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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 15:32:54 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t1481898905r4sauyurhv4momo.htm/, Retrieved Thu, 02 May 2024 17:10:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300315, Retrieved Thu, 02 May 2024 17:10:42 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [autocorrelation f...] [2016-12-16 14:32:54] [31f526a885cd288e1bc58dc4a6a7fb1f] [Current]

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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=300315&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=300315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300315&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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.323043	-3.4642	0.000374
2	-0.091757	-0.984	0.163595
3	-0.045297	-0.4858	0.314033
4	0.073631	0.7896	0.215693
5	-0.064016	-0.6865	0.24689
6	0.068086	0.7301	0.233394
7	-0.023766	-0.2549	0.399641
8	0.085771	0.9198	0.179802
9	-0.107675	-1.1547	0.125307
10	-0.064162	-0.6881	0.246401
11	0.016602	0.178	0.429503
12	0.155579	1.6684	0.048979
13	0.028738	0.3082	0.379252
14	-0.105556	-1.132	0.130003
15	-0.00935	-0.1003	0.460153
16	-0.071939	-0.7715	0.221009
17	0.020793	0.223	0.411973
18	0.058736	0.6299	0.265014
19	-0.056784	-0.6089	0.271881
20	0.085325	0.915	0.18105

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.323043 & -3.4642 & 0.000374 \tabularnewline
2 & -0.091757 & -0.984 & 0.163595 \tabularnewline
3 & -0.045297 & -0.4858 & 0.314033 \tabularnewline
4 & 0.073631 & 0.7896 & 0.215693 \tabularnewline
5 & -0.064016 & -0.6865 & 0.24689 \tabularnewline
6 & 0.068086 & 0.7301 & 0.233394 \tabularnewline
7 & -0.023766 & -0.2549 & 0.399641 \tabularnewline
8 & 0.085771 & 0.9198 & 0.179802 \tabularnewline
9 & -0.107675 & -1.1547 & 0.125307 \tabularnewline
10 & -0.064162 & -0.6881 & 0.246401 \tabularnewline
11 & 0.016602 & 0.178 & 0.429503 \tabularnewline
12 & 0.155579 & 1.6684 & 0.048979 \tabularnewline
13 & 0.028738 & 0.3082 & 0.379252 \tabularnewline
14 & -0.105556 & -1.132 & 0.130003 \tabularnewline
15 & -0.00935 & -0.1003 & 0.460153 \tabularnewline
16 & -0.071939 & -0.7715 & 0.221009 \tabularnewline
17 & 0.020793 & 0.223 & 0.411973 \tabularnewline
18 & 0.058736 & 0.6299 & 0.265014 \tabularnewline
19 & -0.056784 & -0.6089 & 0.271881 \tabularnewline
20 & 0.085325 & 0.915 & 0.18105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300315&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.323043[/C][C]-3.4642[/C][C]0.000374[/C][/ROW]
[ROW][C]2[/C][C]-0.091757[/C][C]-0.984[/C][C]0.163595[/C][/ROW]
[ROW][C]3[/C][C]-0.045297[/C][C]-0.4858[/C][C]0.314033[/C][/ROW]
[ROW][C]4[/C][C]0.073631[/C][C]0.7896[/C][C]0.215693[/C][/ROW]
[ROW][C]5[/C][C]-0.064016[/C][C]-0.6865[/C][C]0.24689[/C][/ROW]
[ROW][C]6[/C][C]0.068086[/C][C]0.7301[/C][C]0.233394[/C][/ROW]
[ROW][C]7[/C][C]-0.023766[/C][C]-0.2549[/C][C]0.399641[/C][/ROW]
[ROW][C]8[/C][C]0.085771[/C][C]0.9198[/C][C]0.179802[/C][/ROW]
[ROW][C]9[/C][C]-0.107675[/C][C]-1.1547[/C][C]0.125307[/C][/ROW]
[ROW][C]10[/C][C]-0.064162[/C][C]-0.6881[/C][C]0.246401[/C][/ROW]
[ROW][C]11[/C][C]0.016602[/C][C]0.178[/C][C]0.429503[/C][/ROW]
[ROW][C]12[/C][C]0.155579[/C][C]1.6684[/C][C]0.048979[/C][/ROW]
[ROW][C]13[/C][C]0.028738[/C][C]0.3082[/C][C]0.379252[/C][/ROW]
[ROW][C]14[/C][C]-0.105556[/C][C]-1.132[/C][C]0.130003[/C][/ROW]
[ROW][C]15[/C][C]-0.00935[/C][C]-0.1003[/C][C]0.460153[/C][/ROW]
[ROW][C]16[/C][C]-0.071939[/C][C]-0.7715[/C][C]0.221009[/C][/ROW]
[ROW][C]17[/C][C]0.020793[/C][C]0.223[/C][C]0.411973[/C][/ROW]
[ROW][C]18[/C][C]0.058736[/C][C]0.6299[/C][C]0.265014[/C][/ROW]
[ROW][C]19[/C][C]-0.056784[/C][C]-0.6089[/C][C]0.271881[/C][/ROW]
[ROW][C]20[/C][C]0.085325[/C][C]0.915[/C][C]0.18105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300315&T=1

