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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 12:31:22 -0700

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/2009/Dec/04/t1259955136eynobz1w899a66w.htm/, Retrieved Sun, 28 Apr 2024 00:31:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64073, Retrieved Sun, 28 Apr 2024 00:31:22 +0000

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Estimated Impact

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [] [2009-11-27 14:46:03] [b98453cac15ba1066b407e146608df68]
-   PD      [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2009-12-04 19:31:22] [d45d8d97b86162be82506c3c0ea6e4a6] [Current]

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Dataseries X:

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Histogram

Boxplots

1.4
1
-0.8
-2.9
-0.7
-0.7
1.5
3
3.2
3.1
3.9
1
1.3
0.8
1.2
2.9
3.9
4.5
4.5
3.3
2
1.5
1
2.1
3
4
5.1
4.5
4.2
3.3
2.7
1.8
1.4
0.5
-0.4
0.8
0.7
1.9
2
1.1
0.9
0.4
0.7
2.1
2.8
3.9
3.5
2
2
1.5
2.5
3.1
2.7
2.8
2.5
3
3.2
2.8
2.4
2
1.8
1.1
-1.5
-3.7

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64073&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64073&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64073&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.719206	5.7536	0
2	0.400778	3.2062	0.00105
3	0.103386	0.8271	0.20563
4	-0.13139	-1.0511	0.148578
5	-0.192757	-1.5421	0.063995
6	-0.151056	-1.2084	0.115661
7	-0.065622	-0.525	0.300706
8	0.079564	0.6365	0.263357
9	0.12398	0.9918	0.162506
10	0.073576	0.5886	0.279097
11	-0.01729	-0.1383	0.445212
12	-0.162625	-1.301	0.098962
13	-0.236087	-1.8887	0.031733
14	-0.273689	-2.1895	0.016106
15	-0.285341	-2.2827	0.012889
16	-0.221913	-1.7753	0.040301
17	-0.152494	-1.22	0.11348
18	-0.042913	-0.3433	0.366247

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.719206 & 5.7536 & 0 \tabularnewline
2 & 0.400778 & 3.2062 & 0.00105 \tabularnewline
3 & 0.103386 & 0.8271 & 0.20563 \tabularnewline
4 & -0.13139 & -1.0511 & 0.148578 \tabularnewline
5 & -0.192757 & -1.5421 & 0.063995 \tabularnewline
6 & -0.151056 & -1.2084 & 0.115661 \tabularnewline
7 & -0.065622 & -0.525 & 0.300706 \tabularnewline
8 & 0.079564 & 0.6365 & 0.263357 \tabularnewline
9 & 0.12398 & 0.9918 & 0.162506 \tabularnewline
10 & 0.073576 & 0.5886 & 0.279097 \tabularnewline
11 & -0.01729 & -0.1383 & 0.445212 \tabularnewline
12 & -0.162625 & -1.301 & 0.098962 \tabularnewline
13 & -0.236087 & -1.8887 & 0.031733 \tabularnewline
14 & -0.273689 & -2.1895 & 0.016106 \tabularnewline
15 & -0.285341 & -2.2827 & 0.012889 \tabularnewline
16 & -0.221913 & -1.7753 & 0.040301 \tabularnewline
17 & -0.152494 & -1.22 & 0.11348 \tabularnewline
18 & -0.042913 & -0.3433 & 0.366247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64073&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]0.719206[/C][C]5.7536[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.400778[/C][C]3.2062[/C][C]0.00105[/C][/ROW]
[ROW][C]3[/C][C]0.103386[/C][C]0.8271[/C][C]0.20563[/C][/ROW]
[ROW][C]4[/C][C]-0.13139[/C][C]-1.0511[/C][C]0.148578[/C][/ROW]
[ROW][C]5[/C][C]-0.192757[/C][C]-1.5421[/C][C]0.063995[/C][/ROW]
[ROW][C]6[/C][C]-0.151056[/C][C]-1.2084[/C][C]0.115661[/C][/ROW]
[ROW][C]7[/C][C]-0.065622[/C][C]-0.525[/C][C]0.300706[/C][/ROW]
[ROW][C]8[/C][C]0.079564[/C][C]0.6365[/C][C]0.263357[/C][/ROW]
[ROW][C]9[/C][C]0.12398[/C][C]0.9918[/C][C]0.162506[/C][/ROW]
[ROW][C]10[/C][C]0.073576[/C][C]0.5886[/C][C]0.279097[/C][/ROW]
[ROW][C]11[/C][C]-0.01729[/C][C]-0.1383[/C][C]0.445212[/C][/ROW]
[ROW][C]12[/C][C]-0.162625[/C][C]-1.301[/C][C]0.098962[/C][/ROW]
[ROW][C]13[/C][C]-0.236087[/C][C]-1.8887[/C][C]0.031733[/C][/ROW]
[ROW][C]14[/C][C]-0.273689[/C][C]-2.1895[/C][C]0.016106[/C][/ROW]
[ROW][C]15[/C][C]-0.285341[/C][C]-2.2827[/C][C]0.012889[/C][/ROW]
[ROW][C]16[/C][C]-0.221913[/C][C]-1.7753[/C][C]0.040301[/C][/ROW]
[ROW][C]17[/C][C]-0.152494[/C][C]-1.22[/C][C]0.11348[/C][/ROW]
[ROW][C]18[/C][C]-0.042913[/C][C]-0.3433[/C][C]0.366247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64073&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64073&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	0.719206	5.7536	0
2	0.400778	3.2062	0.00105
3	0.103386	0.8271	0.20563
4	-0.13139	-1.0511	0.148578
5	-0.192757	-1.5421	0.063995
6	-0.151056	-1.2084	0.115661
7	-0.065622	-0.525	0.300706
8	0.079564	0.6365	0.263357
9	0.12398	0.9918	0.162506
10	0.073576	0.5886	0.279097
11	-0.01729	-0.1383	0.445212
12	-0.162625	-1.301	0.098962
13	-0.236087	-1.8887	0.031733
14	-0.273689	-2.1895	0.016106
15	-0.285341	-2.2827	0.012889
16	-0.221913	-1.7753	0.040301
17	-0.152494	-1.22	0.11348
18	-0.042913	-0.3433	0.366247

