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Author's title

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

Sun, 21 Dec 2008 15:16:00 -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/21/t1229897800bbbz1ippxaetbad.htm/, Retrieved Sun, 19 May 2024 12:41:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35875, Retrieved Sun, 19 May 2024 12:41:03 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

145

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

-     [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:13:26] [4ddbf81f78ea7c738951638c7e93f6ee]
-   P     [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:16:00] [e8f764b122b426f433a1e1038b457077] [Current]
-   PD      [(Partial) Autocorrelation Function] [autocorrelation v...] [2008-12-21 22:17:35] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   PD        [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:19:34] [4ddbf81f78ea7c738951638c7e93f6ee] 
-               [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:20:27] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   P             [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:22:06] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   PD              [(Partial) Autocorrelation Function] [autocorrelation t...] [2008-12-21 22:23:36] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   PD                [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:24:49] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   P                   [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:26:12] [4ddbf81f78ea7c738951638c7e93f6ee] 
- RMPD                [Spectral Analysis] [cumulatieve perio...] [2008-12-21 22:30:15] [4ddbf81f78ea7c738951638c7e93f6ee] 
-    D                  [Spectral Analysis] [cumulatieve perio...] [2008-12-21 22:31:42] [4ddbf81f78ea7c738951638c7e93f6ee] 
-    D                    [Spectral Analysis] [cumulatieve perio...] [2008-12-21 22:33:19] [4ddbf81f78ea7c738951638c7e93f6ee] 

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Dataseries X:

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

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35875&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35875&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35875&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.377994	2.9034	0.002593
2	-0.05572	-0.428	0.335108
3	-0.361966	-2.7803	0.003638
4	-0.441049	-3.3878	0.00063
5	-0.147176	-1.1305	0.131425
6	0.046895	0.3602	0.359989
7	0.103737	0.7968	0.214375
8	-0.050726	-0.3896	0.349105
9	-0.063802	-0.4901	0.312949
10	-0.072192	-0.5545	0.290662
11	-0.012601	-0.0968	0.461611
12	0.231125	1.7753	0.040503
13	0.055235	0.4243	0.336458
14	0.161837	1.2431	0.109375
15	0.088463	0.6795	0.249739
16	-0.064167	-0.4929	0.311964
17	-0.103357	-0.7939	0.215217

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.377994 & 2.9034 & 0.002593 \tabularnewline
2 & -0.05572 & -0.428 & 0.335108 \tabularnewline
3 & -0.361966 & -2.7803 & 0.003638 \tabularnewline
4 & -0.441049 & -3.3878 & 0.00063 \tabularnewline
5 & -0.147176 & -1.1305 & 0.131425 \tabularnewline
6 & 0.046895 & 0.3602 & 0.359989 \tabularnewline
7 & 0.103737 & 0.7968 & 0.214375 \tabularnewline
8 & -0.050726 & -0.3896 & 0.349105 \tabularnewline
9 & -0.063802 & -0.4901 & 0.312949 \tabularnewline
10 & -0.072192 & -0.5545 & 0.290662 \tabularnewline
11 & -0.012601 & -0.0968 & 0.461611 \tabularnewline
12 & 0.231125 & 1.7753 & 0.040503 \tabularnewline
13 & 0.055235 & 0.4243 & 0.336458 \tabularnewline
14 & 0.161837 & 1.2431 & 0.109375 \tabularnewline
15 & 0.088463 & 0.6795 & 0.249739 \tabularnewline
16 & -0.064167 & -0.4929 & 0.311964 \tabularnewline
17 & -0.103357 & -0.7939 & 0.215217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35875&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]0.377994[/C][C]2.9034[/C][C]0.002593[/C][/ROW]
[ROW][C]2[/C][C]-0.05572[/C][C]-0.428[/C][C]0.335108[/C][/ROW]
[ROW][C]3[/C][C]-0.361966[/C][C]-2.7803[/C][C]0.003638[/C][/ROW]
[ROW][C]4[/C][C]-0.441049[/C][C]-3.3878[/C][C]0.00063[/C][/ROW]
[ROW][C]5[/C][C]-0.147176[/C][C]-1.1305[/C][C]0.131425[/C][/ROW]
[ROW][C]6[/C][C]0.046895[/C][C]0.3602[/C][C]0.359989[/C][/ROW]
[ROW][C]7[/C][C]0.103737[/C][C]0.7968[/C][C]0.214375[/C][/ROW]
[ROW][C]8[/C][C]-0.050726[/C][C]-0.3896[/C][C]0.349105[/C][/ROW]
[ROW][C]9[/C][C]-0.063802[/C][C]-0.4901[/C][C]0.312949[/C][/ROW]
[ROW][C]10[/C][C]-0.072192[/C][C]-0.5545[/C][C]0.290662[/C][/ROW]
[ROW][C]11[/C][C]-0.012601[/C][C]-0.0968[/C][C]0.461611[/C][/ROW]
[ROW][C]12[/C][C]0.231125[/C][C]1.7753[/C][C]0.040503[/C][/ROW]
[ROW][C]13[/C][C]0.055235[/C][C]0.4243[/C][C]0.336458[/C][/ROW]
[ROW][C]14[/C][C]0.161837[/C][C]1.2431[/C][C]0.109375[/C][/ROW]
[ROW][C]15[/C][C]0.088463[/C][C]0.6795[/C][C]0.249739[/C][/ROW]
[ROW][C]16[/C][C]-0.064167[/C][C]-0.4929[/C][C]0.311964[/C][/ROW]
[ROW][C]17[/C][C]-0.103357[/C][C]-0.7939[/C][C]0.215217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35875&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35875&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	0.377994	2.9034	0.002593
2	-0.05572	-0.428	0.335108
3	-0.361966	-2.7803	0.003638
4	-0.441049	-3.3878	0.00063
5	-0.147176	-1.1305	0.131425
6	0.046895	0.3602	0.359989
7	0.103737	0.7968	0.214375
8	-0.050726	-0.3896	0.349105
9	-0.063802	-0.4901	0.312949
10	-0.072192	-0.5545	0.290662
11	-0.012601	-0.0968	0.461611
12	0.231125	1.7753	0.040503
13	0.055235	0.4243	0.336458
14	0.161837	1.2431	0.109375
15	0.088463	0.6795	0.249739
16	-0.064167	-0.4929	0.311964
17	-0.103357	-0.7939	0.215217