As an alternative you can also use a QR Code:

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.323043	-3.4642	0.000374
2	-0.091757	-0.984	0.163595
3	-0.045297	-0.4858	0.314033
4	0.073631	0.7896	0.215693
5	-0.064016	-0.6865	0.24689
6	0.068086	0.7301	0.233394
7	-0.023766	-0.2549	0.399641
8	0.085771	0.9198	0.179802
9	-0.107675	-1.1547	0.125307
10	-0.064162	-0.6881	0.246401
11	0.016602	0.178	0.429503
12	0.155579	1.6684	0.048979
13	0.028738	0.3082	0.379252
14	-0.105556	-1.132	0.130003
15	-0.00935	-0.1003	0.460153
16	-0.071939	-0.7715	0.221009
17	0.020793	0.223	0.411973
18	0.058736	0.6299	0.265014
19	-0.056784	-0.6089	0.271881
20	0.085325	0.915	0.18105

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.323043	-3.4642	0.000374
2	-0.218963	-2.3481	0.010288
3	-0.178448	-1.9136	0.029076
4	-0.036535	-0.3918	0.347968
5	-0.090815	-0.9739	0.166079
6	0.020469	0.2195	0.413321
7	-0.002515	-0.027	0.489264
8	0.104406	1.1196	0.132601
9	-0.028199	-0.3024	0.381448
10	-0.112758	-1.2092	0.114533
11	-0.079387	-0.8513	0.198178
12	0.096428	1.0341	0.151636
13	0.153714	1.6484	0.051
14	0.007649	0.082	0.467386
15	8.7e-05	9e-04	0.499629
16	-0.123993	-1.3297	0.093128
17	-0.072752	-0.7802	0.218444
18	0.008096	0.0868	0.465485
19	-0.090486	-0.9704	0.166954
20	0.042232	0.4529	0.325741

