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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 19 Dec 2015 07:33:13 +0000

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/2015/Dec/19/t1450510415tfdpio7w92talsy.htm/, Retrieved Thu, 16 May 2024 14:43:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286950, Retrieved Thu, 16 May 2024 14:43:35 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

137

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

-       [(Partial) Autocorrelation Function] [Jenkins vraag 8.1] [2015-12-19 07:33:13] [8acc4c3875a0c63009483cc7dfb4f316] [Current]

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Dataseries X:

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Histogram

Boxplots

1.4
1.5
1.8
1.8
1.8
1.7
1.5
1.1
1.3
1.6
1.9
1.9
2
2.2
2.2
2
2.3
2.6
3.2
3.2
3.1
2.8
2.3
1.9
1.9
2
2
1.8
1.6
1.4
0.2
0.3
0.4
0.7
1
1.1
0.8
0.8
1
1.1
1
0.8
1.6
1.5
1.6
1.6
1.6
1.9
2
1.9
2
2.1
2.3
2.3
2.6
2.6
2.7
2.6
2.6
2.4
2.5
2.5
2.5
2.4
2.1
2.1
2.3
2.3
2.3
2.9
2.8
2.9
3
3
2.9
2.6
2.8
2.9
3.1
2.8
2.4
1.6
1.5
1.7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286950&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286950&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286950&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.919222	8.4248	0
2	0.805998	7.3871	0
3	0.691915	6.3415	0
4	0.604985	5.5448	0
5	0.538368	4.9342	2e-06
6	0.485638	4.4509	1.3e-05
7	0.421977	3.8675	0.000108
8	0.32721	2.9989	0.001782
9	0.206459	1.8922	0.030953
10	0.08093	0.7417	0.230159
11	-0.027414	-0.2512	0.401117
12	-0.113381	-1.0392	0.150857
13	-0.133906	-1.2273	0.111575
14	-0.133533	-1.2238	0.112216
15	-0.126217	-1.1568	0.125318
16	-0.141001	-1.2923	0.099899
17	-0.17225	-1.5787	0.059083
18	-0.199511	-1.8285	0.035508
19	-0.216564	-1.9848	0.025213

