Intervention Analysis for Evaluating The Impact of Policy to Tackle The Increase of COVID-19 Cases and Forecasting The Addition of New Cases COVID-19 per day in South Korea, Singapore, and Indonesia
This document discusses analyzing the impact of COVID-19 intervention policies in South Korea, Singapore, and Indonesia using time series analysis and intervention modeling. It describes South Korea's early aggressive testing and tracing strategy that helped curb infections after an initial spike in late February. The document outlines the ARIMA and intervention modeling methodologies used to evaluate the effectiveness of each country's policies on reducing new daily COVID-19 cases.
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Intervention Analysis for Evaluating The Impact of Policy to Tackle The Increase of COVID-19 Cases and Forecasting The Addition of New Cases COVID-19 per day in South Korea, Singapore, and Indonesia
1. Bayu Imadul Bilad
Master Student of Statistics
Institute of Technology Bandung
Indonesia
Intervention Analysis for Evaluating The
Impact of Policy to tackle the increase of
COVID-19 Cases and Forecasting The
Addition of New Cases COVID-19 per day in
South Korea, Singapore, and Indonesia
2. Since the coronavirus disease 2019 outbreak began in the Chinese city of Wuhan on
Dec 31, 2019, 68 imported cases and more than 2.7 million cases of COVID-19 have
been reported in more than 210 countries and territories. We aimed to investigate
options for early intervention in 3 countries such as Singapore, Indonesia, and South
Korea which did lockdown and rapid test as their policies to prevent the distribution of
COVID-19.
Implementing the combined intervention of quarantining infected individuals and their
family members, workplace distancing, and school closure once community transmission
has been detected could substantially reduce the number of SARS-CoV-2 infections.
Background of
COOVID-19
3. SCOPE OF
THE
PROBLEM
In this study modeling and forecasting time series are
only done on data where the time of the intervention
is known and based on the ARIMA method without
any seasonal influence and random walk.
4. The objective of
this research
• For analyzing the impact of the policy made by the
South Korea, Singapore and Indonesia to tackle
the additional of COVID-19 cases in their own
country.
• For forecasting the additional of new cases of
COVID-19 in South Korea, Singapore, and
Indonesia
6. DATA COLLECTION PROCEDURES OF
COVID-19
The data we used in this study is taken from and collected by Johns
Hopkins Whiting School of Engineering, Center for Systems
Science and Engineering.
Link : https://github.com/CSSEGISandData
They started to collect the COVID-19’s data at January, 22th, 2020.
Data collected is more than 250 countries.
We took 3 countries from 250 countries which did any policy as
intervention affecting pandemic spread. These countries are
Singapore, Indonesia, and South Korea. Every country data that we
took has a different amount of data because every data has their
own characteristic. We took the data for the best model for
forecasting.
7. TIME SERIES
Time series analysis was introduced in 1970 by George E. P.
Box and Gwilym M. Jenkins through his book Time-series
Analysis: Forecasting and Control. Since then, time series
have been developed. The rationale of the time series is
that current observations (Zt) depend on 1 or several
previous observations (Zt-k). In other words, the time series
model is created because statistically there is a correlation
(dependency) between the series of observations.
Various methods have been developed in processing time-
series data to obtain a model that provides more accurate
forecast results. The methods used include the Box-Jenkins
ARIMA method (Box and Jenkins, 1976) which are used to
process univariate time series, and the transfer function
analysis method is used to process multivariate time series
data.
8. TIME SERIES
Analisis time series dikenalkan pada tahun 1970 oleh
George E. P. Box dan Gwilym M. Jenkins melalui bukunya
Time series Analysis: Forecasting and Control. Sejak saat
itu, time series mulai banyak dikembangkan. Dasar
pemikiran time series adalah pengamatan sekarang (Zt)
tergantung pada 1 atau beberapa pengamatan sebelumnya
(Zt-k). Dengan kata lain, model time series dibuat karena
secara statistik ada korelasi (dependensi) antar deret
pengamatan.
Berbagai metode telah dikembangkan dalam mengolah
data time series untuk memperoleh suatu model yang
memberikan hasil ramalan yang lebih akurat. Metode yang
digunakan antara lain adalah metode ARIMA Box-Jenkins
(Box dan Jenkins, 1976) yang digunakan untuk mengolah
time series yang univariat dan metode analisis fungsi
transfer digunakan untuk mengolah data time series
multivariat.
9. FORECASTING BY THE BOX-JENKINS METHOD
Stationary and non-stationary are very basic in the
forecasting process. The main requirement for forecasting
with the Box-Jenkins method is that the data pattern is
horizontal or stationary and does not contain seasonal
elements. If a series of time series data has a relatively
constant average and variance from one time period to the
next, then it can be said that the data is stationary.
Testing stationarity in an average can be used Augmented
Dickey-Fuller test (ADF) while stationarity in variance can
use the Bartlett test. In general, if the data is not stationary
on average, it can be overcome by a differentiating process
and to stabilize the variance value using a box-cox
transformation (Rosadi, 2012).
10. FORECASTING BY THE BOX-JENKINS METHOD
Kestasioneran dan ketidakstasioneran merupakan hal yang
sangat mendasar dalam proses peramalan. Syarat utama
peramalan dengan metode Box-Jenkins adalah pola
datanya horisontal atau stasioner serta tidak mengandung
unsur musiman . Jika serangkaian data deret waktu
memiliki rata-rata dan varians yang relatif konstan dari
suatu periode waktu ke periode waktu yang berikutnya,
maka dapat dikatakan bahwa data tersebut stasioner.
Pengujian stasioneritas dalam rata-rata dapat digunakan uji
Augmented Dickey Fuller (ADF) sedangkan stasioneritas
dalam varians dapat menggunakan uji Bartlett. Pada
umumnya jika data tidak stasioner dalam rata-rata dapat
diatasi dengan proses pembedaan (differencing) dan untuk
menstabilkan nilai varians digunakan transformasi box-cox
(Rosadi, 2012).
11. Time Series Data Stationarity
Stationary is an assumption needed in time series data
analysis, because with this assumption the modeling error
can be minimized. Time series data that meet stationary
assumptions have a constant mean and variety with
covariance and correlations that depend only on time
difference (Wei, 2006).
A time series data Zt is said to be (weakly) stationary if for
each t ∈ Z:
where γk is autocovariance in lag-k, the values µ and γk for
each k are constant.
