predicted values obtained by this method are not very reliable.