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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 09 Dec 2008 03:52:15 -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/2008/Dec/09/t122881995767tnzraz19irydg.htm/, Retrieved Wed, 11 Feb 2026 14:00:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31279, Retrieved Wed, 11 Feb 2026 14:00:45 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

415

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

F     [Spectral Analysis] [Diff Spectral] [2008-12-06 12:07:42] [74be16979710d4c4e7c6647856088456]
F RMP   [ARIMA Backward Selection] [Arima backward] [2008-12-06 14:19:09] [74be16979710d4c4e7c6647856088456]
- RMPD      [(Partial) Autocorrelation Function] [] [2008-12-09 10:52:15] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   PD        [(Partial) Autocorrelation Function] [] [2008-12-09 10:56:43] [74be16979710d4c4e7c6647856088456] 
- RMPD        [Spectral Analysis] [] [2008-12-09 11:01:22] [74be16979710d4c4e7c6647856088456] 
F   P           [Spectral Analysis] [] [2008-12-09 11:05:55] [74be16979710d4c4e7c6647856088456] 
F RMP           [ARIMA Backward Selection] [] [2008-12-09 11:11:19] [74be16979710d4c4e7c6647856088456] 
F   PD        [(Partial) Autocorrelation Function] [] [2008-12-09 11:16:28] [74be16979710d4c4e7c6647856088456] 
F   PD        [(Partial) Autocorrelation Function] [] [2008-12-09 11:18:29] [74be16979710d4c4e7c6647856088456] 

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Dataseries X:

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Histogram

Boxplots

5,1
4,9
5,2
5,1
4,6
3,7
3,9
3,1
2,8
2,6
2,2
1,8
1,3
1,2
1,4
1,3
1,3
1,9
1,9
2,1
2,0
1,9
1,9
1,9
1,8
1,7
1,6
1,7
1,9
1,7
1,3
2,0
2,0
2,3
2,0
1,7
2,3
2,4
2,4
2,3
2,1
2,1
2,5
2,0
1,8
1,7
1,9
2,1
1,4
1,6
1,7
1,6
1,9
1,6
1,1
1,3
1,6
1,6
1,7
1,6
1,7
1,6
1,5
1,6
1,1
1,5
1,4
1,3
0,9
1,2
0,9
1,1
1,3
1,3
1,4
1,2
1,7
2,0
3,0
3,1
3,2
2,7
2,8
3,0
2,8
3,1
3,1
3,2
3,1
2,7
2,2
2,2
2,1
2,3
2,5
2,3
2,6

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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31279&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31279&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31279&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.845169	8.324	0
2	0.747451	7.3615	0
3	0.63577	6.2616	0
4	0.534843	5.2676	0
5	0.431795	4.2527	2.4e-05
6	0.3204	3.1556	0.001067
7	0.195261	1.9231	0.0287
8	0.091821	0.9043	0.184029
9	0.028274	0.2785	0.390622
10	-0.050345	-0.4958	0.310564
11	-0.103938	-1.0237	0.154268
12	-0.17397	-1.7134	0.044916
13	-0.121806	-1.1997	0.116598
14	-0.083764	-0.825	0.205704
15	-0.099465	-0.9796	0.164856
16	-0.084211	-0.8294	0.204462
17	-0.098185	-0.967	0.167971
18	-0.106677	-1.0506	0.148015
19	-0.104677	-1.0309	0.152564