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.919222 & 8.4248 & 0 \tabularnewline
2 & 0.805998 & 7.3871 & 0 \tabularnewline
3 & 0.691915 & 6.3415 & 0 \tabularnewline
4 & 0.604985 & 5.5448 & 0 \tabularnewline
5 & 0.538368 & 4.9342 & 2e-06 \tabularnewline
6 & 0.485638 & 4.4509 & 1.3e-05 \tabularnewline
7 & 0.421977 & 3.8675 & 0.000108 \tabularnewline
8 & 0.32721 & 2.9989 & 0.001782 \tabularnewline
9 & 0.206459 & 1.8922 & 0.030953 \tabularnewline
10 & 0.08093 & 0.7417 & 0.230159 \tabularnewline
11 & -0.027414 & -0.2512 & 0.401117 \tabularnewline
12 & -0.113381 & -1.0392 & 0.150857 \tabularnewline
13 & -0.133906 & -1.2273 & 0.111575 \tabularnewline
14 & -0.133533 & -1.2238 & 0.112216 \tabularnewline
15 & -0.126217 & -1.1568 & 0.125318 \tabularnewline
16 & -0.141001 & -1.2923 & 0.099899 \tabularnewline
17 & -0.17225 & -1.5787 & 0.059083 \tabularnewline
18 & -0.199511 & -1.8285 & 0.035508 \tabularnewline
19 & -0.216564 & -1.9848 & 0.025213 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286950&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]0.919222[/C][C]8.4248[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.805998[/C][C]7.3871[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.691915[/C][C]6.3415[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.604985[/C][C]5.5448[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.538368[/C][C]4.9342[/C][C]2e-06[/C][/ROW]
[ROW][C]6[/C][C]0.485638[/C][C]4.4509[/C][C]1.3e-05[/C][/ROW]
[ROW][C]7[/C][C]0.421977[/C][C]3.8675[/C][C]0.000108[/C][/ROW]
[ROW][C]8[/C][C]0.32721[/C][C]2.9989[/C][C]0.001782[/C][/ROW]
[ROW][C]9[/C][C]0.206459[/C][C]1.8922[/C][C]0.030953[/C][/ROW]
[ROW][C]10[/C][C]0.08093[/C][C]0.7417[/C][C]0.230159[/C][/ROW]
[ROW][C]11[/C][C]-0.027414[/C][C]-0.2512[/C][C]0.401117[/C][/ROW]
[ROW][C]12[/C][C]-0.113381[/C][C]-1.0392[/C][C]0.150857[/C][/ROW]
[ROW][C]13[/C][C]-0.133906[/C][C]-1.2273[/C][C]0.111575[/C][/ROW]
[ROW][C]14[/C][C]-0.133533[/C][C]-1.2238[/C][C]0.112216[/C][/ROW]
[ROW][C]15[/C][C]-0.126217[/C][C]-1.1568[/C][C]0.125318[/C][/ROW]
[ROW][C]16[/C][C]-0.141001[/C][C]-1.2923[/C][C]0.099899[/C][/ROW]
[ROW][C]17[/C][C]-0.17225[/C][C]-1.5787[/C][C]0.059083[/C][/ROW]
[ROW][C]18[/C][C]-0.199511[/C][C]-1.8285[/C][C]0.035508[/C][/ROW]
[ROW][C]19[/C][C]-0.216564[/C][C]-1.9848[/C][C]0.025213[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286950&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286950&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	0.919222	8.4248	0
2	0.805998	7.3871	0
3	0.691915	6.3415	0
4	0.604985	5.5448	0
5	0.538368	4.9342	2e-06
6	0.485638	4.4509	1.3e-05
7	0.421977	3.8675	0.000108
8	0.32721	2.9989	0.001782
9	0.206459	1.8922	0.030953
10	0.08093	0.7417	0.230159
11	-0.027414	-0.2512	0.401117
12	-0.113381	-1.0392	0.150857
13	-0.133906	-1.2273	0.111575
14	-0.133533	-1.2238	0.112216
15	-0.126217	-1.1568	0.125318
16	-0.141001	-1.2923	0.099899
17	-0.17225	-1.5787	0.059083
18	-0.199511	-1.8285	0.035508
19	-0.216564	-1.9848	0.025213

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.919222	8.4248	0
2	-0.251381	-2.3039	0.011848
3	-0.028561	-0.2618	0.397073
4	0.113228	1.0378	0.151182
5	0.015259	0.1398	0.444558
6	0.008863	0.0812	0.467726
7	-0.119153	-1.0921	0.138967
8	-0.210658	-1.9307	0.028446
9	-0.159339	-1.4604	0.07396
10	-0.089994	-0.8248	0.205907
11	-0.033369	-0.3058	0.380246
12	-0.046535	-0.4265	0.335416
13	0.313501	2.8733	0.002571
14	-0.002869	-0.0263	0.489542
15	0.063601	0.5829	0.280758
16	-0.050247	-0.4605	0.323166
17	-0.065754	-0.6026	0.274185
18	0.034102	0.3125	0.377699
19	-0.09578	-0.8778	0.191268