12. Box-Cox Transformation
In time series that are not stationary in variety, can be strived to become stationary through
transformation (Wei, 2006). Box and Cox in 1964 introduced a transformation of rank:
where λ is the transformation parameter. Box-Cox transform can only be used if the Zt
observation is more than 0. If there is Zt ≤ 0, then a constant c can be added such that Zt + c>
0, ∀t and the Box-Cox transform can be used with Zt + c . This is possible because a constant
can always be added to the data without affecting the correlation value of the data.
13. INTERVENTION
Intervention model is a model which could be
used to evaluate the impact of an intervention
event that is caused by internal or external
factor on a time series dataset (Suhartono,
2007).
According to Wei (1990), a time-series data that
is influenced by several external events called
interventions will result in changes in data
patterns at one-time t. The usual interventions
are holidays, discounts, wars, bombs, natural
disasters, and policy changes. Intervention
analysis is used to measure the magnitude and
duration of intervention effects that occur at
time T
14. INTERVENTION
Intervention model is a model which could
be used to evaluate the impact of an
intervention event that is caused by internal
or external factor on a time series dataset
(Suhartono, 2007).
Menurut Wei (1990) suatu data time series
yang dipengaruhi oleh beberapa kejadian
eksternal yang disebut intervensi akan
mengakibatkan perubahan pola data pada
satu waktu t. Intervensi yang biasa terjadi
adalah adanya masa liburan, potongan
harga, perang, bom, bencana alam, dan
perubahan kebijakan. Analisis intervensi
digunakan untuk mengukur besar dan
lamanya efek intervensi yang terjadi pada
waktu T
15. INTERVENTION
Generally, there are two common types of intervention, i.e., step
and pulse functions. More detail explanations and applications of
intervention analysis can be found in Wei (1990), Bowerman and
O’Connell (1993), Hamilton (1994), Brockwell and Davis (1996),
Tsay (2005) and Suhartono (2007). Intervention model can be
written as
where Yt is a response variable at time t and
Xt is an intervention variable that show
either exist or not the effect of an intervention
at time t. Xt can be step function St or pulse
function Pt.
Then, ωs (B) and δr (B) are defined as
Equation (1) shows that the magnitude and period of intervention
effect is given by b, s, and r. The delay time is shown by b, s gives
information about the time which is needed for an effect of
intervention to be stable, and r shows the pattern of an
intervention effect. The impact of an intervention model on a time
series dataset (Y^t ) is
(1)
(2)
16. Step Function Single Input Intervention Model
Step function is an intervention type which occurs in a long term. For example, the analysis of
new tax system in Australia since September 2000 (Valadkhani and Platon, 2004) had applied
step function intervention. Intervention step function is written below (Wei, 1990)
where the intervention starts at T. Step function single input intervention model with b=2, s=1,
and r=1 can be obtained by substituting Equation (1) into (2)
Therefore, the effect of step function single input intervention is
(3)
(4)
(5)
17. Pulse Function Single Input Intervention Model
An intervention which occurs only in a certain time (T ) is called pulse intervention. The example
of this intervention is public election and 11 September attacked in USA which affected to
unemployment rate in USA (Dholakia, 2003). Pulse intervention function is
Explanation of single input intervention effect with pulse function can be done the same
with step function intervention in Equation (4) until (5).
(6)
18. Multi Input Intervention Model
Multi input intervention model, based on Equation (1), is (Wei, 1990)
or
20. INTERVENTION FUNCTION
The Function of Permanent Direct Interventions
Interventions occur directly at time t = T and the
effect of the intervention takes place
permanently or permanently at time t = T + 1, T
+ 2, ..., n or illustrative can be seen in Figure
Temporary Intervention Function
Interventions occur directly at time t = T but the
effect of the intervention decreases with time t =
T +1, T + 2, ..., n or illustrative can be seen in
Figure
21. INTERVENTION FUNCTION
The Function of Permanent Gradual Interventions
Interventions occur gradually starting from time
t = T and continue to increase slowly over time,
the effect of these interventions takes place
permanently as can be seen in Figure 3.3.
Temporary Gradual Intervention Function
Interventions occur gradually starting from time
t = T and continue to increase until time t = T +
k then after that the effect of the intervention
slowly decreases for t> T + k, illustrating the
pattern of influence of this intervention can be
seen in Figure 3.4.
26. South
Korea’s Data
The WHO praised the way
South Korea handled the
corona virus, both in curbing
its spread and in treating
infected patients. The cure
ratio reached 48%, while the
death rate was only 1.5% on
March 27
2 1 0 0 0 0 1 1 1 0
73
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114110107
76748493
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898694
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2730322527272222188139
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1010101490
100
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500
600
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800
900
10/02/2020
12/02/2020
14/02/2020
16/02/2020
18/02/2020
20/02/2020
22/02/2020
24/02/2020
26/02/2020
28/02/2020
01/03/2020
03/03/2020
05/03/2020
07/03/2020
09/03/2020
11/03/2020
13/03/2020
15/03/2020
17/03/2020
19/03/2020
21/03/2020
23/03/2020
25/03/2020
27/03/2020
29/03/2020
31/03/2020
02/04/2020
04/04/2020
06/04/2020
08/04/2020
10/04/2020
12/04/2020
14/04/2020
16/04/2020
18/04/2020
20/04/2020
22/04/2020
24/04/2020
26/04/2020
28/04/2020
SOUTH KOREA
Starting with one patient in
early February, the number of
Covid-19 cases in South
Korea (South Korea) jumped
dramatically. From an average
of two cases per day, there
were additional new cases of
up to 900 people at the end of
February. This is due to a 61-
year-old woman who was later
identified as Patient 31.
27. STOP
COVID-19
Policies adopted by the Korean
government
Initial March – 24 March 2020
Rapid Test
24 March – 3 April 2020
Social Distancing.
7 May 2020
Expired Social Distancing.
28. Multi Intervention
Scheme
In analyzing this multi intervention, we
divided the data into 3 parts. The green
line is the first intervention which
happened at April 20, 2020, and the red
line is the second intervention, at May
07, 2020. The First intervention is
Massive Rapid Test and The second
intervention is the Opening of several
public sectors. The South Korean time-
series data before the first intervention
and the second intervention are at t <24
and t <86 respectively.
The number of Korea COVID-19 data
taken for analyzing are 87 data which
started from 10 March 2020 until 8 May
2020.
Preintervention
Intervention Effect 1
T1
Intervention Effect 2
T2
29. known that the data of
South Korea before the
intervention increased.
