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# Granger Causality Test (Effective reproduction Rate (Rt) and Daily Changes ...

Author*Unverified author*
R Software Modulerwasp_grangercausality.wasp
Title produced by softwareBivariate Granger Causality
Date of computationMon, 02 Nov 2020 14:35:00 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/Nov/02/t16043257103rgpy4em30x1b68.htm/, Retrieved Wed, 21 Apr 2021 08:38:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319286, Retrieved Wed, 21 Apr 2021 08:38:10 +0000
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Original text written by user:The effective reproduction number (Rt) characterizes the COVID-19 spread rate, defined as the average number of secondary infectious cases produced by a primary infectious case. It's used to define the potential for spread at a specific time. If Rt > 1, the virus will spread out and the disease will become an epidemic; if Rt = 1, the virus will spread locally and the disease is endemic; if Rt < 1, the virus will stop spreading and the disease will disappear eventually.
IsPrivate?No (this computation is public)
User-defined keywordsCOVID-19, Granger Causality, coronavirus, causation
Estimated Impact23
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Bivariate Granger Causality] [Granger Causality...] [2020-11-02 13:35:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
3.13268334113438
3.23680175944288
2.88201788002659
2.84782400562102
2.71810149609755
2.44065988251605
2.23863300087288
2.19514358951984
2.07242710819333
1.97638531045049
1.8236525166409
1.72029114049977
1.70546130097739
1.65189829656141
1.58557088082452
1.53894154228052
1.49890695043382
1.43296771300372
1.37572106858207
1.31423896028701
1.27620068211179
1.23719073110979
1.19271666481855
1.13273494034869
1.10008117322411
1.06044449130108
1.03677437952325
1.02239801876862
1.00505120394206
1.00228622950044
0.996280565089463
0.991838295278499
1.00731273460677
0.994311104170129
0.991710369994506
1.0033423688786
1.00696376428079
1.02490805403557
1.02701356651755
0.99542207468205
0.989034234689879
0.985004268905044
0.969155426103344
0.978515180807519
0.964710637720008
0.958262701191528
0.96779905761605
0.973896659619999
0.965037828796574
0.962528307649591
0.931864319745562
0.928295648674492
0.912508443218754
0.907232210922053
0.914672848097462
0.907180332185469
0.920934890065206
0.926441998360512
0.93379692152295
0.941178044132804
0.967004251523819
0.962413397673273
0.983596585704783
0.97641511760466
0.968251869809063
0.956481286638731
0.976924780768252
0.958734424114706
0.956082934690587
0.933412009280572
0.928026320506047
0.947944321990947
0.975753943365337
0.973851641940048
0.971206612381403
0.988559795454045
1.00000716273254
0.991154837705696
0.997439579256495
0.984444459756276
0.977552760781905
0.983153216023638
0.966344206791663
0.978198607446143
0.993148066564895
0.992304739349162
1.01673010010048
1.02436458134856
1.03486638638068
1.06400087170071
1.08440752216375
1.09834323737949
1.11799150592697
1.13583550166198
1.14658171273992
1.17628421610042
1.20537865074223
1.20475666592013
1.22204768277372
1.24161241025079
1.23357487859282
1.23952191204384
1.22886276385055
1.21937613097321
1.23750440412637
1.23952983100443
1.21029425558432
1.1739173894269
1.17227938102655
1.14893115937397
1.16214641209852
1.15272007173472
1.14426130206149
1.15843072361637
1.16605354979179
1.15428275707241
1.16036415630809
1.14358083358139
1.13374779242332
1.14062940178436
1.12139015721312
1.10150220246048
1.08636184599063
1.07513620858528
1.05493059592553
1.05282553633104
1.0250868838384
1.02297926010526
1.02813978914988
1.00932479770758
0.995826213799495
1.00051752098514
1.0014652334907
0.998755287241208
0.986161601577111
0.970138474598601
0.959655141801341
0.941806761941038
0.934331200923467
0.906914443528443
0.90500092463194
0.902386780589967
0.915024819499958
0.927914125485945
0.953211578757473
0.934911815023185
0.954023952851286
0.943176562431584
0.968967316713541
0.953422452935177
0.948387360630864
0.921140580418662
0.931012875548141
0.918096781913661
0.910584453847272
0.880492915267113
0.892675641160665
0.892150684081569
0.916914204819174
0.910119824087103
0.918106572010934
0.938504776903768
0.94292251946294
0.957639200494041
0.968032599722392
0.962076403731244
0.982489196564965
0.970671992408838
0.968404822516469
0.987432873894959
0.983369171615036
0.971386059732191
0.940899820213446
0.897349008498947
0.891553872879251
0.885427050387315
0.896898456954474
0.90455205325297
0.935131024647991
0.985379980765945
1.0357580497798
1.04584663162617