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.919222 & 8.4248 & 0 \tabularnewline
2 & -0.251381 & -2.3039 & 0.011848 \tabularnewline
3 & -0.028561 & -0.2618 & 0.397073 \tabularnewline
4 & 0.113228 & 1.0378 & 0.151182 \tabularnewline
5 & 0.015259 & 0.1398 & 0.444558 \tabularnewline
6 & 0.008863 & 0.0812 & 0.467726 \tabularnewline
7 & -0.119153 & -1.0921 & 0.138967 \tabularnewline
8 & -0.210658 & -1.9307 & 0.028446 \tabularnewline
9 & -0.159339 & -1.4604 & 0.07396 \tabularnewline
10 & -0.089994 & -0.8248 & 0.205907 \tabularnewline
11 & -0.033369 & -0.3058 & 0.380246 \tabularnewline
12 & -0.046535 & -0.4265 & 0.335416 \tabularnewline
13 & 0.313501 & 2.8733 & 0.002571 \tabularnewline
14 & -0.002869 & -0.0263 & 0.489542 \tabularnewline
15 & 0.063601 & 0.5829 & 0.280758 \tabularnewline
16 & -0.050247 & -0.4605 & 0.323166 \tabularnewline
17 & -0.065754 & -0.6026 & 0.274185 \tabularnewline
18 & 0.034102 & 0.3125 & 0.377699 \tabularnewline
19 & -0.09578 & -0.8778 & 0.191268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286950&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]0.919222[/C][C]8.4248[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.251381[/C][C]-2.3039[/C][C]0.011848[/C][/ROW]
[ROW][C]3[/C][C]-0.028561[/C][C]-0.2618[/C][C]0.397073[/C][/ROW]
[ROW][C]4[/C][C]0.113228[/C][C]1.0378[/C][C]0.151182[/C][/ROW]
[ROW][C]5[/C][C]0.015259[/C][C]0.1398[/C][C]0.444558[/C][/ROW]
[ROW][C]6[/C][C]0.008863[/C][C]0.0812[/C][C]0.467726[/C][/ROW]
[ROW][C]7[/C][C]-0.119153[/C][C]-1.0921[/C][C]0.138967[/C][/ROW]
[ROW][C]8[/C][C]-0.210658[/C][C]-1.9307[/C][C]0.028446[/C][/ROW]
[ROW][C]9[/C][C]-0.159339[/C][C]-1.4604[/C][C]0.07396[/C][/ROW]
[ROW][C]10[/C][C]-0.089994[/C][C]-0.8248[/C][C]0.205907[/C][/ROW]
[ROW][C]11[/C][C]-0.033369[/C][C]-0.3058[/C][C]0.380246[/C][/ROW]
[ROW][C]12[/C][C]-0.046535[/C][C]-0.4265[/C][C]0.335416[/C][/ROW]
[ROW][C]13[/C][C]0.313501[/C][C]2.8733[/C][C]0.002571[/C][/ROW]
[ROW][C]14[/C][C]-0.002869[/C][C]-0.0263[/C][C]0.489542[/C][/ROW]
[ROW][C]15[/C][C]0.063601[/C][C]0.5829[/C][C]0.280758[/C][/ROW]
[ROW][C]16[/C][C]-0.050247[/C][C]-0.4605[/C][C]0.323166[/C][/ROW]
[ROW][C]17[/C][C]-0.065754[/C][C]-0.6026[/C][C]0.274185[/C][/ROW]
[ROW][C]18[/C][C]0.034102[/C][C]0.3125[/C][C]0.377699[/C][/ROW]
[ROW][C]19[/C][C]-0.09578[/C][C]-0.8778[/C][C]0.191268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286950&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286950&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	0.919222	8.4248	0
2	-0.251381	-2.3039	0.011848
3	-0.028561	-0.2618	0.397073
4	0.113228	1.0378	0.151182
5	0.015259	0.1398	0.444558
6	0.008863	0.0812	0.467726
7	-0.119153	-1.0921	0.138967
8	-0.210658	-1.9307	0.028446
9	-0.159339	-1.4604	0.07396
10	-0.089994	-0.8248	0.205907
11	-0.033369	-0.3058	0.380246
12	-0.046535	-0.4265	0.335416
13	0.313501	2.8733	0.002571
14	-0.002869	-0.0263	0.489542
15	0.063601	0.5829	0.280758
16	-0.050247	-0.4605	0.323166
17	-0.065754	-0.6026	0.274185
18	0.034102	0.3125	0.377699
19	-0.09578	-0.8778	0.191268

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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