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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

Tue, 11 Dec 2012 13:01:14 -0500

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/2012/Dec/11/t1355248893zhx9jfct2723xms.htm/, Retrieved Sat, 20 Apr 2024 08:44:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198602, Retrieved Sat, 20 Apr 2024 08:44:31 +0000

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User-defined keywords

Estimated Impact

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

-     [(Partial) Autocorrelation Function] [] [2011-12-20 16:21:00] [2417ae1b112c0bd5f0a8e2d9469d5871]
- R       [(Partial) Autocorrelation Function] [tt] [2012-12-11 18:01:14] [69fed4bf76000787e6433dea6d892b14] [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	3 seconds
R Server	'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198602&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198602&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198602&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	3 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.953029	18.3814	0
2	0.905905	17.4725	0
3	0.866941	16.721	0
4	0.848243	16.3603	0
5	0.836163	16.1273	0
6	0.803428	15.496	0
7	0.780384	15.0515	0
8	0.739074	14.2547	0
9	0.707557	13.6469	0
10	0.697309	13.4492	0
11	0.701438	13.5288	0
12	0.705868	13.6143	0
13	0.650143	12.5395	0
14	0.597708	11.5282	0
15	0.559117	10.7839	0
16	0.54447	10.5014	0
17	0.542013	10.454	0
18	0.524014	10.1068	0
19	0.518523	10.0009	0
20	0.494943	9.5461	0
21	0.481482	9.2865	0
22	0.490365	9.4578	0
23	0.50954	9.8276	0
24	0.5309	10.2396	0
25	0.492619	9.5013	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.953029 & 18.3814 & 0 \tabularnewline
2 & 0.905905 & 17.4725 & 0 \tabularnewline
3 & 0.866941 & 16.721 & 0 \tabularnewline
4 & 0.848243 & 16.3603 & 0 \tabularnewline
5 & 0.836163 & 16.1273 & 0 \tabularnewline
6 & 0.803428 & 15.496 & 0 \tabularnewline
7 & 0.780384 & 15.0515 & 0 \tabularnewline
8 & 0.739074 & 14.2547 & 0 \tabularnewline
9 & 0.707557 & 13.6469 & 0 \tabularnewline
10 & 0.697309 & 13.4492 & 0 \tabularnewline
11 & 0.701438 & 13.5288 & 0 \tabularnewline
12 & 0.705868 & 13.6143 & 0 \tabularnewline
13 & 0.650143 & 12.5395 & 0 \tabularnewline
14 & 0.597708 & 11.5282 & 0 \tabularnewline
15 & 0.559117 & 10.7839 & 0 \tabularnewline
16 & 0.54447 & 10.5014 & 0 \tabularnewline
17 & 0.542013 & 10.454 & 0 \tabularnewline
18 & 0.524014 & 10.1068 & 0 \tabularnewline
19 & 0.518523 & 10.0009 & 0 \tabularnewline
20 & 0.494943 & 9.5461 & 0 \tabularnewline
21 & 0.481482 & 9.2865 & 0 \tabularnewline
22 & 0.490365 & 9.4578 & 0 \tabularnewline
23 & 0.50954 & 9.8276 & 0 \tabularnewline
24 & 0.5309 & 10.2396 & 0 \tabularnewline