1.06560420943611
1.05507324918537
1.05317158472571
1.04747823838632
1.10469357834037
1.08248738128835
1.06247193897359
1.04746683064293
1.0446198617158
1.03904768090427
1.03219190851599
0.961937290742673
0.979425771696781
0.996538467352552
0.999946765189486
1.01328936614376
1.02839631206512
1.01920753474297
1.03558329907384
1.02816505016485
1.05145171522686
1.07903197304015
1.07148241431483
1.06994350548963
1.08407024940122
1.07315126230609
1.08932340936452
1.09863711849644
1.09927176679916
1.11168977921657
1.09612294570503
1.08518071711069
1.11323983150607
1.11113647331645
1.09519919396093
1.0955607901256
1.11272620180715
1.15363536166823
1.15017795006617
1.13526166644376
1.13544017437059
1.14075946110941
1.146400928383
1.14693019704503
Dataseries Y:
13.6402425130708
19.325194499493
18.1960956532842
26.731111662798
34.0550781033943
32.1034368181463
36.525740632464
54.3090474602526
56.5763507885267
59.4810486267574
57.4595974666094
66.8019798554015
80.0324687549287
78.3661373931851
92.2370560146211
97.1176768337172
100.155923997844
85.5474488720292
91.6209079883297
95.2995848743648
97.1753458608085
105.167058930883
101.788868028113
89.1077524919295
81.8262790186637
78.2811514585242
86.7797449246119
91.0806402608427
95.6789863683866
99.5731633030261
84.533688080003
77.9472781437851
86.2667941046945
79.0308488107112
88.9226045628469
101.470170773135
101.879924386678
96.522775291091
82.2542439039202
70.3349665677322
74.8908197079457
84.51547680829
89.5539286488991
103.8649530034
84.9920050847813
74.3687632521717
71.0300301047801
74.5539111812543
76.326474961324
84.3515753628726
81.5925676983462
75.786207233837
57.2319565701963
59.0318372578356
69.0692831836756
63.639289001236
82.9007440497333
76.7756863302458
72.8997206673194
54.9950053614439
66.8201911271145
63.8365777781273
71.3547977836627
77.8987147525503
71.1392977350584
64.3404229621882
61.0502532060314
55.6020477518788
59.265548578153
56.424590190918
69.652043878493
73.9134814593456
72.3715937876411
58.2001891829399
52.7034203375524
64.8746202657709
60.6374643805357
65.9824726283144
76.3932496242719
66.2829586115797
53.9903502052743
53.201195097709
55.762913985344
63.2113241159794
70.4381637741061
75.488756462524
76.6846299716806
58.813301997279
60.4765981470705
72.2289388258889
78.6393064688808
85.5686953556944
95.0780144018561
97.9037967293303
79.2463488593156
92.5345067859341
108.651482251979
104.59036865997
123.096055932376
137.56491130839
128.565507870194
119.447731165863
123.499739122015
140.14787667969
155.779218233387
167.303918015793
159.536810630179
138.854876388064
151.708999005522
135.522213664577
182.604421466703
179.629913753572
192.059106697725
205.538482977331
182.616562314512
178.777019195011
180.537442127272
203.28939092077
205.265313901635
234.858630435333
218.599000007536
190.499007754308
186.03421097266
188.204387518464
195.604234257865
216.480422064919
209.702793775714
221.925592307119
201.786961004444
166.478340364801
171.771750009393
199.780685904057
216.492562912728
205.848074596453
203.823588224353
175.76001851455
143.66568733226
136.120150419155
174.451842163163
162.86036771781
181.053428159142
177.095511773507
169.061305736102
139.999151294034
151.0503580119
142.390898312347
173.040468605402
157.812810241344
196.062551262643
143.950997255765
125.700267787341
109.082482349188
137.686319786477
143.686933815926
133.804283699646
146.367025969695
134.808938855816
104.496277089453
114.904018873458
116.042223355523
136.86681255939
139.258559577703
140.260179521921
139.704735734673
107.331165052783
104.75730531734
129.099705173776
123.178006655085
133.264015972159
152.103576559305
133.834635819168
94.5407818863213
73.0393404171194
81.152461965281
101.852607479109
110.357271369101
144.266659298791
124.610626696511
105.312749104587
103.057586624122
118.986378949132
117.034737663884
135.795382740273
147.887667157735
133.770896368173
109.983940298984
159.242395070818
118.345949227223
116.694793925241
134.007642900442
153.5635135083
136.220312413577
110.548489722088
101.130227034491
127.840092213624
125.709373423198
135.88947431079
165.531354235723
151.954851173648
107.649862307762
120.05780876825
127.336247029563
152.792569672448
170.666932858802
174.354715380693
165.850051490701
135.431157306012
126.486387682955
159.196866891536
180.704378784642
193.209452027599
209.930434672127
174.667342211767
146.367025969695
177.241201947211
183.190217373472
190.538465509686
217.627732182841
254.189895358731
254.138296755544
184.562133175855
202.746087981331
223.488726462489
237.833138148464
268.67999721841
301.460286301891

