IEEE Computational Intelligence Magazine - November 2020 - 41

Temperature (°C)

evident from the KPSS test results, the first
A set of multivariate stacked RNNs is developed to
IMF of this decomposition in both cases is
non-stationary while the remainder are staforecast the future values of each CC-IMF signals
tionary (Tables IV and V).
using the results of the previous section.
The same procedure is followed for signals
T and H corresponding to Maharashtra (Figures 8 and 9) and Tamil Nadu (Figures 10
and 11). These signals are first decomposed into three IMFs,
35
then the KPSS test is run on each IMF.
Tables VI and VII show respectively the results of KPSS tests
34
run on IMFs of signals T and H corresponding to Maharashtra.
There is no non-stationary trend in the IMFs of these signals.
33
Likewise, Tables VIII and IX show respectively the results of
KPSS tests run on IMFs of signals T and H corresponding to
32
Tamil Nadu. As expected, regarding the H signal, H-IMF1 has a
non-stationary trend whereas other IMFs are stationary. As for
31
the T signal, all IMFs show stationary trends again as expected.
The following conclusions can be made from the decom30
position and KPSS test results. Regarding the decomposition of
29
signals corresponding to Maharashtra:
0 10 20 30 40 50 60 70 80
1)	Signals CC-IMF1 (Figure 6(a)) and TR (Figure 2(c)) are
Day
trend non-stationary and, therefore, are used to train a
(a)
separate RNN.
2
2)	Signals CC-IMF2 (Figure 6(b)), T-IMF2 (Figure 8(b))
1.5
and H-IMF2 (Figure 9(b)) are stationary and have sim1
ilar center frequencies of 0.1423, 0.1507, and 0.1858
respectively and, therefore, are used to train a separate
0.5
RNN.
0
3)	Signals CC-IMF3 (Figure 6(c)), T-IMF3 (Figure 8(c)) and
-0.5
H-IMF3 (Figure 9(c)) are stationary and have similar center frequencies of 0.3480, 0.3986, and 0.3860 respectively
-1
and, therefore, are used to train a separate RNN.
-1.5
4)	Signals T-IMF1 (Figure 8(a)) and H-IMF1 (Figure 9(a))
are stationary but are excluded from training process as
-2
0 10 20 30 40 50 60 70 80
they have no similarity to any other stationary IMFs in
Day
terms of center frequency.
(b)
Regarding decomposition of signals corresponding to
2
Tamil Nadu:
Temperature (°C)

90

90

TABLE IV KPSS test for the IMFs corresponding to the signal
CC of Maharashtra.
SIGNAL

LAG

P-VALUE

H

ST

CC-IMF1

7, 9, 11

0.02, 0.03, 0.04

1, 1, 1

✕

CC-IMF2

7, 9, 11

0.10, 0.10, 0.10

0, 0, 0



CC-IMF3

7, 9, 11

0.10, 0.10, 0.10

0, 0, 0



Temperature (°C)

1.5
1
0.5
0

-0.5
-1
-1.5
-2

TABLE V KPSS test for the IMFs corresponding to the signal
CC of Tamil Nadu.
SIGNAL

LAG

P-VALUE

H

ST

CC-IMF1

7, 9, 11

0.01, 0.01, 0.02

1, 1, 1

✕

CC-IMF2

7, 9, 11

0.10, 0.10, 0.10

0, 0, 0



CC-IMF3

7, 9, 11

0.10, 0.10, 0.10

0, 0, 0



0

10

20

30

40 50
Day
(c)

60

70

80

90

FIGURE 8 IMFs corresponding to the decomposition of temperature
(T) time series of Maharashtra along with their center frequencies,
(a) T-IMF1, ~ 1 = 10 -5 . (b) T-IMF2, ~ 2 = 0.1507. (c) T-IMF3,
~ 3 = 0.3986.

NOVEMBER 2020 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE

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IEEE Computational Intelligence Magazine - November 2020

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