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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 08:18:37 -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/t1228231172q1bxjgui6w1g9mn.htm/, Retrieved Fri, 13 Feb 2026 21:22:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27937, Retrieved Fri, 13 Feb 2026 21:22:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact427

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD    [Cross Correlation Function] [W7Q7] [2008-12-02 15:18:37] [823d674fbf3a4e0ec71bbbd5140f82c6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
115,6
120,3
121,9
121,7
118,9
113,4
114
117,5
120,9
125,1
124,7
128,2
149,7
163,6
173,9
164,5
154,2
147,9
159,3
170,3
170
174,2
190,8
179,9
240,8
241,9
241,1
239,6
220,8
209,3
209,9
228,3
242,1
226,4
231,5
229,7
257,6
260
264,4
268,8
271,4
273,8
277,4
268,2
264,6
266,6
266
267,4
289,8
294
310,3
311,7
302,1
298,2
299,2
296,2
299
300
299,4
300,2
470,2
472,1
484,8
513,4
547,2
548,1
544,7
521,1
459
413,2
Dataseries Y:
Download CSV
Histogram 
114,9
115,5
112,5
111,4
115,3
110,8
103,7
111,1
113
111,2
117,6
121,7
127,3
129,8
137,1
141,4
137,4
130,7
117,2
110,8
111,4
108,2
108,8
110,2
109,5
109,5
116
111,2
112,1
114
119,1
114,1
115,1
115,4
110,8
116
119,2
126,5
127,8
131,3
140,3
137,3
143
134,5
139,9
159,3
170,4
175
175,8
180,9
180,3
169,6
172,3
184,8
177,7
184,6
211,4
215,3
215,9
244,7
259,3
289
310,9
321
315,1
333,2
314,1
284,7
273,9
216

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=27937&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=27937&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27937&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])
-150.317489955024081
-140.325905889915048
-130.333260232130198
-120.33896910809355
-110.345401875424925
-100.349825995787298
-90.374858730887124
-80.417944315978846
-70.464649937288574
-60.529093689639198
-50.604049613843573
-40.676501052651564
-30.754349003276396
-20.828498754539066
-10.884360290701664
00.916099677350798
10.904848026944065
20.858149320167995
30.799618890219433
40.727701764496038
50.639288620128695
60.553838737574561
70.474061762584396
80.399486141586387
90.334514954336022
100.285838848995985
110.242115250989198
120.205205660170584
130.173035017003657
140.145631029740339
150.123469738826651

\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 & 0.317489955024081 \tabularnewline
-14 & 0.325905889915048 \tabularnewline
-13 & 0.333260232130198 \tabularnewline
-12 & 0.33896910809355 \tabularnewline
-11 & 0.345401875424925 \tabularnewline
-10 & 0.349825995787298 \tabularnewline
-9 & 0.374858730887124 \tabularnewline
-8 & 0.417944315978846 \tabularnewline
-7 & 0.464649937288574 \tabularnewline
-6 & 0.529093689639198 \tabularnewline
-5 & 0.604049613843573 \tabularnewline
-4 & 0.676501052651564 \tabularnewline
-3 & 0.754349003276396 \tabularnewline
-2 & 0.828498754539066 \tabularnewline
-1 & 0.884360290701664 \tabularnewline
0 & 0.916099677350798 \tabularnewline
1 & 0.904848026944065 \tabularnewline
2 & 0.858149320167995 \tabularnewline
3 & 0.799618890219433 \tabularnewline
4 & 0.727701764496038 \tabularnewline
5 & 0.639288620128695 \tabularnewline
6 & 0.553838737574561 \tabularnewline
7 & 0.474061762584396 \tabularnewline
8 & 0.399486141586387 \tabularnewline
9 & 0.334514954336022 \tabularnewline
10 & 0.285838848995985 \tabularnewline
11 & 0.242115250989198 \tabularnewline
12 & 0.205205660170584 \tabularnewline
13 & 0.173035017003657 \tabularnewline
14 & 0.145631029740339 \tabularnewline
15 & 0.123469738826651 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27937&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]0.317489955024081[/C][/ROW]
[ROW][C]-14[/C][C]0.325905889915048[/C][/ROW]
[ROW][C]-13[/C][C]0.333260232130198[/C][/ROW]
[ROW][C]-12[/C][C]0.33896910809355[/C][/ROW]
[ROW][C]-11[/C][C]0.345401875424925[/C][/ROW]
[ROW][C]-10[/C][C]0.349825995787298[/C][/ROW]
[ROW][C]-9[/C][C]0.374858730887124[/C][/ROW]
[ROW][C]-8[/C][C]0.417944315978846[/C][/ROW]
[ROW][C]-7[/C][C]0.464649937288574[/C][/ROW]
[ROW][C]-6[/C][C]0.529093689639198[/C][/ROW]
[ROW][C]-5[/C][C]0.604049613843573[/C][/ROW]
[ROW][C]-4[/C][C]0.676501052651564[/C][/ROW]
[ROW][C]-3[/C][C]0.754349003276396[/C][/ROW]
[ROW][C]-2[/C][C]0.828498754539066[/C][/ROW]
[ROW][C]-1[/C][C]0.884360290701664[/C][/ROW]
[ROW][C]0[/C][C]0.916099677350798[/C][/ROW]
[ROW][C]1[/C][C]0.904848026944065[/C][/ROW]
[ROW][C]2[/C][C]0.858149320167995[/C][/ROW]
[ROW][C]3[/C][C]0.799618890219433[/C][/ROW]
[ROW][C]4[/C][C]0.727701764496038[/C][/ROW]
[ROW][C]5[/C][C]0.639288620128695[/C][/ROW]
[ROW][C]6[/C][C]0.553838737574561[/C][/ROW]
[ROW][C]7[/C][C]0.474061762584396[/C][/ROW]
[ROW][C]8[/C][C]0.399486141586387[/C][/ROW]
[ROW][C]9[/C][C]0.334514954336022[/C][/ROW]
[ROW][C]10[/C][C]0.285838848995985[/C][/ROW]
[ROW][C]11[/C][C]0.242115250989198[/C][/ROW]
[ROW][C]12[/C][C]0.205205660170584[/C][/ROW]
[ROW][C]13[/C][C]0.173035017003657[/C][/ROW]
[ROW][C]14[/C][C]0.145631029740339[/C][/ROW]
[ROW][C]15[/C][C]0.123469738826651[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27937&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27937&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])
-150.317489955024081
-140.325905889915048
-130.333260232130198
-120.33896910809355
-110.345401875424925
-100.349825995787298
-90.374858730887124
-80.417944315978846
-70.464649937288574
-60.529093689639198
-50.604049613843573
-40.676501052651564
-30.754349003276396
-20.828498754539066
-10.884360290701664
00.916099677350798
10.904848026944065
20.858149320167995
30.799618890219433
40.727701764496038
50.639288620128695
60.553838737574561
70.474061762584396
80.399486141586387
90.334514954336022
100.285838848995985
110.242115250989198
120.205205660170584
130.173035017003657
140.145631029740339
150.123469738826651


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')