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319286&T=0

[TABLE]
[ROW]
 Summary of computational transaction[/C][/ROW] [ROW] Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW] Raw Output[/C] view raw output of R engine [/C][/ROW] [ROW] Computing time[/C] 1 seconds[/C][/ROW] [ROW] R Server[/C] Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319286&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319286&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server Big Analytics Cloud Computing Center

 Granger Causality Test: Y = f(X) Model Res.DF Diff. DF F p-value Complete model 221 Reduced model 222 -1 6.26013307920756 0.0130730973627266

\begin{tabular}{lllllllll}
\hline
Granger Causality Test: Y = f(X) \tabularnewline
Model & Res.DF & Diff. DF & F & p-value \tabularnewline
Complete model & 221 &  &  &  \tabularnewline
Reduced model & 222 & -1 & 6.26013307920756 & 0.0130730973627266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319286&T=1

[TABLE]
[ROW][C]Granger Causality Test: Y = f(X)[/C][/ROW]
[ROW][C]Model[/C][C]Res.DF[/C][C]Diff. DF[/C][C]F[/C][C]p-value[/C][/ROW]
[ROW][C]Complete model[/C][C]221[/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Reduced model[/C][C]222[/C][C]-1[/C][C]6.26013307920756[/C][C]0.0130730973627266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319286&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319286&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Granger Causality Test: Y = f(X) Model Res.DF Diff. DF F p-value Complete model 221 Reduced model 222 -1 6.26013307920756 0.0130730973627266

 Granger Causality Test: X = f(Y) Model Res.DF Diff. DF F p-value Complete model 221 Reduced model 222 -1 1.41665097909288 0.235232397134477

\begin{tabular}{lllllllll}
\hline
Granger Causality Test: X = f(Y) \tabularnewline
Model & Res.DF & Diff. DF & F & p-value \tabularnewline
Complete model & 221 &  &  &  \tabularnewline
Reduced model & 222 & -1 & 1.41665097909288 & 0.235232397134477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319286&T=2

[TABLE]
[ROW][C]Granger Causality Test: X = f(Y)[/C][/ROW]
[ROW][C]Model[/C][C]Res.DF[/C][C]Diff. DF[/C][C]F[/C][C]p-value[/C][/ROW]
[ROW][C]Complete model[/C][C]221[/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Reduced model[/C][C]222[/C][C]-1[/C][C]1.41665097909288[/C][C]0.235232397134477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319286&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319286&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

