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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 17 Dec 2008 12:39:27 -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/17/t12295428315wykijqmcck4xel.htm/, Retrieved Sun, 19 May 2024 05:55:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34519, Retrieved Sun, 19 May 2024 05:55:06 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Van Dooren Leen

Estimated Impact

165

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

-       [(Partial) Autocorrelation Function] [PAPER] [2008-12-17 19:39:27] [d175f84d503eb4f2a43145d5e67795b5] [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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34519&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34519&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34519&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.052686	-0.3978	0.346142
2	0.040913	0.3089	0.379268
3	0.106381	0.8032	0.21261
4	0.080831	0.6103	0.272057
5	-0.078124	-0.5898	0.27882
6	0.084705	0.6395	0.262526
7	0.011807	0.0891	0.464641
8	0.094143	0.7108	0.240064
9	-0.01951	-0.1473	0.44171
10	-0.105503	-0.7965	0.214515
11	0.174021	1.3138	0.097083
12	-0.258993	-1.9554	0.027725
13	-0.165985	-1.2532	0.107631
14	0.096147	0.7259	0.235437
15	-0.039812	-0.3006	0.382417
16	-0.148843	-1.1237	0.132917
17	-0.013496	-0.1019	0.459601
18	0.030457	0.2299	0.409478

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.052686 & -0.3978 & 0.346142 \tabularnewline
2 & 0.040913 & 0.3089 & 0.379268 \tabularnewline
3 & 0.106381 & 0.8032 & 0.21261 \tabularnewline
4 & 0.080831 & 0.6103 & 0.272057 \tabularnewline
5 & -0.078124 & -0.5898 & 0.27882 \tabularnewline
6 & 0.084705 & 0.6395 & 0.262526 \tabularnewline
7 & 0.011807 & 0.0891 & 0.464641 \tabularnewline
8 & 0.094143 & 0.7108 & 0.240064 \tabularnewline
9 & -0.01951 & -0.1473 & 0.44171 \tabularnewline
10 & -0.105503 & -0.7965 & 0.214515 \tabularnewline
11 & 0.174021 & 1.3138 & 0.097083 \tabularnewline
12 & -0.258993 & -1.9554 & 0.027725 \tabularnewline
13 & -0.165985 & -1.2532 & 0.107631 \tabularnewline
14 & 0.096147 & 0.7259 & 0.235437 \tabularnewline
15 & -0.039812 & -0.3006 & 0.382417 \tabularnewline
16 & -0.148843 & -1.1237 & 0.132917 \tabularnewline
17 & -0.013496 & -0.1019 & 0.459601 \tabularnewline
18 & 0.030457 & 0.2299 & 0.409478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34519&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]-0.052686[/C][C]-0.3978[/C][C]0.346142[/C][/ROW]
[ROW][C]2[/C][C]0.040913[/C][C]0.3089[/C][C]0.379268[/C][/ROW]
[ROW][C]3[/C][C]0.106381[/C][C]0.8032[/C][C]0.21261[/C][/ROW]
[ROW][C]4[/C][C]0.080831[/C][C]0.6103[/C][C]0.272057[/C][/ROW]
[ROW][C]5[/C][C]-0.078124[/C][C]-0.5898[/C][C]0.27882[/C][/ROW]
[ROW][C]6[/C][C]0.084705[/C][C]0.6395[/C][C]0.262526[/C][/ROW]
[ROW][C]7[/C][C]0.011807[/C][C]0.0891[/C][C]0.464641[/C][/ROW]
[ROW][C]8[/C][C]0.094143[/C][C]0.7108[/C][C]0.240064[/C][/ROW]
[ROW][C]9[/C][C]-0.01951[/C][C]-0.1473[/C][C]0.44171[/C][/ROW]
[ROW][C]10[/C][C]-0.105503[/C][C]-0.7965[/C][C]0.214515[/C][/ROW]
[ROW][C]11[/C][C]0.174021[/C][C]1.3138[/C][C]0.097083[/C][/ROW]
[ROW][C]12[/C][C]-0.258993[/C][C]-1.9554[/C][C]0.027725[/C][/ROW]
[ROW][C]13[/C][C]-0.165985[/C][C]-1.2532[/C][C]0.107631[/C][/ROW]
[ROW][C]14[/C][C]0.096147[/C][C]0.7259[/C][C]0.235437[/C][/ROW]
[ROW][C]15[/C][C]-0.039812[/C][C]-0.3006[/C][C]0.382417[/C][/ROW]
[ROW][C]16[/C][C]-0.148843[/C][C]-1.1237[/C][C]0.132917[/C][/ROW]
[ROW][C]17[/C][C]-0.013496[/C][C]-0.1019[/C][C]0.459601[/C][/ROW]
[ROW][C]18[/C][C]0.030457[/C][C]0.2299[/C][C]0.409478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34519&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34519&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	-0.052686	-0.3978	0.346142
2	0.040913	0.3089	0.379268
3	0.106381	0.8032	0.21261
4	0.080831	0.6103	0.272057
5	-0.078124	-0.5898	0.27882
6	0.084705	0.6395	0.262526
7	0.011807	0.0891	0.464641
8	0.094143	0.7108	0.240064
9	-0.01951	-0.1473	0.44171
10	-0.105503	-0.7965	0.214515
11	0.174021	1.3138	0.097083
12	-0.258993	-1.9554	0.027725
13	-0.165985	-1.2532	0.107631
14	0.096147	0.7259	0.235437
15	-0.039812	-0.3006	0.382417
16	-0.148843	-1.1237	0.132917
17	-0.013496	-0.1019	0.459601
18	0.030457	0.2299	0.409478

