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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 14:39:53 -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/t12282540753xzngtrjeq8e9nf.htm/, Retrieved Sun, 19 May 2024 12:18:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28487, Retrieved Sun, 19 May 2024 12:18:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191

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]
F RMPD  [Cross Correlation Function] [] [2008-12-02 21:28:41] [74be16979710d4c4e7c6647856088456]
F   PD      [Cross Correlation Function] [] [2008-12-02 21:39:53] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- RMPD        [Variance Reduction Matrix] [] [2008-12-04 15:53:33] [996314793dac993597edc1ca2281ff39]
- RMPD        [(Partial) Autocorrelation Function] [] [2008-12-04 16:04:36] [996314793dac993597edc1ca2281ff39]
- RMPD        [(Partial) Autocorrelation Function] [] [2008-12-04 16:11:33] [996314793dac993597edc1ca2281ff39]
- RMPD        [Standard Deviation-Mean Plot] [] [2008-12-04 16:15:59] [996314793dac993597edc1ca2281ff39]
- RMPD        [Spectral Analysis] [] [2008-12-04 16:21:06] [996314793dac993597edc1ca2281ff39]
Feedback Forum
2008-12-04 16:36:35 [Angelique Van de Vijver] [reply] 
Q8: Foute uitvoering van de opdracht. De student heeft de kruiscorrelatie berekend.Dit moest je doen bij Q9 en niet bij Q8.
Bij deze opgave(Q8) moest je beide tijdreeksen apart differentiëren en kijken welke de beste differentiatie vormt voor elke tijdreeks maar dit heeft de student niet gedaan. Het is dus de bedoeling om de tijdreeksen stationair te maken en dus om trenden en seizoenaliteit eruit te halen.
Hierbij kun je je antwoord staven met een ACF, VRM en een spectraalanalyse.

Ik heb zelf een analyse gemaakt van data X(duurzame consumptiegoederen) van de student:
Eerst heb ik een ACF gemaakt zonder differentiatie(d=0;D=0):
http://www.freestatistics.org/blog/date/2008/Dec/04/t1228406695x0jn4zu66f5yklv.htm
Hierop zien we dat er geen langetermijntrend is maar wel seizoenaliteit. Er zijn telkens pieken om de 6 maanden. Hieruit kunnen we dus concluderen dat we seizoenaal moeten differentiëren => D=1.
Na deze differentiatie (d=0;D=1): http://www.freestatistics.org/blog/date/2008/Dec/04/t1228407119cc0dadeadlzv4vp.htm
We zien dat de seizoenaliteit weggewerkt is. Dit is dus een goede differentiatie.

Ik heb ook een standard deviation-meanplot uitgevoerd:
http://www.freestatistics.org/blog/date/2008/Dec/04/t1228407383xkugu2xev7ltzlv.htm
In de tabel zien we dat de optimale lambda voor de transformatie gelijk is aan -3.09609593452547

Ik heb ook een variantiereductiematrix van data X geproduceerd:
http://www.freestatistics.org/blog/date/2008/Dec/04/t12284060379rzy4pk0q2rrsm4.htm
Hierin zien we dat de differentiatie d=0 en D=1 de kleinste variantie (40.9986125886525) weergeeft. Ook de getrimde variantie (24.1392195121951) is bij deze differentiatie het kleinst. We kunnen dus bij deze differentiatie het meeste verklaren.

