State whether the following statement is True or False: The secular trend component of time series represents irregular variations - Mathematics and Statistics

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MCQ
True or False

State whether the following statement is True or False:

The secular trend component of time series represents irregular variations

Options

  • True

  • False

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Solution

False

Concept: Measurement of Secular Trend
  Is there an error in this question or solution?
Chapter 2.4: Time Series - Q.3

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  2. Plot the original time series and trend values obtained above on the same graph.

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Solution:

Year IMR 3 yearly
moving total
3-yearly moving
average

(trend value)
1980 10
1985 7 `square` 7.33
1990 5 16 `square`
1995 4 12 4
2000 3 8 `square`
2005 1 `square` 1.33
2010 0

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xi
10 15 20 25 30
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Production
xi
35 40 45 50 55

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Solution:

We take origin to 18, we get, the number of accidents as follows:

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2008 21 1 -4 16 -84
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  `sumx_t=68` - `sumu=0` `sumu^2=60` `square`

The equation of trend is xt =a'+ b'u.

The normal equations are,

`sumx_t=na^'+b^'sumu             ...(1)`

`sumux_t=a^'sumu+b^'sumu^2      ...(2)`

Here, n = 9, `sumx_t=68,sumu=0,sumu^2=60,sumux_t=-44`

Putting these values in normal equations, we get

68 = 9a' + b'(0)     ...(3)

∴ a' = `square`

-44 = a'(0) + b'(60)          ...(4)

∴ b' = `square`

The equation of trend line is given by

xt = `square`


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