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.719206	5.7536	0
2	-0.241284	-1.9303	0.029003
3	-0.17788	-1.423	0.07979
4	-0.132331	-1.0586	0.14687
5	0.10833	0.8666	0.194689
6	0.038257	0.3061	0.380276
7	0.007716	0.0617	0.475487
8	0.135353	1.0828	0.141474
9	-0.100384	-0.8031	0.212453
10	-0.100932	-0.8075	0.211198
11	-0.050929	-0.4074	0.342525
12	-0.119561	-0.9565	0.171212
13	0.014077	0.1126	0.455343
14	-0.11177	-0.8942	0.187294
15	-0.099177	-0.7934	0.215233
16	-0.022238	-0.1779	0.429681
17	-0.054817	-0.4385	0.331236
18	0.097521	0.7802	0.219084

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.719206 & 5.7536 & 0 \tabularnewline
2 & -0.241284 & -1.9303 & 0.029003 \tabularnewline
3 & -0.17788 & -1.423 & 0.07979 \tabularnewline
4 & -0.132331 & -1.0586 & 0.14687 \tabularnewline
5 & 0.10833 & 0.8666 & 0.194689 \tabularnewline
6 & 0.038257 & 0.3061 & 0.380276 \tabularnewline
7 & 0.007716 & 0.0617 & 0.475487 \tabularnewline
8 & 0.135353 & 1.0828 & 0.141474 \tabularnewline
9 & -0.100384 & -0.8031 & 0.212453 \tabularnewline
10 & -0.100932 & -0.8075 & 0.211198 \tabularnewline
11 & -0.050929 & -0.4074 & 0.342525 \tabularnewline
12 & -0.119561 & -0.9565 & 0.171212 \tabularnewline
13 & 0.014077 & 0.1126 & 0.455343 \tabularnewline
14 & -0.11177 & -0.8942 & 0.187294 \tabularnewline
15 & -0.099177 & -0.7934 & 0.215233 \tabularnewline
16 & -0.022238 & -0.1779 & 0.429681 \tabularnewline
17 & -0.054817 & -0.4385 & 0.331236 \tabularnewline
18 & 0.097521 & 0.7802 & 0.219084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64073&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]0.719206[/C][C]5.7536[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.241284[/C][C]-1.9303[/C][C]0.029003[/C][/ROW]
[ROW][C]3[/C][C]-0.17788[/C][C]-1.423[/C][C]0.07979[/C][/ROW]
[ROW][C]4[/C][C]-0.132331[/C][C]-1.0586[/C][C]0.14687[/C][/ROW]
[ROW][C]5[/C][C]0.10833[/C][C]0.8666[/C][C]0.194689[/C][/ROW]
[ROW][C]6[/C][C]0.038257[/C][C]0.3061[/C][C]0.380276[/C][/ROW]
[ROW][C]7[/C][C]0.007716[/C][C]0.0617[/C][C]0.475487[/C][/ROW]
[ROW][C]8[/C][C]0.135353[/C][C]1.0828[/C][C]0.141474[/C][/ROW]
[ROW][C]9[/C][C]-0.100384[/C][C]-0.8031[/C][C]0.212453[/C][/ROW]
[ROW][C]10[/C][C]-0.100932[/C][C]-0.8075[/C][C]0.211198[/C][/ROW]
[ROW][C]11[/C][C]-0.050929[/C][C]-0.4074[/C][C]0.342525[/C][/ROW]
[ROW][C]12[/C][C]-0.119561[/C][C]-0.9565[/C][C]0.171212[/C][/ROW]
[ROW][C]13[/C][C]0.014077[/C][C]0.1126[/C][C]0.455343[/C][/ROW]
[ROW][C]14[/C][C]-0.11177[/C][C]-0.8942[/C][C]0.187294[/C][/ROW]
[ROW][C]15[/C][C]-0.099177[/C][C]-0.7934[/C][C]0.215233[/C][/ROW]
[ROW][C]16[/C][C]-0.022238[/C][C]-0.1779[/C][C]0.429681[/C][/ROW]
[ROW][C]17[/C][C]-0.054817[/C][C]-0.4385[/C][C]0.331236[/C][/ROW]
[ROW][C]18[/C][C]0.097521[/C][C]0.7802[/C][C]0.219084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64073&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64073&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	0.719206	5.7536	0
2	-0.241284	-1.9303	0.029003
3	-0.17788	-1.423	0.07979
4	-0.132331	-1.0586	0.14687
5	0.10833	0.8666	0.194689
6	0.038257	0.3061	0.380276
7	0.007716	0.0617	0.475487
8	0.135353	1.0828	0.141474
9	-0.100384	-0.8031	0.212453
10	-0.100932	-0.8075	0.211198
11	-0.050929	-0.4074	0.342525
12	-0.119561	-0.9565	0.171212
13	0.014077	0.1126	0.455343
14	-0.11177	-0.8942	0.187294
15	-0.099177	-0.7934	0.215233
16	-0.022238	-0.1779	0.429681
17	-0.054817	-0.4385	0.331236
18	0.097521	0.7802	0.219084

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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