25 & 0.492619 & 9.5013 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198602&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]0.953029[/C][C]18.3814[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.905905[/C][C]17.4725[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.866941[/C][C]16.721[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.848243[/C][C]16.3603[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.836163[/C][C]16.1273[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.803428[/C][C]15.496[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.780384[/C][C]15.0515[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.739074[/C][C]14.2547[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.707557[/C][C]13.6469[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.697309[/C][C]13.4492[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.701438[/C][C]13.5288[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.705868[/C][C]13.6143[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.650143[/C][C]12.5395[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.597708[/C][C]11.5282[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.559117[/C][C]10.7839[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.54447[/C][C]10.5014[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.542013[/C][C]10.454[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.524014[/C][C]10.1068[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.518523[/C][C]10.0009[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.494943[/C][C]9.5461[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.481482[/C][C]9.2865[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.490365[/C][C]9.4578[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.50954[/C][C]9.8276[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.5309[/C][C]10.2396[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.492619[/C][C]9.5013[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198602&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198602&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	0.953029	18.3814	0
2	0.905905	17.4725	0
3	0.866941	16.721	0
4	0.848243	16.3603	0
5	0.836163	16.1273	0
6	0.803428	15.496	0
7	0.780384	15.0515	0
8	0.739074	14.2547	0
9	0.707557	13.6469	0
10	0.697309	13.4492	0
11	0.701438	13.5288	0
12	0.705868	13.6143	0
13	0.650143	12.5395	0
14	0.597708	11.5282	0
15	0.559117	10.7839	0
16	0.54447	10.5014	0
17	0.542013	10.454	0
18	0.524014	10.1068	0
19	0.518523	10.0009	0
20	0.494943	9.5461	0
21	0.481482	9.2865	0
22	0.490365	9.4578	0
23	0.50954	9.8276	0
24	0.5309	10.2396	0
25	0.492619	9.5013	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.953029	18.3814	0
2	-0.025716	-0.496	0.310095
3	0.064285	1.2399	0.107901
4	0.200462	3.8664	6.5e-05
5	0.073321	1.4142	0.079076
6	-0.203911	-3.9329	5e-05
7	0.154527	2.9804	0.001534
8	-0.232935	-4.4927	5e-06
9	0.043252	0.8342	0.202348
10	0.244823	4.722	2e-06
11	0.141231	2.724	0.003377
12	-0.026246	-0.5062	0.306502
13	-0.55096	-10.6265	0
14	0.041869	0.8075	0.209937
15	0.131743	2.541	0.00573
16	0.094142	1.8158	0.035107
17	0.147384	2.8426	0.00236
18	0.049	0.9451	0.172619
19	0.115029	2.2186	0.013559
20	-0.048429	-0.9341	0.175436
21	-0.001037	-0.02	0.492025
22	0.09784	1.8871	0.029964
23	-0.048905	-0.9432	0.173084
24	0.070517	1.3601	0.087315
25	-0.284097	-5.4795	0

