The time delay is dealt in the calculations of granger causality, as described in the article with a time shift of up to 3 weeks, and nothing came of it.
It's ONE Test and ONE p-value. "lag" only defines what is considered as "the past". This makes sense to me because mostly it is not likely that very old values are influencing the present.
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.1837907 0.4588082
sample estimates:
cor
0.3282377
Pearson's product-moment correlation
data: all_cause_deaths.ts and c19_pos_rate.ts
t = 5.4223, df = 161, p-value = 0.0000002119
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.2546181 0.5155373
sample estimates:
cor
0.3929582
Pearson's product-moment correlation
data: c19_deaths_weekly.ts and c19_pos_rate.ts
t = 1.1078, df = 161, p-value = 0.2696
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.06764915 0.23752066
sample estimates:
cor
0.08697581
So PCR positive rate slightly correlates with excess deaths and all cause deaths, but does not with C19 deaths. What a funny data swamp, just Witzbold-like. :-)
I would like to see the correlation of C19 cases, shifted 1, 2, 3, o 4 weeks backwards, and C19 death, ACD and excess deaths.
The same, if possible, for same large countries, such as England or UK, France, Italy, Spain.
The time delay is dealt in the calculations of granger causality, as described in the article with a time shift of up to 3 weeks, and nothing came of it.
Thank you very much.
Do I understand the Granger test correctly: It compares C19-cases in week n with (e.g.) C19-deaths in week n+1 or n+2 or n+3.
You wrote: "I applied the test with a lag of max 3 weeks."
Which time shift do you show in the table above? The best, the worst, or the last?
How would be the result for n+1? How for n+2?
The Granger test in R uses all previous weeks within a given time span. The hypothesis decision is then based on two models.
Model 1 attempts to predict the dependend variable using the independend variable and the dependend variable.
Model 2 attempts to predict the dependend variable from itself alone.
So, if lag is set to 3, then the target variable at time t is to predict by values at time t-1, t-2 and t-3.
OK, nevertheless I would expect different p-values for t-1, t-2, t-3.
Hence: To which of these time points the p-values in Table 2 refer to?
It's ONE Test and ONE p-value. "lag" only defines what is considered as "the past". This makes sense to me because mostly it is not likely that very old values are influencing the present.
I would be interested to see if there was any correlation between PCR test-positivity rates and Covid deaths or all-cause deaths?
The results printed directly from R:
Pearson's product-moment correlation
data: excess_deaths.ts and c19_pos_rate.ts
t = 4.4092, df = 161, p-value = 0.0000189
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.1837907 0.4588082
sample estimates:
cor
0.3282377
Pearson's product-moment correlation
data: all_cause_deaths.ts and c19_pos_rate.ts
t = 5.4223, df = 161, p-value = 0.0000002119
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.2546181 0.5155373
sample estimates:
cor
0.3929582
Pearson's product-moment correlation
data: c19_deaths_weekly.ts and c19_pos_rate.ts
t = 1.1078, df = 161, p-value = 0.2696
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.06764915 0.23752066
sample estimates:
cor
0.08697581
So PCR positive rate slightly correlates with excess deaths and all cause deaths, but does not with C19 deaths. What a funny data swamp, just Witzbold-like. :-)