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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_cross.wasp
Title produced by softwareCross Correlation Function
Date of computationTue, 02 Dec 2008 07:37:27 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/02/t1228228700pfc6a36w9211j8e.htm/, Retrieved Sun, 19 May 2024 12:34:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27868, Retrieved Sun, 19 May 2024 12:34:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact210

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Cross Correlation Function] [Non-stationary ti...] [2008-12-02 14:37:27] [a57a97ff9690154d18ed2c72b6ae351a] [Current]
F RMPD    [Standard Deviation-Mean Plot] [non stationary ti...] [2008-12-02 14:58:33] [6c955a33a02d5e30e404487434e7a5c9]
F    D      [Standard Deviation-Mean Plot] [non stationary ti...] [2008-12-02 15:02:16] [6c955a33a02d5e30e404487434e7a5c9]
F RM D        [Variance Reduction Matrix] [non stationary ti...] [2008-12-02 15:05:11] [6c955a33a02d5e30e404487434e7a5c9]
F RM D        [Variance Reduction Matrix] [non stationary ti...] [2008-12-02 15:09:02] [6c955a33a02d5e30e404487434e7a5c9]
F   PD    [Cross Correlation Function] [Non-stationary ti...] [2008-12-02 15:13:35] [6c955a33a02d5e30e404487434e7a5c9]
Feedback Forum
2008-12-04 10:58:18 [Steven Vercammen] [reply] 
Deze vraag heb ik correct opgelost.
Met de cross correlatiefunctie kan men nagaan in hoeverre Y te verklaren valt door het verleden van X. X = de industriële productie van investeringsgoederen (2000=100) en Y= gewogen gemiddelde rente op basis her-financieringstransacties. rho(Y[t],X[t+k]) geeft de correlatie aan tussen het verleden van X en het heden van Y wanneer k kleiner is dan 0. (is er sprake van een leading indicator?) Wanneer k groter is dan 0 geeft het de correlatie weer tussen de toekomstige x en het heden van Y (is er sprake van een lagging indicator)? Uit de grafiek kunnen we afleiden we afleiden dat er van beiden sprake is. Zowel de verticale lijntjes voor als na k=0 overstijgen het betrouwbaarheidsinterval en verschillen dus significant van 0. Volgens deze grafiek zou dus zowel het vroegere als de toekomstige X-waarden informatie bevatten om Y te voorspellen.
2008-12-07 10:05:31 [Käthe Vanderheggen] [reply] 
Wanneer de beide kanten buiten het betrouwbaarheidsinterval liggen, wil dat zeggen dat het verleden van X iets zegt over de toekomst van Y en dat het verleden van Y ook iets zegt over de toekomst van X. Op deze grafiek echter liggen alle autocorrelaties buiten het betrouwbaarheidsinterval, met uitzondering van de uiterst rechtse.
2008-12-08 18:52:32 [Koen Van Baelen] [reply] 
Correct geantwoord, enkel kan er nog wat informatie gegeven worden bij de tabel. Als k=0, dan kan je de waarde 0.16 aflezen in de tabel. Dit geeft de correlatie weer tussen Yt en Xt zonder verschuiving in de tijd. Al de waarden hieronder (als k>0) geven een toekomstige waarde van Xt weer met een huidige Yt. De waarden erboven (als k<0) geven weer (ahv correlaties) in welke mate Xt van het verleden Yt kan verklaren in de toekomst. Hier kan men dus ook zeggen dat het verleden van X iets zegt over de toekomst van Y en dat het verleden van Y ook iets zegt over de toekomst van X

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93,4
101,5
110,4
105,9
108,4
113,9
86,1
69,4
101,2
100,5
98,0
106,6
90,1
96,9
125,9
112,0
100,0
123,9
79,8
83,4
113,6
112,9
104,0
109,9
99,0
106,3
128,9
111,1
102,9
130,0
87,0
87,5
117,6
103,4
110,8
112,6
102,5
112,4
135,6
105,1
127,7
137,0
91,0
90,5
122,4
123,3
124,3
120,0
118,1
119,0
142,7
123,6
129,6
151,6
110,4
99,2
130,5
136,2
129,7
128,0
121,6
135,8
143,8
147,5
136,2
156,6
123,3
104,5
143,6
Dataseries Y:
Download CSV
Histogram 
2,84
2,78
2,63
2,54
2,56
2,19
2,09
2,06
2,08
2,05
2,03
2,04
2,03
2,01
2,01
2,01
2,01
2,01
2,01
2,02
2,02
2,03
2,05
2,08
2,07
2,06
2,05
2,05
2,05
2,05
2,05
2,06
2,06
2,07
2,07
2,30
2,31
2,31
2,53
2,58
2,59
2,73
2,82
3,00
3,04
3,23
3,32
3,49
3,57
3,56
3,72
3,82
3,82
3,98
4,06
4,08
4,19
4,16
4,17
4,21
4,21
4,17
4,19
4,25
4,25
4,20
4,33
4,41
4,56