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.845169 & 8.324 & 0 \tabularnewline
2 & 0.747451 & 7.3615 & 0 \tabularnewline
3 & 0.63577 & 6.2616 & 0 \tabularnewline
4 & 0.534843 & 5.2676 & 0 \tabularnewline
5 & 0.431795 & 4.2527 & 2.4e-05 \tabularnewline
6 & 0.3204 & 3.1556 & 0.001067 \tabularnewline
7 & 0.195261 & 1.9231 & 0.0287 \tabularnewline
8 & 0.091821 & 0.9043 & 0.184029 \tabularnewline
9 & 0.028274 & 0.2785 & 0.390622 \tabularnewline
10 & -0.050345 & -0.4958 & 0.310564 \tabularnewline
11 & -0.103938 & -1.0237 & 0.154268 \tabularnewline
12 & -0.17397 & -1.7134 & 0.044916 \tabularnewline
13 & -0.121806 & -1.1997 & 0.116598 \tabularnewline
14 & -0.083764 & -0.825 & 0.205704 \tabularnewline
15 & -0.099465 & -0.9796 & 0.164856 \tabularnewline
16 & -0.084211 & -0.8294 & 0.204462 \tabularnewline
17 & -0.098185 & -0.967 & 0.167971 \tabularnewline
18 & -0.106677 & -1.0506 & 0.148015 \tabularnewline
19 & -0.104677 & -1.0309 & 0.152564 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31279&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]0.845169[/C][C]8.324[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.747451[/C][C]7.3615[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.63577[/C][C]6.2616[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.534843[/C][C]5.2676[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.431795[/C][C]4.2527[/C][C]2.4e-05[/C][/ROW]
[ROW][C]6[/C][C]0.3204[/C][C]3.1556[/C][C]0.001067[/C][/ROW]
[ROW][C]7[/C][C]0.195261[/C][C]1.9231[/C][C]0.0287[/C][/ROW]
[ROW][C]8[/C][C]0.091821[/C][C]0.9043[/C][C]0.184029[/C][/ROW]
[ROW][C]9[/C][C]0.028274[/C][C]0.2785[/C][C]0.390622[/C][/ROW]
[ROW][C]10[/C][C]-0.050345[/C][C]-0.4958[/C][C]0.310564[/C][/ROW]
[ROW][C]11[/C][C]-0.103938[/C][C]-1.0237[/C][C]0.154268[/C][/ROW]
[ROW][C]12[/C][C]-0.17397[/C][C]-1.7134[/C][C]0.044916[/C][/ROW]
[ROW][C]13[/C][C]-0.121806[/C][C]-1.1997[/C][C]0.116598[/C][/ROW]
[ROW][C]14[/C][C]-0.083764[/C][C]-0.825[/C][C]0.205704[/C][/ROW]
[ROW][C]15[/C][C]-0.099465[/C][C]-0.9796[/C][C]0.164856[/C][/ROW]
[ROW][C]16[/C][C]-0.084211[/C][C]-0.8294[/C][C]0.204462[/C][/ROW]
[ROW][C]17[/C][C]-0.098185[/C][C]-0.967[/C][C]0.167971[/C][/ROW]
[ROW][C]18[/C][C]-0.106677[/C][C]-1.0506[/C][C]0.148015[/C][/ROW]
[ROW][C]19[/C][C]-0.104677[/C][C]-1.0309[/C][C]0.152564[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31279&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31279&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	0.845169	8.324	0
2	0.747451	7.3615	0
3	0.63577	6.2616	0
4	0.534843	5.2676	0
5	0.431795	4.2527	2.4e-05
6	0.3204	3.1556	0.001067
7	0.195261	1.9231	0.0287
8	0.091821	0.9043	0.184029
9	0.028274	0.2785	0.390622
10	-0.050345	-0.4958	0.310564
11	-0.103938	-1.0237	0.154268
12	-0.17397	-1.7134	0.044916
13	-0.121806	-1.1997	0.116598
14	-0.083764	-0.825	0.205704
15	-0.099465	-0.9796	0.164856
16	-0.084211	-0.8294	0.204462
17	-0.098185	-0.967	0.167971
18	-0.106677	-1.0506	0.148015
19	-0.104677	-1.0309	0.152564

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.845169	8.324	0
2	0.116001	1.1425	0.128033
3	-0.07349	-0.7238	0.235467
4	-0.039998	-0.3939	0.347247
5	-0.06306	-0.6211	0.268005
6	-0.104175	-1.026	0.153721
7	-0.143417	-1.4125	0.080502
8	-0.041019	-0.404	0.343555
9	0.07399	0.7287	0.233965
10	-0.081495	-0.8026	0.212075
11	-0.007901	-0.0778	0.469069
12	-0.096694	-0.9523	0.171649
13	0.347406	3.4216	0.000456
14	0.073761	0.7265	0.234654
15	-0.271929	-2.6782	0.004347
16	0.035027	0.345	0.365431
17	-0.071827	-0.7074	0.240502
18	-0.103994	-1.0242	0.154139
19	-0.057211	-0.5635	0.28721

