Time series COVID-19 circa 8 May 2020 by Dean Luis Dumlao, PhD

May 09, 2020
January 30
The first case of positive COVID-19 was detected.
 
February 1
The first death was reported.
The number of cases remain two for the rest of February. With both cases being non-Filipinos, it seemed that the Philippines will not be hit by what was still then an epidemic.
 
March 6
The cumulative number of cases doubled to four (Figure 1).

March 9
The cumulative number of cases more than quintupled in three days to 23 (Figure 1).
 
March 11
The cumulative number of cases more than doubled in two days to 48 (Figure 1).
The World Health Organization (WHO) elevated the epidemic to a pandemic.
It became obvious that the country will be hit hard.
 
March 17
The cumulative number of cases reaches 186 (Figure 1).
The enhanced community quarantine (ECQ) became effective in the whole of Luzon
 
While the cumulative number of cases will only increase, the key to further understand the data is to look at the additional cases per day i.e. the first difference or the first integration in economics parlance. Still, the number of cases fluctuates daily. In finance and in time series, scientists and practitioners try to understand erratic series of numbers by smoothening the data using moving averages (MA). For example, stock market players often use MA to eliminate idiosyncratic changes and capture the long run trend or the secular movement of stock prices and indices. Known examples of applying the MA on COVID-19 include the New York Times 5-day MA and John King of CNN’s 7-day MA. Suppose we use halfway of the one to fourteen days of incubation COVID-19 in accordance to WHO which conveniently translates to a 7-day MA or 1-week MA.
 
March 20
The number of incidences and admittances to the hospital began to increase at an increasing rate (Figure 2).

April 3
The incidences and admittances per day peaked at 316 and 171, respectively (Figure 2).
 
April 5
The incidences and admittances per day declined to 261 and 143, respectively
 
April 6
The incidences and admittances per day increased to 302 and 162, respectively.
After that day, the said numbers declined for four consecutive days.
 
What occurred from April 3 to April 10 reveals that the numbers fluctuate in an unpredictable manner. It became apparent that the one-week MA needed further smoothing. Applying a second application of the one-week MA will reveal whether such inclines or declines statistically reveal official upswings or downswings. These are shown in Figures 3, 4 and 5.

April 7
President Duterte decided to extend the ECQ to 30 April.
It has become statistically official that we have passed the apex of incidences and admittances per day (Figure 3).
The number of recoveries then at five per day started to pick up (Figure 4).
For the next three days, the number of new cases and admittances declined for three consecutive days.
Having passed the apex, with recoveries picking up and the number of incidences and admittances declining for three consecutive days, was the decision to extend the ECQ overly careful? 
 
A key scientific question was whether the incidences and admittances per day would move in cycles or permanently decline. On hindsight or at least on the moment of the writing of this narrative, the evidence is strong that it moves in cycles but is not yet strong whether it will decline. As the numbers move in cycles, what we see are what mathematicians refer to as local maximums and local minimums.

April 10
The number of incidences and admittances per day reaches the first local minimum at 168 and 91 respectively (Figure 2).
 
April 13
For the first time, the number of recoveries per day at 24 topped the number of deaths per day at 22 (Figure 2).
The incidences and admittances per day became statistically officially on the upswing again (Figure 3). It became apparent that President Duterte’s decision in 7 April to extend the ECQ was the right.
 
April 15
The one-week MA number of deaths per day peaked at 24 (Figure 5).
 
April 17 
The number of incidences and admittances per day reached its new peak or what mathematicians call the local maximum with 241 and 126, respectively (Figure 2).
 
April 18
The number of deaths per day was statistically officially on a downswing (Figure 5)
 
April 19
The incidences and admittances per day would be statistically officially on a downswing (Figure 3).
The number of recoveries per day at 54 reached its first local maximum (Figure 4).

April 22 
It became statistically official that recoveries per day was on a downswing (Figure 4). This is mysterious. If people were getting infected by the hundreds the past twenty to thirty days, they should sooner or later either recover or die. But given that the deaths per day tops at 24, either infected people remain sick for extended periods of time, number of recoveries have not been correctly reported, or that recoveries will cyclically increase.
 
April 24
President Duterte decided to extend the ECQ further to May 15. 
For the first time, the recoveries per day at 42 is greater than the admittances per day at 39 (Figure 2). Technically and on a macro perspective, it will mark the peak when hospitals are most distressed. After that, the net number of patients in hospitals will start to decline. The medical front liners’ work will start to “ease” for lack of better term.
 
April 25
Incidences per day reached its second local maximum.
The local maximums and minimums and vice versa appear to occur in a week. Case in point, the incidences per day peaked on 3 April, troughed on 10 April, peaked again on 17 April and then troughed on 25 April. However, this pattern will be broken from this day to the writing of this report. 
 
April 27
Incidences per day is statistically officially on the upswing (Figure 3).
Recoveries per day is statistically officially on the upswing (Figure 4). This upswing should be theoretically permanent unless the mystery that started in 22 April manifests again. 
 
April 28
The Department of Health stopped publishing the number of admittances per day on its website. It replaced the statistics of number of admittances per day by the number of active cases per day which any person can derive anyway as it is the identity equal to the number of accumulated incidences less deaths and recovery.

29 April
The number of deaths per day was statistically officially on the upswing (Figure 5).
 
May 7 
The trend in deaths per day switched from upswing to downswing (Figure 5). With the switch in a short span of less than three days, data might be starting to stabilize. In economics parlance, the rate of increase of deaths may finally have found its mean; it may no longer be explosive; and it may already be stationary and mean reverting.
Between 3 April and 7 May, the cyclically has become apparent. But whether that cyclicality is on a downward, upward or vertical trend is still unknown.
 
May 8 
The number of incidences per day is officially statistically on the downswing.
Incidences per day is statistically officially on the downswing (Figure 3).
The actual number of recoveries per day is on its highest at 116. The actual number of recoveries per day at 116 is only four less than the number of incidences per day at 120.
 
If trends remain which in likelihood will not, the following are trending to occur. 
 
June 2
For the first time, the number of recoveries per day at 486 will be greater than the number of new incidences per day 470 (Figure 2).
The active number of COVID positives will peak at 19,659 (Figure 6).
The healing process of the nation will begin. 
 
June 23
For the first time since 6 March, the country will reach zero active case of COVID-19 (Figure 6). 
The cumulative incidences will reach 32,509.
The number of deaths per day will peak at 37, while the cumulative deaths will reach 1,886. 
 
But that is if nothing mysterious comes up when recoveries started to drop as what had happened in 22 April. But that is if trends remain. That is if conditions remain the same. But ECQ and post-ECQ are totally different.
 
 
Note: forecasts and conclusions drawn are author’s and is not necessarily that of the John Gokongwei School of Management, Ateneo de Manila University.