Trend Linear
Preintervention
5 10 15 20
0200400600800
Jumlah Terinfeksi korsel 10 Februari - 28 April 2020
Waktu
Totalterinfeksi
30. Stationary Test of Korean’s COVID Data
First Data Dicky-Fuller
Test
First Differencing Dicky-
Fuller Test
Second Differencing Dicky-
Fuller Test
31. ACF and PACF Korea’s Covid Data
-0.40.00.20.4
Lag
ACF
ACF for Data korselpreintervention
1 2 3 4 5 6 7 8 9 10 12 14
-0.40.00.20.4
Lag
ACF
ACF for Diff 1x korsel preintervention
1 2 3 4 5 6 7 8 9 10 12 14
-0.40.00.20.4
Lag
ACF
ACF for Diff 2x korsel preintervention
1 2 3 4 5 6 7 8 9 10 12 14
-0.40.00.20.4
Lag
PartialACF
PACF for Data korsel preintervention
1 2 3 4 5 6 7 8 9 10 12 14
-0.40.00.20.4
Lag
PartialACF
PACF for Diff 1x korsel preintervention
1 2 3 4 5 6 7 8 9 10 12 14
-0.40.00.20.4
Lag
PartialACF
PACF for Diff 2x korsel preintervention
1 2 3 4 5 6 7 8 9 10 12 14
32. Transformation
BOX-COX
-1.0 -0.5 0.0 0.5 1.0
-350-300-250
log-Likelihood
95%
95% confidence interval for λ.
Korean data from January to May is not
stationary because it has a value of λ =
0.1388286. This is shown by the plot between
the log likelihood with some Lambda values
presented in the Figure beside, where the
maximum log likelihood function is at
0.1388286. To make the data stationary in a
variety, transformation is performed. The Box-
Cox transformation function that corresponds
to λ = 0.1388286 based on the Box-Cox
equation is Yt.
33. Model Identification
> summary(korsel_model_122)
Series: newkorsel
ARIMA(0,2,1)
Box Cox transformation: lambda= 0.5264055
Coefficients:
ma1
-0.9727
s.e. 0.4514
sigma^2 estimated as 51.28: log likelihood=-71.91
AIC=147.82 AICc=148.49 BIC=149.91
Training set error measures:
ME RMSE MAE MPE MAPE MASE ACF1
Training set 16.57357 105.2887 64.4944 9.072488 34.24168 0.8851383 -0.2275212
> coeftest(korsel_model_122)
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
ma1 -0.97270 0.45138 -2.1549 0.03117 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
ARIMA(0,1,0) = random walk:
If the series Y is not stationary, the simplest
possible model for it is a random walk model,
which can be considered as a limiting case of an
AR(1) model in which the autoregressive
coefficient is equal to 1, i.e., a series with
infinitely slow mean reversion. The prediction
equation for this model can be written as:
So We got the model for Korean Data is
ARIMA (0,2,1)
34. Ljung - Box Test for korsel_arima &
Kolmogorov - Smirnov Test
> Box.test(korsel_model_122$residuals, lag =
round(length(newkorsel)/5,0) ,
+ type = "Ljung-Box", fitdf = 1)
Box-Ljung test
data: korsel_model_122$residuals
X-squared = 6.7712, df = 4, p-value = 0.1485
> # --- Kolmogorov - Smirnov Test
> ks.test (korsel_model_122$residuals, "pnorm",
+ mean(korsel_model_122$residuals),
+ sd(korsel_model_122$residuals))
One-sample Kolmogorov-Smirnov test
data: korsel_model_122$residuals
D = 0.19322, p-value = 0.3151
alternative hypothesis: two-sided
37. Forecasting of South Korean Data
before intervention
Based on Figure 3 (a), the data pattern
of the ARIMA model forecasting before
the first intervention (blue line) shows
significant differences from the actual
data pattern (red line). the result of
forecasting using data before the first
intervention shows an increasing trend
while actual data pattern after the first
intervention did decrease abruptly
JumlahTerinfeksi
0 20 40 60 80
0100020003000
24
(t =24)
tskorsel
Peramalan Nt
38. First intervention event which affected Korean
data is T= 24 which is Policy to do Rapid Test.
It is a step function intervention. Based on Figure.
The first step in intervention modeling is
identifying the value of b, s, and r. This
identification is done by evaluating into residual
bar chart of pre-intervention model (Figure 3 (b)).
Based on Figure 3 (b), we got b=0, s=0 and r=2.
The result of parameter estimation and
signification test show that all of parameters are
significant, so intervention model is written as
Identification of Intervention Order of Korea
COVID-19 Data
-10000-6000-2000
Waktu(T)
Residual
T =24
T-24 T-9 T T+33 T+53
39. The intervention model in the equation
above states that the policy for
conducting a rapid test from early March
to 24 March 2020 has a direct effect on
the reduction of positive cases of
COVID-19 in South Korea. The effect of
this decline continues until the last
observation during the study, which is
until May 16, 2020.
Intervention and Outliers Model of South
Korean Data
40. Quantitatively, based on the intervention model in equation (1.a)
and the elucidation of the effect of the intervention on table 1,
showing that the policy of applying the rapid test has a permanent
effect on addition of positive cases of COVID- 19 in South Korea
per day is -26.36. The effect is negative, namely a decrease in the
number of positive cases of COVID- 19.
The effect of South Korea’s first
intervention
Effects of Applying Rapid Test
Time (t) Data Effect's Magnitude
t 24 -23.26
t+1 35 -23.26
t+k 24+k -23.26
41. Significance Test and The Final Model
Model of South Korea COVID-19 Data is ARIMA (0,2,1) + Intervensi (0,2,0)
42. Ljung - Box Test for The Final Model &
Kolmogorov - Smirnov Test
> Box.test(tskorsel_arima$residuals, lag =
round(length(newkorsel2)/5,0) ,
+ type = "Ljung-Box", fitdf = 1)
Box-Ljung test
data: tskorsel_arima$residuals
X-squared = 25.996, df = 16, p-value = 0.05408
> # --- Kolmogorov - Smirnov Test
> ks.test (tskorsel_arima$residuals, "pnorm",
+ mean(tskorsel_arima$residuals),
+ sd(tskorsel_arima$residuals))
One-sample Kolmogorov-Smirnov test
data: tskorsel_arima$residuals
D = 0.15903, p-value = 0.02409
alternative hypothesis: two-sided
The model does not satisfy the Normal
distribution assumptions. P-value < 0.05
43. First Forecasting after Intervention
We have saved several data to compare the result of forecasting and the actual data to
show the accuracy of the model of forecasting.
