Second differencing in time series can help to eliminate which trend? (I) Quadratic trend (II) Linear trend
Only (I)
For a series with trend \(Y_t = a + bt + ct^2 + \epsilon_t\), applying the difference operator \(\Delta\) once removes the constant and reduces the polynomial degree by one, leaving a linear trend in \(\Delta Y_t\). Applying \(\Delta\) a second time gives:
\[\Delta^2 Y_t = 2c + (\epsilon_t - 2\epsilon_{t-1} + \epsilon_{t-2})\]
which is stationary, so the quadratic component is eliminated. A pure linear trend is already removed by first differencing; second differencing is specifically the tool for a quadratic trend. Hence only statement (I) holds — Only (I).
Similar Questions
What is the mode of the given data?
5, 7, 9, 7, 3, 7, 5, 7, 8, 6, 7
The prices (in Rs) of different yarns (per kg) in two consecutive years are as follows.
Commodity
Silk
Cotton
Jute
Rayon
Price(in 2016)
600
700
400
300
Price (in 2017)
700
600
480
270
By simple aggregative method, the net price changes in % is:
The 4 th decile for the given data is:
x
f
0
1
1
9
2
26
3
59
4
72
5
52
6
29
7
7
8
1
If the random sample size n is drawn without replacement from a finite population of size N, the correction factor for standard error of sample mean will be:
For the given figures of production of a sugar factory, the estimate of the production for 1976 using straight line trend with origin at the year 1972 by the least squares method (∑x = 0, ∑x 2= 28, ∑xy = 56) is:
Year
Production(‘000 tons) (year)
1969
76
1970
87
1971
95
1972
81
1973
91
1974
96
1975
90
Which of the following methods is NOT used in computation of a seasonal index for time series?
With reference to index numbers, which of the following statements is true?
Marshall-Edgeworth Index number.
By the method of moving averages, the seasonal index for four quarters equals to:
The null hypothesis in ANOVA one-way classification, the study of the variances due to k different sources, is:
Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
What will be the difference between mean and median of the given data?
21, 11, 27, 8, 5, 12, 7, 23, 3, 14, 9, 19Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