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.845169 & 8.324 & 0 \tabularnewline
2 & 0.116001 & 1.1425 & 0.128033 \tabularnewline
3 & -0.07349 & -0.7238 & 0.235467 \tabularnewline
4 & -0.039998 & -0.3939 & 0.347247 \tabularnewline
5 & -0.06306 & -0.6211 & 0.268005 \tabularnewline
6 & -0.104175 & -1.026 & 0.153721 \tabularnewline
7 & -0.143417 & -1.4125 & 0.080502 \tabularnewline
8 & -0.041019 & -0.404 & 0.343555 \tabularnewline
9 & 0.07399 & 0.7287 & 0.233965 \tabularnewline
10 & -0.081495 & -0.8026 & 0.212075 \tabularnewline
11 & -0.007901 & -0.0778 & 0.469069 \tabularnewline
12 & -0.096694 & -0.9523 & 0.171649 \tabularnewline
13 & 0.347406 & 3.4216 & 0.000456 \tabularnewline
14 & 0.073761 & 0.7265 & 0.234654 \tabularnewline
15 & -0.271929 & -2.6782 & 0.004347 \tabularnewline
16 & 0.035027 & 0.345 & 0.365431 \tabularnewline
17 & -0.071827 & -0.7074 & 0.240502 \tabularnewline
18 & -0.103994 & -1.0242 & 0.154139 \tabularnewline
19 & -0.057211 & -0.5635 & 0.28721 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31279&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]0.845169[/C][C]8.324[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.116001[/C][C]1.1425[/C][C]0.128033[/C][/ROW]
[ROW][C]3[/C][C]-0.07349[/C][C]-0.7238[/C][C]0.235467[/C][/ROW]
[ROW][C]4[/C][C]-0.039998[/C][C]-0.3939[/C][C]0.347247[/C][/ROW]
[ROW][C]5[/C][C]-0.06306[/C][C]-0.6211[/C][C]0.268005[/C][/ROW]
[ROW][C]6[/C][C]-0.104175[/C][C]-1.026[/C][C]0.153721[/C][/ROW]
[ROW][C]7[/C][C]-0.143417[/C][C]-1.4125[/C][C]0.080502[/C][/ROW]
[ROW][C]8[/C][C]-0.041019[/C][C]-0.404[/C][C]0.343555[/C][/ROW]
[ROW][C]9[/C][C]0.07399[/C][C]0.7287[/C][C]0.233965[/C][/ROW]
[ROW][C]10[/C][C]-0.081495[/C][C]-0.8026[/C][C]0.212075[/C][/ROW]
[ROW][C]11[/C][C]-0.007901[/C][C]-0.0778[/C][C]0.469069[/C][/ROW]
[ROW][C]12[/C][C]-0.096694[/C][C]-0.9523[/C][C]0.171649[/C][/ROW]
[ROW][C]13[/C][C]0.347406[/C][C]3.4216[/C][C]0.000456[/C][/ROW]
[ROW][C]14[/C][C]0.073761[/C][C]0.7265[/C][C]0.234654[/C][/ROW]
[ROW][C]15[/C][C]-0.271929[/C][C]-2.6782[/C][C]0.004347[/C][/ROW]
[ROW][C]16[/C][C]0.035027[/C][C]0.345[/C][C]0.365431[/C][/ROW]
[ROW][C]17[/C][C]-0.071827[/C][C]-0.7074[/C][C]0.240502[/C][/ROW]
[ROW][C]18[/C][C]-0.103994[/C][C]-1.0242[/C][C]0.154139[/C][/ROW]
[ROW][C]19[/C][C]-0.057211[/C][C]-0.5635[/C][C]0.28721[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31279&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31279&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	0.845169	8.324	0
2	0.116001	1.1425	0.128033
3	-0.07349	-0.7238	0.235467
4	-0.039998	-0.3939	0.347247
5	-0.06306	-0.6211	0.268005
6	-0.104175	-1.026	0.153721
7	-0.143417	-1.4125	0.080502
8	-0.041019	-0.404	0.343555
9	0.07399	0.7287	0.233965
10	-0.081495	-0.8026	0.212075
11	-0.007901	-0.0778	0.469069
12	-0.096694	-0.9523	0.171649
13	0.347406	3.4216	0.000456
14	0.073761	0.7265	0.234654
15	-0.271929	-2.6782	0.004347
16	0.035027	0.345	0.365431
17	-0.071827	-0.7074	0.240502
18	-0.103994	-1.0242	0.154139
19	-0.057211	-0.5635	0.28721

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -0.5 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -0.5 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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