No of Data Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
86 2 0 17 -1 35
87 1 -2 20 -12 50
88 0 -10 21 -38 62
89 0 -25 20 -80 69
90 0 -49 19 -140 75
91 -1 -82 17 -218 78
92 -3 -125 14 -315 80
93 -6 -180 12 -433 80
94 -12 -246 10 -572 80
95 -19 -325 8 -734 79
0 20 40 60 80
02006001000
44. Identification Second Intervention
The second intervention event which affected South Korea data is
T= 86 which is Policy to allow public to open several public
sectors.
It is a pulse function intervention with the order intervention b = 0,
r = 1, s = 4.
-100102030
Waktu(T)
Residual
T =86
T-66 T-50 T-30 T-10 T+4
0 20 40 60 80
02006001000
Based on Figure beside, the data pattern of the ARIMA model
forecasting before the second intervention (blue line) shows
significant differences from the actual data pattern (red line). the
result of forecasting using data before the second intervention
shows an decrease stably while actual data pattern after the
second intervention did an increase gradually.
45. Quantitatively, an elucidation of the effects of the second intervention shows that there are five different
periods due to the results of the opening of several public sectors to an increase in positive cases of
COVID-19 in South Korea. The effects are positive and negative, namely an increase in and decrease in the
number of positive cases of COVID-19. The first, second, and third periods were increases in the addition
of positive cases of COVID-19 in South Korea, which were 1.27, 0.9, and 0.3 respectively. For the fourth
period, there was a decrease in positive cases of -0.04. Finally, for the fifth, sixth, and T + n periods, the
effect of the second intervention showed an increase of 0.22.
The effect of South Korea’s second
intervention
Effects of the Opening of Several Public Sectors
Time (t) Data Effect's Magnitude
t 86 1.27
t+1 87 1.27 -0.37 = 0.9
t+2 88 1.27 -0.37 - 0.63 = 0.3
t+3 89 1.27 -0.37 - 0.63 -0.34 = -0.04
t+4 90 1.27 -0.37 - 0.63 -0.34 + 0.26 = 0.22
47. Forecasting Model for
South Korea COVID Data
First Model ARIMA Model (0,2,1) + Intv 1 (2,0,2) + Intv 2 (0,1,4)
48. Ljung - Box Test for Singapore Final ARIMA Model &
Kolmogorov - Smirnov Test
> Box.test(tskorsel_arima2$residuals, lag =
round(length(newkorsel3)/5,0) ,
+ type = "Ljung-Box", fitdf = 1)
Box-Ljung test
data: tskorsel_arima2$residuals
X-squared = 28.252, df = 18, p-value = 0.05833
> # --- Kolmogorov - Smirnov Test
> ks.test (tskorsel_arima2$residuals, "pnorm",
+ mean(tskorsel_arima2$residuals),
+ sd(tskorsel_arima2$residuals))
One-sample Kolmogorov-Smirnov test
data: tskorsel_arima2$residuals
D = 0.16244, p-value = 0.01171
alternative hypothesis: two-sided
The model does not satisfy the Normal
distribution assumptions. P-value < 0.05
49. Actual versus Forecasting
We have saved several data to compare the result of forecasting and the actual data to
show the accuracy of the model of forecasting.
0 20 40 60 80
02006001000
Actual 15 13 32 12 20 23 25 16
Forecast 13 14 14 14 14 14 14 15
Error 0.133333 0.076923 0.5625 0.166667 0.3 0.391304 0.44 0.0625
MAPE 27%
50. The Result of Forecasting of
Korea COVID-19 Data
We got the result of forecasting the Korean Data for the next 10 days as shown below :
Q
0 20 40 60 80
02006001000
Date Forecast
25/05/2020 15
26/05/2020 15
27/05/2020 15
28/05/2020 15
29/05/2020 15
30/05/2020 16
31/05/2020 16
01/06/2020 16
02/06/2020 16
03/06/2020 16
52. Singapore’s
COVID Data
The first case relating to the
C O V I D - 1 9 p a n d e m i c i n
Singapore was confirmed on 23
January. Early cases were
primarily imported until local
transmission began to develop
in February and March. By late-
March and April, COVID-19
clusters were detected at multi-
ple dormitories for foreign
workers, which soon contributed
to an overwhelming proportion of
new cases in the country.
Singapore currently has the
highest number of confirmed
COVID-19 cases in Southeast
A s i a , h a v i n g o v e r t a k e n
Indonesia on 19 April.
2 1 0 0 0 0 1 1 1 0
73
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114110107
76748493
152
87
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0
76
100104
91
146
105
78
125
101
898694
81
474753
39
2730322527272222188139
25
1010101490
100
200
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900
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01/03/2020
03/03/2020
05/03/2020
07/03/2020
09/03/2020
11/03/2020
13/03/2020
15/03/2020
17/03/2020
19/03/2020
21/03/2020
23/03/2020
25/03/2020
27/03/2020
29/03/2020
31/03/2020
02/04/2020
04/04/2020
06/04/2020
08/04/2020
10/04/2020
12/04/2020
14/04/2020
16/04/2020
18/04/2020
20/04/2020
22/04/2020
24/04/2020
26/04/2020
28/04/2020
SOUTH KOREA
0
200
400
600
800
1000
1200
1400
1600
05/03/2020
07/03/2020
09/03/2020
11/03/2020
13/03/2020
15/03/2020
17/03/2020
19/03/2020
21/03/2020
23/03/2020
25/03/2020
27/03/2020
29/03/2020
31/03/2020
02/04/2020
04/04/2020
06/04/2020
08/04/2020
10/04/2020
12/04/2020
14/04/2020
16/04/2020
18/04/2020
20/04/2020
22/04/2020
24/04/2020
26/04/2020
28/04/2020
30/04/2020
02/05/2020
04/05/2020
06/05/2020
08/05/2020
10/05/2020
12/05/2020
SINGAPORE
53. STOP
COVID-19
Policies adopted by the Singapore
government
5 March 20 – 20 April 2020
Social Distancing and Lockdown
24 March 20 – 3 April 20
Opening several public sector
54. Multi Intervention
Scheme
95% confidence interval for λ.
In analyzing multi intervention, we divided the
data into 3 parts. The green line is the first
intervention which happened at 20 April 2020,
and the red line is the second intervention, at
2 May 2020. The First intervention is social
distancing and lockdown, and the second
intervention is opening access for public.
Preintervention happened in time t < T1 in
which T1 is first intervention with T1 = 47, and
second intervention T2 = 57.