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.953029 & 18.3814 & 0 \tabularnewline
2 & -0.025716 & -0.496 & 0.310095 \tabularnewline
3 & 0.064285 & 1.2399 & 0.107901 \tabularnewline
4 & 0.200462 & 3.8664 & 6.5e-05 \tabularnewline
5 & 0.073321 & 1.4142 & 0.079076 \tabularnewline
6 & -0.203911 & -3.9329 & 5e-05 \tabularnewline
7 & 0.154527 & 2.9804 & 0.001534 \tabularnewline
8 & -0.232935 & -4.4927 & 5e-06 \tabularnewline
9 & 0.043252 & 0.8342 & 0.202348 \tabularnewline
10 & 0.244823 & 4.722 & 2e-06 \tabularnewline
11 & 0.141231 & 2.724 & 0.003377 \tabularnewline
12 & -0.026246 & -0.5062 & 0.306502 \tabularnewline
13 & -0.55096 & -10.6265 & 0 \tabularnewline
14 & 0.041869 & 0.8075 & 0.209937 \tabularnewline
15 & 0.131743 & 2.541 & 0.00573 \tabularnewline
16 & 0.094142 & 1.8158 & 0.035107 \tabularnewline
17 & 0.147384 & 2.8426 & 0.00236 \tabularnewline
18 & 0.049 & 0.9451 & 0.172619 \tabularnewline
19 & 0.115029 & 2.2186 & 0.013559 \tabularnewline
20 & -0.048429 & -0.9341 & 0.175436 \tabularnewline
21 & -0.001037 & -0.02 & 0.492025 \tabularnewline
22 & 0.09784 & 1.8871 & 0.029964 \tabularnewline
23 & -0.048905 & -0.9432 & 0.173084 \tabularnewline
24 & 0.070517 & 1.3601 & 0.087315 \tabularnewline
25 & -0.284097 & -5.4795 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198602&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]0.953029[/C][C]18.3814[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.025716[/C][C]-0.496[/C][C]0.310095[/C][/ROW]
[ROW][C]3[/C][C]0.064285[/C][C]1.2399[/C][C]0.107901[/C][/ROW]
[ROW][C]4[/C][C]0.200462[/C][C]3.8664[/C][C]6.5e-05[/C][/ROW]
[ROW][C]5[/C][C]0.073321[/C][C]1.4142[/C][C]0.079076[/C][/ROW]
[ROW][C]6[/C][C]-0.203911[/C][C]-3.9329[/C][C]5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.154527[/C][C]2.9804[/C][C]0.001534[/C][/ROW]
[ROW][C]8[/C][C]-0.232935[/C][C]-4.4927[/C][C]5e-06[/C][/ROW]
[ROW][C]9[/C][C]0.043252[/C][C]0.8342[/C][C]0.202348[/C][/ROW]
[ROW][C]10[/C][C]0.244823[/C][C]4.722[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.141231[/C][C]2.724[/C][C]0.003377[/C][/ROW]
[ROW][C]12[/C][C]-0.026246[/C][C]-0.5062[/C][C]0.306502[/C][/ROW]
[ROW][C]13[/C][C]-0.55096[/C][C]-10.6265[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.041869[/C][C]0.8075[/C][C]0.209937[/C][/ROW]
[ROW][C]15[/C][C]0.131743[/C][C]2.541[/C][C]0.00573[/C][/ROW]
[ROW][C]16[/C][C]0.094142[/C][C]1.8158[/C][C]0.035107[/C][/ROW]
[ROW][C]17[/C][C]0.147384[/C][C]2.8426[/C][C]0.00236[/C][/ROW]
[ROW][C]18[/C][C]0.049[/C][C]0.9451[/C][C]0.172619[/C][/ROW]
[ROW][C]19[/C][C]0.115029[/C][C]2.2186[/C][C]0.013559[/C][/ROW]
[ROW][C]20[/C][C]-0.048429[/C][C]-0.9341[/C][C]0.175436[/C][/ROW]
[ROW][C]21[/C][C]-0.001037[/C][C]-0.02[/C][C]0.492025[/C][/ROW]
[ROW][C]22[/C][C]0.09784[/C][C]1.8871[/C][C]0.029964[/C][/ROW]
[ROW][C]23[/C][C]-0.048905[/C][C]-0.9432[/C][C]0.173084[/C][/ROW]
[ROW][C]24[/C][C]0.070517[/C][C]1.3601[/C][C]0.087315[/C][/ROW]
[ROW][C]25[/C][C]-0.284097[/C][C]-5.4795[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198602&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198602&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	0.953029	18.3814	0
2	-0.025716	-0.496	0.310095
3	0.064285	1.2399	0.107901
4	0.200462	3.8664	6.5e-05
5	0.073321	1.4142	0.079076
6	-0.203911	-3.9329	5e-05
7	0.154527	2.9804	0.001534
8	-0.232935	-4.4927	5e-06
9	0.043252	0.8342	0.202348
10	0.244823	4.722	2e-06
11	0.141231	2.724	0.003377
12	-0.026246	-0.5062	0.306502
13	-0.55096	-10.6265	0
14	0.041869	0.8075	0.209937
15	0.131743	2.541	0.00573
16	0.094142	1.8158	0.035107
17	0.147384	2.8426	0.00236
18	0.049	0.9451	0.172619
19	0.115029	2.2186	0.013559
20	-0.048429	-0.9341	0.175436
21	-0.001037	-0.02	0.492025
22	0.09784	1.8871	0.029964
23	-0.048905	-0.9432	0.173084
24	0.070517	1.3601	0.087315
25	-0.284097	-5.4795	0

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 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; 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)
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