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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_cross.wasp
Title produced by softwareCross Correlation Function
Date of computationSun, 30 Nov 2008 12:09:57 -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/Nov/30/t12280723220vwf6iwzrkkhq94.htm/, Retrieved Sun, 19 May 2024 00:54:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26696, Retrieved Sun, 19 May 2024 00:54:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsCross correlation function
Estimated Impact203

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:05:16] [b98453cac15ba1066b407e146608df68]
F RMPD    [Cross Correlation Function] [Cross correlation...] [2008-11-30 19:09:57] [f4b2017b314c03698059f43b95818e67] [Current]
-   PD      [Cross Correlation Function] [Cross correlation...] [2008-11-30 19:48:56] [b635de6fc42b001d22cbe6e730fec936]
F   P         [Cross Correlation Function] [Cross correlation...] [2008-11-30 23:03:03] [b635de6fc42b001d22cbe6e730fec936]
Feedback Forum
2008-12-04 17:36:53 [339a57d8a4d5d113e4804fc423e4a59e] [reply] 
Door met de cross correlation function te werken, kan men de correlatie tussen 2 data uit 2 verschillende reeksen berekenen. Dit verschilt dus van de autocorrelatie waarbij men de correlatie enkel kan berekenen tuseen 2 data uit 1 datareeks. De software gaat na in welke mate het verleden gecorreleerd is met het heden. De 'k'-waarde bepaald hier het aantal perioden dat men terug of vooruit gaat.
2008-12-05 15:44:34 [Kristof Van Esbroeck] [reply] 
Student maakt berekeningen maar geeft geen duidelijke uitleg over de gebuikte technieken.

We werken, zoals student correct deed, met de Cross Correlatie functie.
Deze tracht een voorspelling neer te zetten van een datareeks adhv een verschillende variabele. Dit in tegenstelling tot de autocorrelatie, welke tracht een voorspelling te maken adhv het verleden van de reeks.

We noteren voorts op de x as van de cross correlatie functie de verschillende lags.

We merken verschillende k waarden op in de bijhorende tabel.k = 0 verwijst naar de autocorrelatie. Een negatieve waarde heeft betrekking op het verleden, een positieve daarentegen verwijst naar de toekomst.


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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8,4
8,4
8,4
8,6
8,9
8,8
8,3
7,5
7,2
7,5
8,8
9,3
9,3
8,7
8,2
8,3
8,5
8,6
8,6
8,2
8,1
8
8,6
8,7
8,8
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8,1
8,2
8,1
8,1
7,9
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,6
6,2
6,2
6,8
6,9
Dataseries Y:
Download CSV
Histogram 
9,5
9,1
9
9,3
9,9
9,8
9,4
8,3
8
8,5
10,4
11,1
10,9
9,9
9,2
9,2
9,5
9,6
9,5
9,1
8,9
9
10,1
10,3
10,2
9,6
9,2
9,3
9,4
9,4
9,2
9
9
9
9,8
10
9,9
9,3
9
9
9,1
9,1
9,1
9,2
8,8
8,3
8,4
8,1
7,8
7,9
7,9
8
7,9
7,5
7,2
6,9
6,6
6,7
7,3
7,5

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26696&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26696&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26696&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'George Udny Yule' @ 72.249.76.132






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])
-140.116015487414469
-130.237613706654766
-120.351963347465720
-110.389055938418625
-100.386964072027983
-90.394984323661482
-80.448173596314852
-70.510043217194963
-60.529365477283685
-50.479248852838576
-40.422164542131463
-30.4589138204354
-20.620051513508517
-10.817494519209974
00.947355649706108
10.84716375438497
20.655307381789444
30.483394353074862
40.425765423665522
50.44794498130088
60.467288308302152
70.412386373684045
80.3144299118613
90.228938039964146
100.200034235945143
110.203132632602077
120.192135704250823
130.114520516879418
140.0353370149070467