Preintervention
Intervention Effect 1
Intervention Effect 2
T1
T2
The number of Singapore COVID-19 data
taken to be analyzed are 63 data which
started from March, 5, 2020 until May, 8,
2020.
55. known that the data of
Singapore before the
intervention is
increased.
Trend Linear
Preintervention
0 10 20 30 40
0200600
Jumlah Terinfeksi Singapura 5 Maret - 19 April 2020
Waktu
Totalterinfeksi
56. Stationary Test of Singapore’s COVID Data
First Data Dicky-Fuller
Test
First Differencing Dicky-
Fuller Test
Second Differencing Dicky-
Fuller Test
57. ACF and PACF Singapore’s Covid Data
-0.40.00.20.4
Lag
ACF ACF for Data Korea Selatan preintervention
1 2 3 4 5 6 7 8 9 11 13 15
-0.40.00.20.4
Lag
ACF
ACF for Diff 1x Korea Selatan preintervention
1 2 3 4 5 6 7 8 9 11 13 15
-0.40.00.20.4
Lag
ACF
ACF for Diff 2x Korea Selatan preintervention)
1 2 3 4 5 6 7 8 9 11 13 15
-0.40.00.20.4
Lag
PartialACF
PACF for Data Korea Selatan preintervention
1 2 3 4 5 6 7 8 9 11 13 15
-0.40.00.20.4
Lag
PartialACF
PACF for Diff 1x Korea Selatan preintervention
1 2 3 4 5 6 7 8 9 11 13 15
-0.40.00.20.4
Lag
PartialACF
PACF for Diff 2x Korea Selatan preintervention)
1 2 3 4 5 6 7 8 9 11 13 15
58. Transformation
BOX-COX
95% confidence interval for λ.
Singapore data from March to April is not
stationary because it has a value of λ =
0.2779883. This is shown by the plot between
the log likelihood with some Lambda values
presented in the Figure beside, where the
maximum log likelihood function is at
0.2779883. To make the data stationary in a
variety, transformation is performed. The Box-
Cox transformation function that corresponds
to λ = 0.2779883 based on the Box-Cox
equation is Yt.-1.0 -0.5 0.0 0.5 1.0
-180-140-100-60
log-Likelihood
95%
59. Model Identification
> model_011 <- Arima (newsingapore, order=c(3,2,7) , lambda = lambda.model3,
include.drift =
+ F)
> model_011
Series: newsingapore
ARIMA(3,2,7)
Box Cox transformation: lambda= 0.9884472
Coefficients:
ar1 ar2 ar3 ma1 ma2 ma3 ma4 ma5 ma6
-0.8700 -0.8598 -0.7896 -0.9113 0.8612 -0.4957 -0.4956 0.8612 -0.9113
s.e. 0.1852 0.1480 0.1928 0.2009 0.2776 0.3409 0.3687 0.3390 0.2697
ma7
1.0000
s.e. 0.2215
sigma^2 estimated as 2940: log likelihood=-241.19
AIC=504.39 AICc=512.64 BIC=524.01
> coeftest(model_011)
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
ar1 -0.87000 0.18519 -4.6980 2.628e-06 ***
ar2 -0.85976 0.14804 -5.8077 6.335e-09 ***
ar3 -0.78956 0.19283 -4.0946 4.229e-05 ***
ma1 -0.91131 0.20087 -4.5369 5.709e-06 ***
ma2 0.86122 0.27756 3.1028 0.001917 **
ma3 -0.49565 0.34088 -1.4540 0.145940
ma4 -0.49561 0.36874 -1.3441 0.178925
ma5 0.86119 0.33898 2.5406 0.011067 *
ma6 -0.91128 0.26971 -3.3788 0.000728 ***
ma7 0.99997 0.22146 4.5153 6.324e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
So We got the model for Singapore Data is
ARIMAm(3,2,7)
After going through several selections to determine the best model with all the
requirements fulfilled, we get:
60. Ljung - Box Test for Singapore ARIMA Model &
Kolmogorov - Smirnov Test
> Box.test(model_011$residuals, lag =
round(length(newsingapore)/5,0) ,
+ type = "Ljung-Box", fitdf = 1)
Box-Ljung test
data: model_011$residuals
X-squared = 5.9333, df = 8, p-value = 0.6547
> # --- Kolmogorov - Smirnov Test
> ks.test (model_011$residuals, "pnorm",
+ mean(model_011$residuals),
+ sd(model_011$residuals))
One-sample Kolmogorov-Smirnov test
data: model_011$residuals
D = 0.18568, p-value = 0.07333
alternative hypothesis: two-sided
63. Forecasting of Singapore
Preintervention Model
Based on Figure, the data pattern of
the ARIMA model forecasting before
the first intervention (blue line)
shows significant differences from
the actual data pattern (red line).
The result of forecasting using data
before the first intervention shows
an increasing trend while actual
d a t a p a t t e r n a f t e r t h e f i r s t
i n t e r v e n t i o n d i d a d e c r e a s e
gradually.
JumlahTerinfeksi
0 10 20 30 40 50
05001500
tssingapore
Peramalan Nt
tssingapore
Peramalan Nt
64. First intervention event which affected Singapore
data is T= 47 which is Policy to social distancing
and local isolation.
It is a pulse function intervention. Based on Figure.
The first step in intervention modeling is
identifying the value of b, s, and r. This
identification is done by evaluating into residual
bar chart of pre-intervention model (Figure beside)
Based on Figure beside, we got b=2, s=2 and r=0.
The result of parameter estimation and
signification test show that not all of parameters
are significant only ar1, ar2, ar3, ma2, ma6, ma7,
and which are significant.
-1000-5000
Waktu(T)
Residual
T =47
T-47 T-28 T-21 T+4 T+9
Identification of First Intervention Order of
Singapore COVID-19 Data
65. First Intervention Modeling of
Singapore Data
Intervention Model
The intervention model in the equation
above states that the policy for
conducting a lockdown from 5 March 5,
2020, to April 20, 2020, has a significant
effect in the third period after the first
intervention. The effect of this decline is
temporary until the effect of this
intervention is disappeared, which is
until May 16, 2020.
66. Quantitatively, based on the intervention model in equation above and the elucidation of the effect of the
intervention on table 5, showing that the policy of applying the lockdown has a temporary effect on addition
of positive cases of COVID- 19 in Singapore. The initial effect gives positive value until in the fourth period
after the intervention, the effect is negative of -0.35, namely a decrease in the number of positive cases of
COVID-19.
