IEEE Computational Intelligence Magazine - November 2020 - 37
the maximum lag (L max) can be obtained from the following equation [24],
1
L max = ;12 # ` n j4 E (4)
100
where n is the sample size and [$] indicates the integer part of a
number. Regarding the examples of this paper n = 80, a maximum lag (L max) 11 is obtained. Three different values of 7, 9,
and 11 for lags are considered for the KPSS test.
TABLE I The date of the start and end of lockdown phases
in India as of 24 March, 2020.
LOCKDOWN PHASE
TIME PERIOD
I
24/03/2020-13/04/2020
II
14/04/2020-3/05/2020
III
3/05/2020-17/05/2020
IV
17/05/2020-31/05/2020
V
31/05/2020-8/06/2020
UNLOCK
8/06/2020-21/06/2020 (ONGOING)
0.16
0.14
0.14
0.12
0.12
Transmission Rate
Transmission Rate
; z ; 1 1 implies the signal is stationary, 2) ; z ; 2 1 shows that
the signal is non-stationary, and 3) ; z ; = 1, represents a random
walk model [22], [23].
In this paper, the Kwiatkowski-Phillips-Schmidt-Shin
(KPSS) test is run on each signal to explore the stationary
and non-stationary nature of the signal. The KPSS test is
used for testing a null hypothesis of stationary time series
(no unit root) around a deterministic trend (i.e. trend-stationary) against the alternative of non-stationary (unit
root) [24]. The null hypothesis of trend stationary of the
signal is tested against the alternative hypothesis of trend
non-stationary. The test can be conducted on several autocovariance lags in the Newey-West estimator [25] of the
long-run variance, each conducted at 0.1 significance level
using Matlab.
However, before running a KPSS test, one needs to
select an appropriate lag length for the time series. Care
must be taken to ensure that an appropriate lag length is
chosen. For instance, if the lag length is too short, the test
will be biased; if the lag length is too large, the power of
the test will suffer. A common rule of thumb for determining
0.1
0.08
0.06
0.04
0.08
0.06
0.04
0.02
0.02
0
0.1
0
10
20
30
40 50
Day
(a)
60
70
80
0
90
0
10
20
30
40 50
Day
(b)
60
70
80
90
0
10
20
30
40 50
Day
(d)
60
70
80
90
0.14
0.2
0.15
Transmission Rate
Transmission Rate
0.12
0.1
0.05
0.1
0.08
0.06
0.04
0.02
0
0
0
10
20
30
40 50
Day
(c)
60
70
80
90
-0.02
FIGURE 2 Calculated rough (a, b) and smoothed (c, d) transmission rates of COVID-19 corresponding to Maharashtra and Tamil Nadu for different lockdown phases as of 24 March, 2020. (a) Maharashtra. (b) Tamil Nadu. (c) Maharashtra, smoothed. (d) Tamil Nadu, smoothed.
NOVEMBER 2020 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE
37
IEEE Computational Intelligence Magazine - November 2020
Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - November 2020
Contents
IEEE Computational Intelligence Magazine - November 2020 - Cover1
IEEE Computational Intelligence Magazine - November 2020 - Cover2
IEEE Computational Intelligence Magazine - November 2020 - Contents
IEEE Computational Intelligence Magazine - November 2020 - 2
IEEE Computational Intelligence Magazine - November 2020 - 3
IEEE Computational Intelligence Magazine - November 2020 - 4
IEEE Computational Intelligence Magazine - November 2020 - 5
IEEE Computational Intelligence Magazine - November 2020 - 6
IEEE Computational Intelligence Magazine - November 2020 - 7
IEEE Computational Intelligence Magazine - November 2020 - 8
IEEE Computational Intelligence Magazine - November 2020 - 9
IEEE Computational Intelligence Magazine - November 2020 - 10
IEEE Computational Intelligence Magazine - November 2020 - 11
IEEE Computational Intelligence Magazine - November 2020 - 12
IEEE Computational Intelligence Magazine - November 2020 - 13
IEEE Computational Intelligence Magazine - November 2020 - 14
IEEE Computational Intelligence Magazine - November 2020 - 15
IEEE Computational Intelligence Magazine - November 2020 - 16
IEEE Computational Intelligence Magazine - November 2020 - 17
IEEE Computational Intelligence Magazine - November 2020 - 18
IEEE Computational Intelligence Magazine - November 2020 - 19
IEEE Computational Intelligence Magazine - November 2020 - 20
IEEE Computational Intelligence Magazine - November 2020 - 21
IEEE Computational Intelligence Magazine - November 2020 - 22
IEEE Computational Intelligence Magazine - November 2020 - 23
IEEE Computational Intelligence Magazine - November 2020 - 24
IEEE Computational Intelligence Magazine - November 2020 - 25
IEEE Computational Intelligence Magazine - November 2020 - 26
IEEE Computational Intelligence Magazine - November 2020 - 27
IEEE Computational Intelligence Magazine - November 2020 - 28
IEEE Computational Intelligence Magazine - November 2020 - 29
IEEE Computational Intelligence Magazine - November 2020 - 30
IEEE Computational Intelligence Magazine - November 2020 - 31
IEEE Computational Intelligence Magazine - November 2020 - 32