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.323043 & -3.4642 & 0.000374 \tabularnewline
2 & -0.218963 & -2.3481 & 0.010288 \tabularnewline
3 & -0.178448 & -1.9136 & 0.029076 \tabularnewline
4 & -0.036535 & -0.3918 & 0.347968 \tabularnewline
5 & -0.090815 & -0.9739 & 0.166079 \tabularnewline
6 & 0.020469 & 0.2195 & 0.413321 \tabularnewline
7 & -0.002515 & -0.027 & 0.489264 \tabularnewline
8 & 0.104406 & 1.1196 & 0.132601 \tabularnewline
9 & -0.028199 & -0.3024 & 0.381448 \tabularnewline
10 & -0.112758 & -1.2092 & 0.114533 \tabularnewline
11 & -0.079387 & -0.8513 & 0.198178 \tabularnewline
12 & 0.096428 & 1.0341 & 0.151636 \tabularnewline
13 & 0.153714 & 1.6484 & 0.051 \tabularnewline
14 & 0.007649 & 0.082 & 0.467386 \tabularnewline
15 & 8.7e-05 & 9e-04 & 0.499629 \tabularnewline
16 & -0.123993 & -1.3297 & 0.093128 \tabularnewline
17 & -0.072752 & -0.7802 & 0.218444 \tabularnewline
18 & 0.008096 & 0.0868 & 0.465485 \tabularnewline
19 & -0.090486 & -0.9704 & 0.166954 \tabularnewline
20 & 0.042232 & 0.4529 & 0.325741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300315&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.323043[/C][C]-3.4642[/C][C]0.000374[/C][/ROW]
[ROW][C]2[/C][C]-0.218963[/C][C]-2.3481[/C][C]0.010288[/C][/ROW]
[ROW][C]3[/C][C]-0.178448[/C][C]-1.9136[/C][C]0.029076[/C][/ROW]
[ROW][C]4[/C][C]-0.036535[/C][C]-0.3918[/C][C]0.347968[/C][/ROW]
[ROW][C]5[/C][C]-0.090815[/C][C]-0.9739[/C][C]0.166079[/C][/ROW]
[ROW][C]6[/C][C]0.020469[/C][C]0.2195[/C][C]0.413321[/C][/ROW]
[ROW][C]7[/C][C]-0.002515[/C][C]-0.027[/C][C]0.489264[/C][/ROW]
[ROW][C]8[/C][C]0.104406[/C][C]1.1196[/C][C]0.132601[/C][/ROW]
[ROW][C]9[/C][C]-0.028199[/C][C]-0.3024[/C][C]0.381448[/C][/ROW]
[ROW][C]10[/C][C]-0.112758[/C][C]-1.2092[/C][C]0.114533[/C][/ROW]
[ROW][C]11[/C][C]-0.079387[/C][C]-0.8513[/C][C]0.198178[/C][/ROW]
[ROW][C]12[/C][C]0.096428[/C][C]1.0341[/C][C]0.151636[/C][/ROW]
[ROW][C]13[/C][C]0.153714[/C][C]1.6484[/C][C]0.051[/C][/ROW]
[ROW][C]14[/C][C]0.007649[/C][C]0.082[/C][C]0.467386[/C][/ROW]
[ROW][C]15[/C][C]8.7e-05[/C][C]9e-04[/C][C]0.499629[/C][/ROW]
[ROW][C]16[/C][C]-0.123993[/C][C]-1.3297[/C][C]0.093128[/C][/ROW]
[ROW][C]17[/C][C]-0.072752[/C][C]-0.7802[/C][C]0.218444[/C][/ROW]
[ROW][C]18[/C][C]0.008096[/C][C]0.0868[/C][C]0.465485[/C][/ROW]
[ROW][C]19[/C][C]-0.090486[/C][C]-0.9704[/C][C]0.166954[/C][/ROW]
[ROW][C]20[/C][C]0.042232[/C][C]0.4529[/C][C]0.325741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300315&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300315&T=2

As an alternative you can also use a QR Code:

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

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.323043	-3.4642	0.000374
2	-0.218963	-2.3481	0.010288
3	-0.178448	-1.9136	0.029076
4	-0.036535	-0.3918	0.347968
5	-0.090815	-0.9739	0.166079
6	0.020469	0.2195	0.413321
7	-0.002515	-0.027	0.489264
8	0.104406	1.1196	0.132601
9	-0.028199	-0.3024	0.381448
10	-0.112758	-1.2092	0.114533
11	-0.079387	-0.8513	0.198178
12	0.096428	1.0341	0.151636
13	0.153714	1.6484	0.051
14	0.007649	0.082	0.467386
15	8.7e-05	9e-04	0.499629
16	-0.123993	-1.3297	0.093128
17	-0.072752	-0.7802	0.218444
18	0.008096	0.0868	0.465485
19	-0.090486	-0.9704	0.166954
20	0.042232	0.4529	0.325741

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,'ACF(k)',header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,'PACF(k)',header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code