Om mijn antwoord te staven heb ik ook een spectraalanalyse uitgevoerd:
Di is de link van de analyse na de differentiatie:
http://www.freestatistics.org/blog/date/2008/Dec/04/t1228407700s52gzjs6y368xvw.htm
We zien op het raw periodogram dat de schommelingen ongeveer horizontaal lopen.
Bij het cumulatief periodogram zien we dat de lijn volledig binnen het betrouwbaarheidsinterval ligt. Na de differentiatie loop de lijn veel minder volgens trapbewegingen=> minder seizoenaliteit.
Als we naar de tabel kijken, zien we dat na de differentiatie het spectrum bij(6) en(3) veel kleiner is dan voor de differentiatie. De seizoenaliteit is er dus uitgehaald.
2008-12-10 09:02:07 [Peter Van Doninck] [reply] 
De student heeft de opgave verkeerd opgelost. Hij dient eerst de standaard deviation mean plot uit de voeren, om zo de optimale lambda te verkrijgen. Nadien kan hij via de autocorrelatie of de variantie reductiematrix de optimale D en d berekenen. Dit alles kan hij nog eens verifiëren met de spectraal analyse.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.8
100.7
86.2
83.2
71.7
77.5
89.8
80.3
78.7
93.8
57.6
60.6
91
85.3
77.4
77.3
68.3
69.9
81.7
75.1
69.9
84
54.3
60
89.9
77
85.3
77.6
69.2
75.5
85.7
72.2
79.9
85.3
52.2
61.2
82.4
85.4
78.2
70.2
70.2
69.3
77.5
66.1
69
79.2
56.2
63.3
77.8
92
78.1
65.1
71.1
70.9
72
81.9
70.6
72.5
65.1
61.1
Dataseries Y:
Download CSV
Histogram 
127.5
128.6
116.6
127.4
105
108.3
125
111.6
106.5
130.3
115
116.1
134
126.5
125.8
136.4
114.9
110.9
125.5
116.8
116.8
125.5
104.2
115.1
132.8
123.3
124.8
122
117.4
117.9
137.4
114.6
124.7
129.6
109.4
120.9
134.9
136.3
133.2
127.2
122.7
120.5
137.8
119.1
124.3
134.4
121.1
122.2
127.7
137.4
132.2
129.2
124.9
124.8
128.2
134.4
118.6
132.6
123.2
112.3

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=28487&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=28487&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28487&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 series1
Degree of seasonal differencing (D) of X series1
Seasonal Period (s)12
Box-Cox transformation parameter (lambda) of Y series1
Degree of non-seasonal differencing (d) of Y series1
Degree of seasonal differencing (D) of Y series1
krho(Y[t],X[t+k])
-13-0.0781115904816836
-120.0307919403822810
-11-0.00355379287326089
-10-0.133452426140486
-90.196310371393923
-80.0219377970648323
-7-0.284183039313044
-60.323865841645351
-5-0.101316393279531
-4-0.107898908312370
-30.141755540210517
-20.0853838436819786
-1-0.484102852016324
00.68752752398253
1-0.36998150574335
2-0.165410806821592
30.406609836197045
4-0.162786838527194
5-0.127941731049725
60.0583858685668906
70.0130437919758371
8-0.136129378777505
90.267453333443085
10-0.164237034806508
11-0.130037682022957
120.280426708460558
13-0.156301983265120