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27868&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27868&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27868&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Cross Correlation Function
ParameterValue
Box-Cox transformation parameter (lambda) of X series1
Degree of non-seasonal differencing (d) of X series0
Degree of seasonal differencing (D) of X series0
Seasonal Period (s)12
Box-Cox transformation parameter (lambda) of Y series1
Degree of non-seasonal differencing (d) of Y series0
Degree of seasonal differencing (D) of Y series0
krho(Y[t],X[t+k])
-150.346095626276825
-140.339927810294595
-130.326531090789998
-120.355504107194795
-110.391208153711127
-100.429637047425602
-90.448653796055234
-80.446051523526038
-70.48914556506268
-60.53139333410027
-50.559097909854435
-40.578505886225346
-30.633328821597212
-20.621999184823435
-10.591063976995531
00.615865807873296
10.590067571867268
20.573746007914762
30.537965636556496
40.501135653406943
50.484193422500343
60.451136039592166
70.409089518755251
80.378221121471048
90.353939352808999
100.324420251715742
110.290871694634509
120.257731791057554
130.223562295954802
140.188964553045378
150.153443283420943

\begin{tabular}{lllllllll}
\hline
Cross Correlation Function \tabularnewline
Parameter & Value \tabularnewline
Box-Cox transformation parameter (lambda) of X series & 1 \tabularnewline
Degree of non-seasonal differencing (d) of X series & 0 \tabularnewline
Degree of seasonal differencing (D) of X series & 0 \tabularnewline
Seasonal Period (s) & 12 \tabularnewline
Box-Cox transformation parameter (lambda) of Y series & 1 \tabularnewline
Degree of non-seasonal differencing (d) of Y series & 0 \tabularnewline
Degree of seasonal differencing (D) of Y series & 0 \tabularnewline
k & rho(Y[t],X[t+k]) \tabularnewline
-15 & 0.346095626276825 \tabularnewline
-14 & 0.339927810294595 \tabularnewline
-13 & 0.326531090789998 \tabularnewline
-12 & 0.355504107194795 \tabularnewline
-11 & 0.391208153711127 \tabularnewline
-10 & 0.429637047425602 \tabularnewline
-9 & 0.448653796055234 \tabularnewline
-8 & 0.446051523526038 \tabularnewline
-7 & 0.48914556506268 \tabularnewline
-6 & 0.53139333410027 \tabularnewline
-5 & 0.559097909854435 \tabularnewline
-4 & 0.578505886225346 \tabularnewline
-3 & 0.633328821597212 \tabularnewline
-2 & 0.621999184823435 \tabularnewline
-1 & 0.591063976995531 \tabularnewline
0 & 0.615865807873296 \tabularnewline
1 & 0.590067571867268 \tabularnewline
2 & 0.573746007914762 \tabularnewline
3 & 0.537965636556496 \tabularnewline
4 & 0.501135653406943 \tabularnewline
5 & 0.484193422500343 \tabularnewline
6 & 0.451136039592166 \tabularnewline
7 & 0.409089518755251 \tabularnewline
8 & 0.378221121471048 \tabularnewline
9 & 0.353939352808999 \tabularnewline
10 & 0.324420251715742 \tabularnewline
11 & 0.290871694634509 \tabularnewline
12 & 0.257731791057554 \tabularnewline
13 & 0.223562295954802 \tabularnewline
14 & 0.188964553045378 \tabularnewline
15 & 0.153443283420943 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27868&T=1