The effect of Singapore’s first
intervention
Effects of Conducting Lockdown
Time (t) Data Effect's Magnitude
t+3 50 2.95
t+4 51 2.95 - 2.85 = 0.05
t+5 52 2.95 - 2.85 - 0.4 = -0.35
68. First Forecasting after Intervention
We have saved several data to compare the result of forecasting and the actual data to
show the accuracy of the model of forecasting.
No of Data Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
57 882 638 1186 531 1375
58 741 508 1043 409 1234
59 875 580 1264 457 1515
60 949 598 1430 456 1745
61 1092 658 1702 487 2110
62 873 461 1502 312 1943
63 1093 590 1851 405 2377
64 1157 595 2028 395 2644
65 1133 546 2077 346 2760
66 1126 519 2130 318 2866
67 1309 604 2471 371 3321
68 1302 568 2553 334 3486
69 1300 542 2627 308 3628
70 1396 573 2849 321 3952
71 1494 600 3092 330 4312
72 1480 565 3160 299 4461
73 1543 576 3344 299 4748
0 10 20 30 40 50 60 70
05001500
69. Identification Second Intervention
The second intervention event which affected Singapore data is
T= 57 which is Policy to open several public sectors.
It is a step function intervention with the order intervention b = 0, r
= 1, s = 1.
Based on Figure, the data pattern of the ARIMA model
forecasting before the second intervention (blue line) shows
significant differences from the actual data pattern (red line).. It
indicates that opening of several public sectors in Singapore is
not significant enough to increase the positive cases of COVID-19.
It tends to decrease compared to before the second intervention.
It can be seen that the average of the addition of COVID-19
cases is stable in 600’s.
-1200-800-4000
Waktu(T)
Residual
T =57
T-50 T-37 T-22 T-13 T+2
70. Quantitatively, an elucidation of the effects of the second intervention shows that there are two different
periods due to the results of the opening of several public sectors in Singapore to an increase in positive
cases of COVID-19. The effects are negative, namely a decrease in the number of positive cases of COVID-
19. The first, second, and T+k periods were decrease in the addition of positive cases of COVID-19 in
Singapore, which were -1.16, -0.16, and -0.16 respectively.
The effect of Singapore’s second
intervention
Effects of the Opening of Several Public Sectors
Time (t) Data Effect's Magnitude
t 56 -1.16
t+1 57 -1.16 + 1 = -0.16
t+k 56+k -1.16 + 1 = -0.16
73. Ljung - Box Test for Singapore Final ARIMA Model &
Kolmogorov - Smirnov Test
> Box.test(tssingapore_arima3$residuals, lag =
round(length(newsingapore3)/5,0) ,
+ type = "Ljung-Box", fitdf = 1)
Box-Ljung test
data: tssingapore_arima3$residuals
X-squared = 5.3646, df = 14, p-value = 0.9801
> # --- Kolmogorov - Smirnov Test
> ks.test (tssingapore_arima3$residuals, "pnorm",
+ mean(tssingapore_arima3$residuals),
+ sd(tssingapore_arima3$residuals))
One-sample Kolmogorov-Smirnov test
data: tssingapore_arima3$residuals
D = 0.076844, p-value = 0.7526
alternative hypothesis: two-sided
74. Actual versus Forecast
We have saved several data to compare the result of forecasting and the actual data to
show the accuracy of the model of forecasting.
Actual 451 570 448 614 642 548 344 383
Forecast 481 399 342 388 341 384 339 357
Error 0.07 0.30 0.24 0.37 0.47 0.30 0.01 0.07
MAPE 23%
0 20 40 60 80
05001500
75. The Result of Forecasting of
Singapore COVID-19 Data
We got the result of forecasting the Korean Data for the next 7 daya as shown below :
Q
0 20 40 60 80
05001500
Date Forecast
27/05/2020 352
28/05/2020 346
29/05/2020 344
30/05/2020 349
31/05/2020 341
01/06/2020 343
02/06/2020 344
77. Indonesia’s
COVID Data
The COVID-19 pandemic was first
confirmed to have spread to Indonesia
on 2 March 2020, when a dance
instructor and her mother were
infected from a Japanese national. By
9 April, the pandemic had spread to all
34 provinces in the country after
Gorontalo confirmed its first case, with
Jakarta, East Java, and West Java
being the worst-hit.
As of 16 May, Indonesia has recorded
17,025 cases, the second-highest in
Southeast Asia, behind Singapore. In
terms of death numbers, Indonesia
ranks fifth in Asia with 1,089 deaths.
Review of data, however, indicated
that the number of deaths may be
much higher than what has been
reported as those who died with acute
coronavirus symptoms but had not
been confirmed or tested were not
counted in the official death figure
36282218
39
56
85
59
82
6566
108105104
154
110
131130
115
150
114
197
107
182
219
248
219
338
220
331
400
317
283
298
381
408
326328
186
376
641
437
397
276
215
416
608
434
293
350
395
484
367
338336
533
387
233
484
689
568
490
529
13/03/2020
15/03/2020
17/03/2020
19/03/2020
21/03/2020
23/03/2020
25/03/2020
27/03/2020
29/03/2020
31/03/2020
02/04/2020
04/04/2020
06/04/2020
08/04/2020
10/04/2020
12/04/2020
14/04/2020
16/04/2020
18/04/2020
20/04/2020
22/04/2020
24/04/2020
26/04/2020
28/04/2020
30/04/2020
02/05/2020
04/05/2020
06/05/2020
08/05/2020
10/05/2020
12/05/2020
14/05/2020
16/05/2020
INDONESIA
78. STOP
COVID-19
Policies adopted by the Indonesia
government
10 April 2020 – now
Large-Scale Social Restrictions (PSBB)
24 April 2020 – 1 June 2020
Not allowed to transport among the
provinces
79. Multi Intervention
Scheme
In analyzing this multi intervention, we divided
the data into 3 parts. The green line is the first
intervention which happened at 10 April 2020,
and the red line is the second intervention, at
24 April 2020. The First intervention is PSBB
and The second intervention is Homecoming
Ban.
Preintervention happened in time t < T1 in
which T1 is first intervention with T1 = 29, and
second intervention is in t < T2 with T2 = 42.
Preintervention
Intervention Effect 1
Intervention Effect 2
T1
T2
The number of Singapore COVID-19 data
taken to be analyzed are 58 data which
started from March, 13, 2020 until May, 11,
2020.
80. known that the data of
Indonesia before the
intervention is increased.