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.377994	2.9034	0.002593
2	-0.231705	-1.7798	0.040133
3	-0.3063	-2.3527	0.010995
4	-0.254964	-1.9584	0.027457
5	0.053637	0.412	0.340917
6	-0.082698	-0.6352	0.263872
7	-0.133913	-1.0286	0.153933
8	-0.270687	-2.0792	0.020978
9	-0.016336	-0.1255	0.450287
10	-0.12418	-0.9538	0.172026
11	-0.128539	-0.9873	0.163757
12	0.132547	1.0181	0.156391
13	-0.246241	-1.8914	0.031741
14	0.247944	1.9045	0.030863
15	0.03749	0.288	0.387192
16	-0.017573	-0.135	0.446543
17	-0.025871	-0.1987	0.421583

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.377994 & 2.9034 & 0.002593 \tabularnewline
2 & -0.231705 & -1.7798 & 0.040133 \tabularnewline
3 & -0.3063 & -2.3527 & 0.010995 \tabularnewline
4 & -0.254964 & -1.9584 & 0.027457 \tabularnewline
5 & 0.053637 & 0.412 & 0.340917 \tabularnewline
6 & -0.082698 & -0.6352 & 0.263872 \tabularnewline
7 & -0.133913 & -1.0286 & 0.153933 \tabularnewline
8 & -0.270687 & -2.0792 & 0.020978 \tabularnewline
9 & -0.016336 & -0.1255 & 0.450287 \tabularnewline
10 & -0.12418 & -0.9538 & 0.172026 \tabularnewline
11 & -0.128539 & -0.9873 & 0.163757 \tabularnewline
12 & 0.132547 & 1.0181 & 0.156391 \tabularnewline
13 & -0.246241 & -1.8914 & 0.031741 \tabularnewline
14 & 0.247944 & 1.9045 & 0.030863 \tabularnewline
15 & 0.03749 & 0.288 & 0.387192 \tabularnewline
16 & -0.017573 & -0.135 & 0.446543 \tabularnewline
17 & -0.025871 & -0.1987 & 0.421583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35875&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]0.377994[/C][C]2.9034[/C][C]0.002593[/C][/ROW]
[ROW][C]2[/C][C]-0.231705[/C][C]-1.7798[/C][C]0.040133[/C][/ROW]
[ROW][C]3[/C][C]-0.3063[/C][C]-2.3527[/C][C]0.010995[/C][/ROW]
[ROW][C]4[/C][C]-0.254964[/C][C]-1.9584[/C][C]0.027457[/C][/ROW]
[ROW][C]5[/C][C]0.053637[/C][C]0.412[/C][C]0.340917[/C][/ROW]
[ROW][C]6[/C][C]-0.082698[/C][C]-0.6352[/C][C]0.263872[/C][/ROW]
[ROW][C]7[/C][C]-0.133913[/C][C]-1.0286[/C][C]0.153933[/C][/ROW]
[ROW][C]8[/C][C]-0.270687[/C][C]-2.0792[/C][C]0.020978[/C][/ROW]
[ROW][C]9[/C][C]-0.016336[/C][C]-0.1255[/C][C]0.450287[/C][/ROW]
[ROW][C]10[/C][C]-0.12418[/C][C]-0.9538[/C][C]0.172026[/C][/ROW]
[ROW][C]11[/C][C]-0.128539[/C][C]-0.9873[/C][C]0.163757[/C][/ROW]
[ROW][C]12[/C][C]0.132547[/C][C]1.0181[/C][C]0.156391[/C][/ROW]
[ROW][C]13[/C][C]-0.246241[/C][C]-1.8914[/C][C]0.031741[/C][/ROW]
[ROW][C]14[/C][C]0.247944[/C][C]1.9045[/C][C]0.030863[/C][/ROW]
[ROW][C]15[/C][C]0.03749[/C][C]0.288[/C][C]0.387192[/C][/ROW]
[ROW][C]16[/C][C]-0.017573[/C][C]-0.135[/C][C]0.446543[/C][/ROW]
[ROW][C]17[/C][C]-0.025871[/C][C]-0.1987[/C][C]0.421583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35875&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35875&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	0.377994	2.9034	0.002593
2	-0.231705	-1.7798	0.040133
3	-0.3063	-2.3527	0.010995
4	-0.254964	-1.9584	0.027457
5	0.053637	0.412	0.340917
6	-0.082698	-0.6352	0.263872
7	-0.133913	-1.0286	0.153933
8	-0.270687	-2.0792	0.020978
9	-0.016336	-0.1255	0.450287
10	-0.12418	-0.9538	0.172026
11	-0.128539	-0.9873	0.163757
12	0.132547	1.0181	0.156391
13	-0.246241	-1.8914	0.031741
14	0.247944	1.9045	0.030863
15	0.03749	0.288	0.387192
16	-0.017573	-0.135	0.446543
17	-0.025871	-0.1987	0.421583

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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