IEEE Computational Intelligence Magazine - November 2020 - 33
IEEE Computational Intelligence Magazine - November 2020 - 34
IEEE Computational Intelligence Magazine - November 2020 - 35
IEEE Computational Intelligence Magazine - November 2020 - 36
IEEE Computational Intelligence Magazine - November 2020 - 37
IEEE Computational Intelligence Magazine - November 2020 - 38
IEEE Computational Intelligence Magazine - November 2020 - 39
IEEE Computational Intelligence Magazine - November 2020 - 40
IEEE Computational Intelligence Magazine - November 2020 - 41
IEEE Computational Intelligence Magazine - November 2020 - 42
IEEE Computational Intelligence Magazine - November 2020 - 43
IEEE Computational Intelligence Magazine - November 2020 - 44
IEEE Computational Intelligence Magazine - November 2020 - 45
IEEE Computational Intelligence Magazine - November 2020 - 46
IEEE Computational Intelligence Magazine - November 2020 - 47
IEEE Computational Intelligence Magazine - November 2020 - 48
IEEE Computational Intelligence Magazine - November 2020 - 49
IEEE Computational Intelligence Magazine - November 2020 - 50
IEEE Computational Intelligence Magazine - November 2020 - 51
IEEE Computational Intelligence Magazine - November 2020 - 52
IEEE Computational Intelligence Magazine - November 2020 - 53
IEEE Computational Intelligence Magazine - November 2020 - 54
IEEE Computational Intelligence Magazine - November 2020 - 55
IEEE Computational Intelligence Magazine - November 2020 - 56
IEEE Computational Intelligence Magazine - November 2020 - 57
IEEE Computational Intelligence Magazine - November 2020 - 58
IEEE Computational Intelligence Magazine - November 2020 - 59
IEEE Computational Intelligence Magazine - November 2020 - 60
IEEE Computational Intelligence Magazine - November 2020 - 61
IEEE Computational Intelligence Magazine - November 2020 - 62
IEEE Computational Intelligence Magazine - November 2020 - 63
IEEE Computational Intelligence Magazine - November 2020 - 64
IEEE Computational Intelligence Magazine - November 2020 - 65
IEEE Computational Intelligence Magazine - November 2020 - 66
IEEE Computational Intelligence Magazine - November 2020 - 67
IEEE Computational Intelligence Magazine - November 2020 - 68
IEEE Computational Intelligence Magazine - November 2020 - 69
IEEE Computational Intelligence Magazine - November 2020 - 70
IEEE Computational Intelligence Magazine - November 2020 - 71
IEEE Computational Intelligence Magazine - November 2020 - 72
IEEE Computational Intelligence Magazine - November 2020 - 73
IEEE Computational Intelligence Magazine - November 2020 - 74
IEEE Computational Intelligence Magazine - November 2020 - 75
IEEE Computational Intelligence Magazine - November 2020 - 76
IEEE Computational Intelligence Magazine - November 2020 - Cover3
IEEE Computational Intelligence Magazine - November 2020 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202311
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202308
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202305
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202302
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202211
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202208
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202205
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202202
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202111
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202108
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202105
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202102
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202011
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202008
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202005
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_202002
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201911
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201908
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201905
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201902
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201811
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201808
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201805
https://www.nxtbook.com/nxtbooks/ieee/computationalintelligence_201802
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring17
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring16
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring15
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring14
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_summer13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_spring13
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_winter12
https://www.nxtbook.com/nxtbooks/ieee/computational_intelligence_fall12
https://www.nxtbookmedia.com