Trend Linear
Preintervention
Jumlah Terinfeksi Indonesia 13 Maret - 10 April 2020
Waktu
Totalterinfeksi
0 5 10 15 20 25
50150250350
81. Stationary Test of Indonesia’s COVID Data
First Data Dicky-Fuller
Test
First Differencing Dicky-
Fuller Test
Second Differencing Dicky-
Fuller Test
82. ACF and PACF Indonesia’s COVID Data
-0.40.00.4
Lag
ACF ACF for Data indonesia preintervention
1 3 5 7 9 11 13 15
-0.40.00.4
Lag
ACF
ACF for Diff 1x indonesia preintervention
1 3 5 7 9 11 13 15
-0.40.00.4
Lag
ACF
ACF for Diff 2x indonesia preintervention)
1 3 5 7 9 11 13 15
-0.40.00.4
Lag
PartialACF
PACF for Data indonesia preintervention
1 3 5 7 9 11 13 15
-0.40.00.4
Lag
PartialACF
PACF for Diff 1x indonesia preintervention
1 3 5 7 9 11 13 15
-0.40.00.4
Lag
PartialACF
PACF for Diff 2x indonesia preintervention)
1 3 5 7 9 11 13 15
83. Transformation
BOX-COX
95% confidence interval for λ.
Singapore data from March to April is not
stationary because it has a value of λ = 0.39.
This is shown by the plot between the log
likelihood with some Lambda values
presented in the Figure beside, where the
maximum log likelihood function is at 0.39. To
make the data stationary in a variety,
transformation is performed. The Box-Cox
transformation function that corresponds to λ
= 0.39 based on the Box-Cox equation is Yt.
-1.0 -0.5 0.0 0.5 1.0
-35-25-15
log-Likelihood
95%
84. Model Identification
> indo_model_011d <- Arima(newindo, order=c(5,3,3),lambda = indo_lambda.model3,
include.drift =
+ F)
> indo_model_011d
Series: newindo
ARIMA(5,3,3)
Box Cox transformation: lambda= 0.9677095
Coefficients:
ar1 ar2 ar3 ar4 ar5 ma1 ma2 ma3
-0.5516 -0.4855 -0.6612 -0.7119 -0.6336 -2.1074 2.1072 -0.9996
s.e. 0.1873 0.1785 0.1420 0.1520 0.1608 0.2612 0.4103 0.2574
sigma^2 estimated as 856.6: log likelihood=-121.54
AIC=261.08 AICc=273.08 BIC=272.04
> coeftest(indo_model_011d)
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
ar1 -0.55164 0.18731 -2.9450 0.0032294 **
ar2 -0.48546 0.17850 -2.7197 0.0065345 **
ar3 -0.66118 0.14199 -4.6564 3.217e-06 ***
ar4 -0.71194 0.15196 -4.6851 2.798e-06 ***
ar5 -0.63358 0.16084 -3.9391 8.178e-05 ***
ma1 -2.10745 0.26120 -8.0684 7.124e-16 ***
ma2 2.10720 0.41027 5.1362 2.804e-07 ***
ma3 -0.99959 0.25744 -3.8827 0.0001033 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
So We got the model for Indoneisa Data is ARIMA
(5,3,3)
After going through several selections to determine the best model with all the
requirements fulfilled, we get:
85. Ljung - Box Test for Indonesia ARIMA Model &
Kolmogorov - Smirnov Test
> Box.test(indo_model_011d$residuals, lag =
round(length(newindo)/5,0) ,
+ type = "Ljung-Box", fitdf = 1)
Box-Ljung test
data: indo_model_011d$residuals
X-squared = 1.4356, df = 5, p-value = 0.9204
> # --- Kolmogorov - Smirnov Test
> ks.test (indo_model_011d$residuals, "pnorm",
+ mean(indo_model_011d$residuals),
+ sd(indo_model_011d$residuals))
One-sample Kolmogorov-Smirnov test
data: indo_model_011d$residuals
D = 0.13704, p-value = 0.6203
alternative hypothesis: two-sided
88. Forecasting of Indonesia
Preintervention Model
Based on Figure beside, the data pattern
of the ARIMA model forecasting before
the first intervention (blue line) shows
significant differences from the actual
data pattern (red line). The result of
forecasting using data before the first
intervention shows an increasing trend
while actual data pattern after the first
intervention did a decrease.
89. Identification of First Intervention Order of
Indonesia COVID-19 Data
First intervention event which affected Indonesia
data is T= 29 which is Policy to do PSBB in ever
red zone in Indonesia.
It is a pulse function intervention. Based on Figure.
The first step in intervention modeling is
identifying the value of b, s, and r. This
identification is done by evaluating into residual
bar chart of pre-intervention model (Figure beside).
Based on Figure, we got b=2, r=1 and s=6.
90. First Intervention Model of
Indonesia Data
The intervention model in the equation above (5.a)
states that the policy for conducting a Large-Scale
Social Restrictions (PSBB) from April 10, 2020, to May
21, 2020, has a significant effect in the third period after
the first intervention. It means there is delay for two
days until the intervention gave the effect. The effect of
this intervention makes the addition of positive cases of
COVID-19 in Indonesia more stable, which is the
i n c r e a s e o f p o s i t i v e c a s e s o f C O V I D - 1 9 i n
approximately 300’s. This is continue until the second
intervention.
Intervention Model
91. Quantitatively, based on the intervention model in equation (3.a) and the elucidation of the effect of the
intervention on table 9, showing that every period of the effect has different effect’s magnitude. The policy of
applying the large-scale social restrictions gives negative effect, namely a decrease in the number of
positive cases of COVID-19 in Indonesia.
The effect of Indonesia’s first
intervention
Effects of Conducting Lockdown
Time (t) Data Effect's Magnitude
t+3 31 -0.93
t+4 32 -0.93 - 2 = -2.93
t+5 33 -0.93 - 2 + 1.4 = -1.53
t+6 34 -0.93 - 2 + 1.4 - 1.17 = -2.7
t+7 35 -0.93 - 2 + 1.4 - 1.17 - 0.35 = -3.05
t+8 36 -0.93 - 2 + 1.4 - 1.17 - 0.35 + 1.1 = -1.95
t+9 37 -0.93 - 2 + 1.4 - 1.17 - 0.35 + 1.1 - 2.43 = -4.38
93. Forecasting ARIMA Model with First Intervention
We have saved several data to compare the result of forecasting and the actual data to
show the accuracy of the model of forecasting.