\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
-14 & 0.116015487414469 \tabularnewline
-13 & 0.237613706654766 \tabularnewline
-12 & 0.351963347465720 \tabularnewline
-11 & 0.389055938418625 \tabularnewline
-10 & 0.386964072027983 \tabularnewline
-9 & 0.394984323661482 \tabularnewline
-8 & 0.448173596314852 \tabularnewline
-7 & 0.510043217194963 \tabularnewline
-6 & 0.529365477283685 \tabularnewline
-5 & 0.479248852838576 \tabularnewline
-4 & 0.422164542131463 \tabularnewline
-3 & 0.4589138204354 \tabularnewline
-2 & 0.620051513508517 \tabularnewline
-1 & 0.817494519209974 \tabularnewline
0 & 0.947355649706108 \tabularnewline
1 & 0.84716375438497 \tabularnewline
2 & 0.655307381789444 \tabularnewline
3 & 0.483394353074862 \tabularnewline
4 & 0.425765423665522 \tabularnewline
5 & 0.44794498130088 \tabularnewline
6 & 0.467288308302152 \tabularnewline
7 & 0.412386373684045 \tabularnewline
8 & 0.3144299118613 \tabularnewline
9 & 0.228938039964146 \tabularnewline
10 & 0.200034235945143 \tabularnewline
11 & 0.203132632602077 \tabularnewline
12 & 0.192135704250823 \tabularnewline
13 & 0.114520516879418 \tabularnewline
14 & 0.0353370149070467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26696&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]-14[/C][C]0.116015487414469[/C][/ROW]
[ROW][C]-13[/C][C]0.237613706654766[/C][/ROW]
[ROW][C]-12[/C][C]0.351963347465720[/C][/ROW]
[ROW][C]-11[/C][C]0.389055938418625[/C][/ROW]
[ROW][C]-10[/C][C]0.386964072027983[/C][/ROW]
[ROW][C]-9[/C][C]0.394984323661482[/C][/ROW]
[ROW][C]-8[/C][C]0.448173596314852[/C][/ROW]
[ROW][C]-7[/C][C]0.510043217194963[/C][/ROW]
[ROW][C]-6[/C][C]0.529365477283685[/C][/ROW]
[ROW][C]-5[/C][C]0.479248852838576[/C][/ROW]
[ROW][C]-4[/C][C]0.422164542131463[/C][/ROW]
[ROW][C]-3[/C][C]0.4589138204354[/C][/ROW]
[ROW][C]-2[/C][C]0.620051513508517[/C][/ROW]
[ROW][C]-1[/C][C]0.817494519209974[/C][/ROW]
[ROW][C]0[/C][C]0.947355649706108[/C][/ROW]
[ROW][C]1[/C][C]0.84716375438497[/C][/ROW]
[ROW][C]2[/C][C]0.655307381789444[/C][/ROW]
[ROW][C]3[/C][C]0.483394353074862[/C][/ROW]
[ROW][C]4[/C][C]0.425765423665522[/C][/ROW]
[ROW][C]5[/C][C]0.44794498130088[/C][/ROW]
[ROW][C]6[/C][C]0.467288308302152[/C][/ROW]
[ROW][C]7[/C][C]0.412386373684045[/C][/ROW]
[ROW][C]8[/C][C]0.3144299118613[/C][/ROW]
[ROW][C]9[/C][C]0.228938039964146[/C][/ROW]
[ROW][C]10[/C][C]0.200034235945143[/C][/ROW]
[ROW][C]11[/C][C]0.203132632602077[/C][/ROW]
[ROW][C]12[/C][C]0.192135704250823[/C][/ROW]
[ROW][C]13[/C][C]0.114520516879418[/C][/ROW]
[ROW][C]14[/C][C]0.0353370149070467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26696&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26696&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])
-140.116015487414469
-130.237613706654766
-120.351963347465720
-110.389055938418625
-100.386964072027983
-90.394984323661482
-80.448173596314852
-70.510043217194963
-60.529365477283685
-50.479248852838576
-40.422164542131463
-30.4589138204354
-20.620051513508517
-10.817494519209974
00.947355649706108
10.84716375438497
20.655307381789444
30.483394353074862
40.425765423665522
50.44794498130088
60.467288308302152
70.412386373684045
80.3144299118613
90.228938039964146
100.200034235945143
110.203132632602077
120.192135704250823
130.114520516879418
140.0353370149070467


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')