[TABLE]
[ROW][C]Cross Correlation Function[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]Box-Cox transformation parameter (lambda) of X series[/C][C]1[/C][/ROW]
[ROW][C]Degree of non-seasonal differencing (d) of X series[/C][C]0[/C][/ROW]
[ROW][C]Degree of seasonal differencing (D) of X series[/C][C]0[/C][/ROW]
[ROW][C]Seasonal Period (s)[/C][C]12[/C][/ROW]
[ROW][C]Box-Cox transformation parameter (lambda) of Y series[/C][C]1[/C][/ROW]
[ROW][C]Degree of non-seasonal differencing (d) of Y series[/C][C]0[/C][/ROW]
[ROW][C]Degree of seasonal differencing (D) of Y series[/C][C]0[/C][/ROW]
[ROW][C]k[/C][C]rho(Y[t],X[t+k])[/C][/ROW]
[ROW][C]-15[/C][C]0.346095626276825[/C][/ROW]
[ROW][C]-14[/C][C]0.339927810294595[/C][/ROW]
[ROW][C]-13[/C][C]0.326531090789998[/C][/ROW]
[ROW][C]-12[/C][C]0.355504107194795[/C][/ROW]
[ROW][C]-11[/C][C]0.391208153711127[/C][/ROW]
[ROW][C]-10[/C][C]0.429637047425602[/C][/ROW]
[ROW][C]-9[/C][C]0.448653796055234[/C][/ROW]
[ROW][C]-8[/C][C]0.446051523526038[/C][/ROW]
[ROW][C]-7[/C][C]0.48914556506268[/C][/ROW]
[ROW][C]-6[/C][C]0.53139333410027[/C][/ROW]
[ROW][C]-5[/C][C]0.559097909854435[/C][/ROW]
[ROW][C]-4[/C][C]0.578505886225346[/C][/ROW]
[ROW][C]-3[/C][C]0.633328821597212[/C][/ROW]
[ROW][C]-2[/C][C]0.621999184823435[/C][/ROW]
[ROW][C]-1[/C][C]0.591063976995531[/C][/ROW]
[ROW][C]0[/C][C]0.615865807873296[/C][/ROW]
[ROW][C]1[/C][C]0.590067571867268[/C][/ROW]
[ROW][C]2[/C][C]0.573746007914762[/C][/ROW]
[ROW][C]3[/C][C]0.537965636556496[/C][/ROW]
[ROW][C]4[/C][C]0.501135653406943[/C][/ROW]
[ROW][C]5[/C][C]0.484193422500343[/C][/ROW]
[ROW][C]6[/C][C]0.451136039592166[/C][/ROW]
[ROW][C]7[/C][C]0.409089518755251[/C][/ROW]
[ROW][C]8[/C][C]0.378221121471048[/C][/ROW]
[ROW][C]9[/C][C]0.353939352808999[/C][/ROW]
[ROW][C]10[/C][C]0.324420251715742[/C][/ROW]
[ROW][C]11[/C][C]0.290871694634509[/C][/ROW]
[ROW][C]12[/C][C]0.257731791057554[/C][/ROW]
[ROW][C]13[/C][C]0.223562295954802[/C][/ROW]
[ROW][C]14[/C][C]0.188964553045378[/C][/ROW]
[ROW][C]15[/C][C]0.153443283420943[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27868&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27868&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Cross Correlation Function
ParameterValue
Box-Cox transformation parameter (lambda) of X series1
Degree of non-seasonal differencing (d) of X series0
Degree of seasonal differencing (D) of X series0
Seasonal Period (s)12
Box-Cox transformation parameter (lambda) of Y series1
Degree of non-seasonal differencing (d) of Y series0
Degree of seasonal differencing (D) of Y series0
krho(Y[t],X[t+k])
-150.346095626276825
-140.339927810294595
-130.326531090789998
-120.355504107194795
-110.391208153711127
-100.429637047425602
-90.448653796055234
-80.446051523526038
-70.48914556506268
-60.53139333410027
-50.559097909854435
-40.578505886225346
-30.633328821597212
-20.621999184823435
-10.591063976995531
00.615865807873296
10.590067571867268
20.573746007914762
30.537965636556496
40.501135653406943
50.484193422500343
60.451136039592166
70.409089518755251
80.378221121471048
90.353939352808999
100.324420251715742
110.290871694634509
120.257731791057554
130.223562295954802
140.188964553045378
150.153443283420943


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ; par5 = 1 ; par6 = 0 ; par7 = 0 ;
Parameters (R input):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ; par5 = 1 ; par6 = 0 ; par7 = 0 ;
R code (references can be found in the software module):
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)
if (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)
x
y
bitmap(file='test1.png')
(r <- ccf(x,y,main='Cross Correlation Function',ylab='CCF',xlab='Lag (k)'))
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Cross Correlation Function',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Box-Cox transformation parameter (lambda) of X series',header=TRUE)
a<-table.element(a,par1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of non-seasonal differencing (d) of X series',header=TRUE)
a<-table.element(a,par2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of seasonal differencing (D) of X series',header=TRUE)
a<-table.element(a,par3)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Seasonal Period (s)',header=TRUE)
a<-table.element(a,par4)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Box-Cox transformation parameter (lambda) of Y series',header=TRUE)
a<-table.element(a,par5)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of non-seasonal differencing (d) of Y series',header=TRUE)
a<-table.element(a,par6)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degree of seasonal differencing (D) of Y series',header=TRUE)
a<-table.element(a,par7)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'k',header=TRUE)
a<-table.element(a,'rho(Y[t],X[t+k])',header=TRUE)
a<-table.row.end(a)
mylength <- length(r$acf)
myhalf <- floor((mylength-1)/2)
for (i in 1:mylength) {
a<-table.row.start(a)
a<-table.element(a,i-myhalf-1,header=TRUE)
a<-table.element(a,r$acf[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')