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# Secular Trend

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### Secular Trend

1. 1. Secular trend or Long Term Trend Basic tendency of a series to grow or decline over a period of time Steady movements over a long time Ex. Temperature of a particular area would change in various seasons but the normal tendency will remain constant
2. 2. How can we determine trend <ul><li>There are four methods to find Trend </li></ul><ul><ul><li>Graphical Method </li></ul></ul><ul><ul><li>(Free hand curve method </li></ul></ul><ul><ul><li>Method of semi average </li></ul></ul><ul><ul><li>Method of moving average </li></ul></ul><ul><ul><li>Method of least square </li></ul></ul>
3. 3. Free hand curve Method <ul><li>Plot the original data on the graph paper </li></ul><ul><li>Draw a smooth free hand line in such a way that it clearly indicates the tendency of the original data . This line is fitted by merely by inspection </li></ul><ul><li>The trend line is drawn in such a manner that area of the curve below the line and above the line are the same </li></ul>
4. 4. Question No 1 <ul><li>With the Help of the Graph Paper obtain the trend Value </li></ul><ul><li>Year 1994 1995 1996 1997 1998 1999 2000 2001 </li></ul><ul><li>Value 64 82 97 71 78 112 115 131 </li></ul>
5. 5. Merit <ul><li>Simplest </li></ul><ul><li>Non Mathematical- No calculations </li></ul><ul><li>Easiest method </li></ul><ul><li>Can Understand The characteristics of TS </li></ul><ul><li>Less Time </li></ul>
6. 6. Limitations <ul><li>Not definite </li></ul><ul><li>We can make different trend lines </li></ul><ul><li>Not suitable fro further analysis </li></ul>
7. 7. Semi -Average Method <ul><li>Divide the original data into two parts </li></ul><ul><li>When the number of years is even no problem. </li></ul><ul><li>If it is odd remove the middle value from the series </li></ul><ul><li>Figures from the two parts are averaged. </li></ul><ul><li>The average for each part is plotted on the graph against the middle years of their respective parts </li></ul><ul><li>The line obtained by joining the two points is the required trend line and may extended both ways to estimate the intermediate or future values </li></ul>
8. 8. Advantage and Disadvantage <ul><li>Those who applied this method will get the same results </li></ul><ul><li>But this method assumes linear relation ship between the plotted points which may not exist in practice </li></ul>
9. 9. Question 1 <ul><li>Fit a trend line to the following data by the method of semi averages and estimate the value for 2004 and 2007 </li></ul><ul><li>Year 91 92 93 94 95 96 97 98 99 00 </li></ul><ul><li>Sales 53 79 76 66 69 94 105 87 79 104 </li></ul><ul><li>(1000 units) </li></ul><ul><li>Year 01 02 03 </li></ul><ul><li>Sales 97 92 101 </li></ul>
10. 10. Home work 1 <ul><li>Apply the method of semi averages for determining the trend of the following data and estimate the values for 2000 </li></ul><ul><li>Years 1993 1994 1995 1996 1997 1998 </li></ul><ul><li>Sales 20 24 22 30 28 32 </li></ul><ul><li>(1000 units) </li></ul>
11. 11. Home work 2 <ul><li>From the following series of annual data ,find the trend line by the method of semi averages . Also estimate the value for 1999. </li></ul><ul><li>Year 90 91 92 93 94 95 96 97 98 </li></ul><ul><li>Actual 170 231 261 267 278 302 299 298 340 </li></ul><ul><li>value </li></ul>