No of Data Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
42 534 446 622 399 668
43 423 321 524 268 578
44 359 257 462 202 516
45 392 289 495 235 549
46 560 457 664 402 719
47 642 527 757 466 818
48 579 444 713 372 785
49 502 358 646 282 722
50 489 342 635 265 713
51 570 421 719 342 797
52 674 518 829 435 912
53 697 526 867 435 957
54 650 464 835 365 933
55 613 418 808 315 911
56 640 439 841 332 947
57 717 508 925 398 1036
58 777 555 998 437 1115
59 778 540 1016 413 1142
0 10 20 30 40 50 60 70
02006001000
94. Identification Second Intervention
Based on Figure beside, the data pattern of the ARIMA
model forecasting before the second intervention (blue
line) does not show significant differences from actual
data pattern (red line). the result of forecasting using data
before the second intervention shows an increasing trend
in which actual data pattern after the second intervention
in Indonesia did an increase gradually too. It indicates
that the homecoming ban applied by Indonesia
Government is not significant enough to decrease the
positive cases of COVID-19.
-300-100100300
Waktu(T)
Residual
T =42
T-32 T-20 T-12 T+3 T=12
Second intervention event which affected Indonesia data is T= 42
which is Policy to not allow transport among the province.
Based on the graph, It is a pulse function intervention with the
order intervention b = 6, r = 1, s = 2.
95. Quantitatively, an explanation of the effects of the second intervention shows that there are three different
periods due to the results of the homecoming ban in Indonesia to an increase in positive cases of COVID-19.
The effects are negative, namely a decrease in the number of positive cases of COVID-19. The first,
second, and third periods were decrease in the addition of positive cases of COVID-19 in Singapore, which
were -0.33, -0.43, and -1.21 respectively.
The effect of Indonesia’s second
intervention
Effects of the Opening of Several Public Sectors
Time (t) Data Effect's Magnitude
t+7 49 -0.33
t+8 50 -0.33 - 0.1 = -0.43
t+9 51 -0.33 - 0.1 - 0.78 = -1.21
98. Ljung - Box Test for Final Indonesia ARIMA Model &
Kolmogorov - Smirnov Test
> Box.test(tsindo_arima3$residuals, lag =
round(length(newindo3)/5,0) ,
+ type = "Ljung-Box", fitdf = 1)
Box-Ljung test
data: tsindo_arima3$residuals
X-squared = 5.2384, df = 13, p-value = 0.9696
> # --- Kolmogorov - Smirnov Test
> ks.test (tsindo_arima3$residuals, "pnorm",
+ mean(tsindo_arima3$residuals),
+ sd(tsindo_arima3$residuals))
One-sample Kolmogorov-Smirnov test
data: tsindo_arima3$residuals
D = 0.12809, p-value = 0.1904
alternative hypothesis: two-sided
99. Actual versus Forecasting
We have saved several data to compare the result of forecasting and the actual data to
show the accuracy of the model of forecasting.
Actual 949 526 479 415
Forecast 522 680 801 857
Error 0.45 0.29 0.67 1.06
MAPE 61%
0 20 40 60 80
05001500
100. The Result of Forecasting of
Indonesia COVID-19 DataWe got the result of forecasting the Korean Data for the next 7 days as shown below :
Q
Date Forecast
27/05/2020 856
28/05/2020 824
29/05/2020 833
30/05/2020 891
31/05/2020 951
01/06/2020 985
02/06/2020 998
0 20 40 60 80
05001500
101. SOUTH KOREA
1. Based on the identification of intervention order in South Korea for COVID-19 cases, the first intervention
function is a step function and the second intervention function is pulse function. It means that the policy to
enforce the Massive Rapid Test significantly and permanently can reduce the increase in positive cases of
COVID-19 in South Korea. In the other hand, the policy to open the several public sectors significantly and
temporarily can increase the addition of positive cases of COVID-19 in South Korea of 5 times.
2. The best model chosen for forecasting South Korea data is the ARIMA model (1,2,1) with the addition of an
intervention model built by the order of intervention (0, 2,0) for the first intervention and (0,1,4) for the second
intervention, with the following models
3. Forecasting the number of COVId-19 cases in South Korea from May 25, 2020 to June 03, 2020, per day using
the above model and assuming no policy changes were 15, 15, 15, 15, 15, 16, 16, 16, 16, and 16.
Conclusion
102. SINGAPORE
1. Based on the identification of intervention order in Singapore for COVID-19 cases, the first intervention occurred
on April 20, 2020, and the second intervention occurred on May 5, 2020. Based on the results of the intervention
identification, the first intervention function is pulse function which means the effect of this intervention only
happens temporarily. The policy to enforce lockdown and social distancing can reduce the increase in positive
cases of COVID-19 in Singapore until the second intervention occurs. In the second intervention which is a step
function, it has a direct effect and the effect of this decrease is continue until the last observation. it is not
significant enough to increase the positive cases of COVID-19. It tends to decrease compared to before the
second intervention.
2. The best model chosen for forecasting Singapore data is the ARIMA model (3,2,7) with the addition of an
intervention model built by the order of intervention (2,0,2) for the first intervention and (0,1,1) for the second
intervention, with the following models
3. Forecasting the number of COVId-19 cases in Singapore from May 27, 2020 to June 02, 2020 per day using the
above model and assuming no policy changes were 352, 346, 344, 349, 341, 343, and 344.
Conclusion
103. INDONESIA
1. Based on the identification of intervention order in Indonesia for COVID-19 cases, the first intervention occurred
on April 10, 2020, and the second intervention occurred on April 24, 2020. The first intervention function is pulse
function, which means intervention is only a temporary effect until the effect is slowly diminishing. the policy for
conducting a Large-Scale Social Restrictions (PSBB) has a significant effect in the third period after the first
intervention. The effect of this intervention makes the addition of positive cases of COVID-19 in Indonesia more
stable, which is the increase of positive cases of COVID-19 in approximately 300’s. In the second intervention,
the policy for banning homecoming in Indonesia on April 24, 2020, has a significant effect in the seventh period
after the first intervention. It means there is delay for six days until the intervention gave the effect.
2. The best model chosen for forecasting Indonesia data is the ARIMA model (5,3,3) with the addition of an
intervention model built by the order of intervention (2,1,6) for the first intervention and (6,1,2) for the second
intervention, with the following models
3. Forecasting the number of COVId-19 cases in Indonesia from May 27, 2020 to June 02, 2020 per day using the
above model and assuming no policy change is 856, 824, 833, 891, 951, 985, and 998.
Conclusion