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.052686	-0.3978	0.346142
2	0.038243	0.2887	0.386918
3	0.110939	0.8376	0.202886
4	0.092244	0.6964	0.244495
5	-0.078942	-0.596	0.276767
6	0.05761	0.4349	0.332621
7	0.008122	0.0613	0.475661
8	0.102628	0.7748	0.220822
9	-0.013463	-0.1016	0.459699
10	-0.141753	-1.0702	0.144517
11	0.159899	1.2072	0.116168
12	-0.27052	-2.0424	0.022875
13	-0.170775	-1.2893	0.101247
14	0.091927	0.694	0.24524
15	-0.024093	-0.1819	0.428153
16	-0.054046	-0.408	0.342386
17	-0.084402	-0.6372	0.263267
18	0.079729	0.6019	0.274799

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.052686 & -0.3978 & 0.346142 \tabularnewline
2 & 0.038243 & 0.2887 & 0.386918 \tabularnewline
3 & 0.110939 & 0.8376 & 0.202886 \tabularnewline
4 & 0.092244 & 0.6964 & 0.244495 \tabularnewline
5 & -0.078942 & -0.596 & 0.276767 \tabularnewline
6 & 0.05761 & 0.4349 & 0.332621 \tabularnewline
7 & 0.008122 & 0.0613 & 0.475661 \tabularnewline
8 & 0.102628 & 0.7748 & 0.220822 \tabularnewline
9 & -0.013463 & -0.1016 & 0.459699 \tabularnewline
10 & -0.141753 & -1.0702 & 0.144517 \tabularnewline
11 & 0.159899 & 1.2072 & 0.116168 \tabularnewline
12 & -0.27052 & -2.0424 & 0.022875 \tabularnewline
13 & -0.170775 & -1.2893 & 0.101247 \tabularnewline
14 & 0.091927 & 0.694 & 0.24524 \tabularnewline
15 & -0.024093 & -0.1819 & 0.428153 \tabularnewline
16 & -0.054046 & -0.408 & 0.342386 \tabularnewline
17 & -0.084402 & -0.6372 & 0.263267 \tabularnewline
18 & 0.079729 & 0.6019 & 0.274799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34519&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]-0.052686[/C][C]-0.3978[/C][C]0.346142[/C][/ROW]
[ROW][C]2[/C][C]0.038243[/C][C]0.2887[/C][C]0.386918[/C][/ROW]
[ROW][C]3[/C][C]0.110939[/C][C]0.8376[/C][C]0.202886[/C][/ROW]
[ROW][C]4[/C][C]0.092244[/C][C]0.6964[/C][C]0.244495[/C][/ROW]
[ROW][C]5[/C][C]-0.078942[/C][C]-0.596[/C][C]0.276767[/C][/ROW]
[ROW][C]6[/C][C]0.05761[/C][C]0.4349[/C][C]0.332621[/C][/ROW]
[ROW][C]7[/C][C]0.008122[/C][C]0.0613[/C][C]0.475661[/C][/ROW]
[ROW][C]8[/C][C]0.102628[/C][C]0.7748[/C][C]0.220822[/C][/ROW]
[ROW][C]9[/C][C]-0.013463[/C][C]-0.1016[/C][C]0.459699[/C][/ROW]
[ROW][C]10[/C][C]-0.141753[/C][C]-1.0702[/C][C]0.144517[/C][/ROW]
[ROW][C]11[/C][C]0.159899[/C][C]1.2072[/C][C]0.116168[/C][/ROW]
[ROW][C]12[/C][C]-0.27052[/C][C]-2.0424[/C][C]0.022875[/C][/ROW]
[ROW][C]13[/C][C]-0.170775[/C][C]-1.2893[/C][C]0.101247[/C][/ROW]
[ROW][C]14[/C][C]0.091927[/C][C]0.694[/C][C]0.24524[/C][/ROW]
[ROW][C]15[/C][C]-0.024093[/C][C]-0.1819[/C][C]0.428153[/C][/ROW]
[ROW][C]16[/C][C]-0.054046[/C][C]-0.408[/C][C]0.342386[/C][/ROW]
[ROW][C]17[/C][C]-0.084402[/C][C]-0.6372[/C][C]0.263267[/C][/ROW]
[ROW][C]18[/C][C]0.079729[/C][C]0.6019[/C][C]0.274799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34519&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34519&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	-0.052686	-0.3978	0.346142
2	0.038243	0.2887	0.386918
3	0.110939	0.8376	0.202886
4	0.092244	0.6964	0.244495
5	-0.078942	-0.596	0.276767
6	0.05761	0.4349	0.332621
7	0.008122	0.0613	0.475661
8	0.102628	0.7748	0.220822
9	-0.013463	-0.1016	0.459699
10	-0.141753	-1.0702	0.144517
11	0.159899	1.2072	0.116168
12	-0.27052	-2.0424	0.022875
13	-0.170775	-1.2893	0.101247
14	0.091927	0.694	0.24524
15	-0.024093	-0.1819	0.428153
16	-0.054046	-0.408	0.342386
17	-0.084402	-0.6372	0.263267
18	0.079729	0.6019	0.274799

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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')

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