\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 & 1 \tabularnewline
Degree of seasonal differencing (D) of X series & 1 \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 & 1 \tabularnewline
Degree of seasonal differencing (D) of Y series & 1 \tabularnewline
k & rho(Y[t],X[t+k]) \tabularnewline
-13 & -0.0781115904816836 \tabularnewline
-12 & 0.0307919403822810 \tabularnewline
-11 & -0.00355379287326089 \tabularnewline
-10 & -0.133452426140486 \tabularnewline
-9 & 0.196310371393923 \tabularnewline
-8 & 0.0219377970648323 \tabularnewline
-7 & -0.284183039313044 \tabularnewline
-6 & 0.323865841645351 \tabularnewline
-5 & -0.101316393279531 \tabularnewline
-4 & -0.107898908312370 \tabularnewline
-3 & 0.141755540210517 \tabularnewline
-2 & 0.0853838436819786 \tabularnewline
-1 & -0.484102852016324 \tabularnewline
0 & 0.68752752398253 \tabularnewline
1 & -0.36998150574335 \tabularnewline
2 & -0.165410806821592 \tabularnewline
3 & 0.406609836197045 \tabularnewline
4 & -0.162786838527194 \tabularnewline
5 & -0.127941731049725 \tabularnewline
6 & 0.0583858685668906 \tabularnewline
7 & 0.0130437919758371 \tabularnewline
8 & -0.136129378777505 \tabularnewline
9 & 0.267453333443085 \tabularnewline
10 & -0.164237034806508 \tabularnewline
11 & -0.130037682022957 \tabularnewline
12 & 0.280426708460558 \tabularnewline
13 & -0.156301983265120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28487&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]1[/C][/ROW]
[ROW][C]Degree of seasonal differencing (D) of X series[/C][C]1[/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]1[/C][/ROW]
[ROW][C]Degree of seasonal differencing (D) of Y series[/C][C]1[/C][/ROW]
[ROW][C]k[/C][C]rho(Y[t],X[t+k])[/C][/ROW]
[ROW][C]-13[/C][C]-0.0781115904816836[/C][/ROW]
[ROW][C]-12[/C][C]0.0307919403822810[/C][/ROW]
[ROW][C]-11[/C][C]-0.00355379287326089[/C][/ROW]
[ROW][C]-10[/C][C]-0.133452426140486[/C][/ROW]
[ROW][C]-9[/C][C]0.196310371393923[/C][/ROW]
[ROW][C]-8[/C][C]0.0219377970648323[/C][/ROW]
[ROW][C]-7[/C][C]-0.284183039313044[/C][/ROW]
[ROW][C]-6[/C][C]0.323865841645351[/C][/ROW]
[ROW][C]-5[/C][C]-0.101316393279531[/C][/ROW]
[ROW][C]-4[/C][C]-0.107898908312370[/C][/ROW]
[ROW][C]-3[/C][C]0.141755540210517[/C][/ROW]
[ROW][C]-2[/C][C]0.0853838436819786[/C][/ROW]
[ROW][C]-1[/C][C]-0.484102852016324[/C][/ROW]
[ROW][C]0[/C][C]0.68752752398253[/C][/ROW]
[ROW][C]1[/C][C]-0.36998150574335[/C][/ROW]
[ROW][C]2[/C][C]-0.165410806821592[/C][/ROW]
[ROW][C]3[/C][C]0.406609836197045[/C][/ROW]
[ROW][C]4[/C][C]-0.162786838527194[/C][/ROW]
[ROW][C]5[/C][C]-0.127941731049725[/C][/ROW]
[ROW][C]6[/C][C]0.0583858685668906[/C][/ROW]
[ROW][C]7[/C][C]0.0130437919758371[/C][/ROW]
[ROW][C]8[/C][C]-0.136129378777505[/C][/ROW]
[ROW][C]9[/C][C]0.267453333443085[/C][/ROW]
[ROW][C]10[/C][C]-0.164237034806508[/C][/ROW]
[ROW][C]11[/C][C]-0.130037682022957[/C][/ROW]
[ROW][C]12[/C][C]0.280426708460558[/C][/ROW]
[ROW][C]13[/C][C]-0.156301983265120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28487&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28487&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 series1
Degree of seasonal differencing (D) of X series1
Seasonal Period (s)12
Box-Cox transformation parameter (lambda) of Y series1
Degree of non-seasonal differencing (d) of Y series1
Degree of seasonal differencing (D) of Y series1
krho(Y[t],X[t+k])
-13-0.0781115904816836
-120.0307919403822810
-11-0.00355379287326089
-10-0.133452426140486
-90.196310371393923
-80.0219377970648323
-7-0.284183039313044
-60.323865841645351
-5-0.101316393279531
-4-0.107898908312370
-30.141755540210517
-20.0853838436819786
-1-0.484102852016324
00.68752752398253
1-0.36998150574335
2-0.165410806821592
30.406609836197045
4-0.162786838527194
5-0.127941731049725
60.0583858685668906
70.0130437919758371
8-0.136129378777505
90.267453333443085
10-0.164237034806508
11-0.130037682022957
120.280426708460558
13-0.156301983265120


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ; par5 = 1 ; par6 = 1 ; par7 = 1 ;
Parameters (R input):
par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ; par5 = 1 ; par6 = 1 ; par7 = 1 ;
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')