 Granger Causality Test: X = f(Y) Model Res.DF Diff. DF F p-value Complete model 221 Reduced model 222 -1 1.41665097909288 0.235232397134477

par8 <- '1'par7 <- '0'par6 <- '0'par5 <- '1'par4 <- '1'par3 <- '0'par2 <- '1'par1 <- '1'library(lmtest)par1 <- as.numeric(par1)par2 <- as.numeric(par2)par3 <- as.numeric(par3)par4 <- as.numeric(par4)par5 <- as.numeric(par5)par6 <- as.numeric(par6)par7 <- as.numeric(par7)par8 <- as.numeric(par8)ox <- xoy <- yif (par1 == 0) {x <- log(x)} else {x <- (x ^ par1 - 1) / par1}if (par5 == 0) {y <- log(y)} else {y <- (y ^ par5 - 1) / par5}if (par2 > 0) x <- diff(x,lag=1,difference=par2)if (par6 > 0) y <- diff(y,lag=1,difference=par6)if (par3 > 0) x <- diff(x,lag=par4,difference=par3)if (par7 > 0) y <- diff(y,lag=par4,difference=par7)print(x)print(y)(gyx <- grangertest(y ~ x, order=par8))(gxy <- grangertest(x ~ y, order=par8))bitmap(file='test1.png')op <- par(mfrow=c(2,1))(r <- ccf(ox,oy,main='Cross Correlation Function (raw data)',ylab='CCF',xlab='Lag (k)'))(r <- ccf(x,y,main='Cross Correlation Function (transformed and differenced)',ylab='CCF',xlab='Lag (k)'))par(op)dev.off()bitmap(file='test2.png')op <- par(mfrow=c(2,1))acf(ox,lag.max=round(length(x)/2),main='ACF of x (raw)')acf(x,lag.max=round(length(x)/2),main='ACF of x (transformed and differenced)')par(op)dev.off()bitmap(file='test3.png')op <- par(mfrow=c(2,1))acf(oy,lag.max=round(length(y)/2),main='ACF of y (raw)')acf(y,lag.max=round(length(y)/2),main='ACF of y (transformed and differenced)')par(op)dev.off()load(file='createtable')a<-table.start()a<-table.row.start(a)a<-table.element(a,'Granger Causality Test: Y = f(X)',5,TRUE)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Model',header=TRUE)a<-table.element(a,'Res.DF',header=TRUE)a<-table.element(a,'Diff. DF',header=TRUE)a<-table.element(a,'F',header=TRUE)a<-table.element(a,'p-value',header=TRUE)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Complete model',header=TRUE)a<-table.element(a,gyx$Res.Df[1])a<-table.element(a,'')a<-table.element(a,'')a<-table.element(a,'')a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Reduced model',header=TRUE)a<-table.element(a,gyx$Res.Df[2])a<-table.element(a,gyx$Df[2])a<-table.element(a,gyx$F[2])a<-table.element(a,gyx$Pr[2])a<-table.row.end(a)a<-table.end(a)table.save(a,file='mytable1.tab')a<-table.start()a<-table.row.start(a)a<-table.element(a,'Granger Causality Test: X = f(Y)',5,TRUE)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Model',header=TRUE)a<-table.element(a,'Res.DF',header=TRUE)a<-table.element(a,'Diff. DF',header=TRUE)a<-table.element(a,'F',header=TRUE)a<-table.element(a,'p-value',header=TRUE)a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Complete model',header=TRUE)a<-table.element(a,gxy$Res.Df[1])a<-table.element(a,'')a<-table.element(a,'')a<-table.element(a,'')a<-table.row.end(a)a<-table.row.start(a)a<-table.element(a,'Reduced model',header=TRUE)a<-table.element(a,gxy$Res.Df[2])a<-table.element(a,gxy$Df[2])a<-table.element(a,gxy$F[2])a<-table.element(a,gxy$Pr[2])a<-table.row.end(a)a<-table.end(a)table.save(a,file='mytable2.tab')