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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

Thu, 22 Dec 2011 18:47:48 -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/2011/Dec/22/t1324597847k0cykbhdqr163sl.htm/, Retrieved Fri, 03 May 2024 08:09:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160098, Retrieved Fri, 03 May 2024 08:09:02 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

127

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [WS9 3.1 ACF d=0, D=0] [2010-12-07 10:00:49] [afe9379cca749d06b3d6872e02cc47ed]
- R PD              [(Partial) Autocorrelation Function] [PAPER: aantal fai...] [2011-12-22 23:47:48] [6baf48ba14bcb50d9e72b77bece8a45b] [Current]
-                     [(Partial) Autocorrelation Function] [PAPER: aantal fai...] [2011-12-22 23:52:01] [f0cb027b41af06223bae4ee77475f3bc] 
-                     [(Partial) Autocorrelation Function] [PAPER: aantal fai...] [2011-12-22 23:53:54] [f0cb027b41af06223bae4ee77475f3bc] 
-                     [(Partial) Autocorrelation Function] [PAPER: aantal fai...] [2011-12-22 23:56:18] [f0cb027b41af06223bae4ee77475f3bc] 
-    D                [(Partial) Autocorrelation Function] [PAPER: werklooshe...] [2011-12-23 00:22:43] [f0cb027b41af06223bae4ee77475f3bc] 
-    D                [(Partial) Autocorrelation Function] [PAPER: werklooshe...] [2011-12-23 00:24:11] [f0cb027b41af06223bae4ee77475f3bc] 
-    D                [(Partial) Autocorrelation Function] [PAPER: werklooshe...] [2011-12-23 00:26:35] [f0cb027b41af06223bae4ee77475f3bc] 
-    D                [(Partial) Autocorrelation Function] [PAPER: werklooshe...] [2011-12-23 00:28:44] [f0cb027b41af06223bae4ee77475f3bc] 
-    D                [(Partial) Autocorrelation Function] [PAPER: inflatie] [2011-12-23 00:33:05] [f0cb027b41af06223bae4ee77475f3bc] 
-    D                [(Partial) Autocorrelation Function] [PAPER: inflatie] [2011-12-23 00:34:28] [f0cb027b41af06223bae4ee77475f3bc] 
-    D                [(Partial) Autocorrelation Function] [PAPER: inflatie] [2011-12-23 00:36:23] [f0cb027b41af06223bae4ee77475f3bc] 
-    D                [(Partial) Autocorrelation Function] [PAPER: inflatie] [2011-12-23 00:40:04] [f0cb027b41af06223bae4ee77475f3bc] 

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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	'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160098&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160098&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160098&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.215268	2.3581	0.009992
2	-0.153239	-1.6787	0.047911
3	0.241168	2.6419	0.004672
4	0.176549	1.934	0.027734
5	0.088188	0.9661	0.16798
6	0.278948	3.0557	0.001384
7	0.081123	0.8887	0.187982
8	0.16009	1.7537	0.041018
9	0.202692	2.2204	0.014135
10	-0.15939	-1.746	0.041683
11	0.169566	1.8575	0.032845
12	0.752979	8.2485	0
13	0.116753	1.279	0.101689
14	-0.183727	-2.0126	0.023196
15	0.18105	1.9833	0.024809
16	0.103008	1.1284	0.130701
17	0.031289	0.3428	0.36619
18	0.193454	2.1192	0.018068
19	-0.006142	-0.0673	0.473234
20	0.059745	0.6545	0.257031

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.215268 & 2.3581 & 0.009992 \tabularnewline
2 & -0.153239 & -1.6787 & 0.047911 \tabularnewline
3 & 0.241168 & 2.6419 & 0.004672 \tabularnewline
4 & 0.176549 & 1.934 & 0.027734 \tabularnewline
5 & 0.088188 & 0.9661 & 0.16798 \tabularnewline
6 & 0.278948 & 3.0557 & 0.001384 \tabularnewline
7 & 0.081123 & 0.8887 & 0.187982 \tabularnewline
8 & 0.16009 & 1.7537 & 0.041018 \tabularnewline
9 & 0.202692 & 2.2204 & 0.014135 \tabularnewline
10 & -0.15939 & -1.746 & 0.041683 \tabularnewline
11 & 0.169566 & 1.8575 & 0.032845 \tabularnewline
12 & 0.752979 & 8.2485 & 0 \tabularnewline
13 & 0.116753 & 1.279 & 0.101689 \tabularnewline
14 & -0.183727 & -2.0126 & 0.023196 \tabularnewline
15 & 0.18105 & 1.9833 & 0.024809 \tabularnewline
16 & 0.103008 & 1.1284 & 0.130701 \tabularnewline
17 & 0.031289 & 0.3428 & 0.36619 \tabularnewline
18 & 0.193454 & 2.1192 & 0.018068 \tabularnewline
19 & -0.006142 & -0.0673 & 0.473234 \tabularnewline
20 & 0.059745 & 0.6545 & 0.257031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160098&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]0.215268[/C][C]2.3581[/C][C]0.009992[/C][/ROW]
[ROW][C]2[/C][C]-0.153239[/C][C]-1.6787[/C][C]0.047911[/C][/ROW]
[ROW][C]3[/C][C]0.241168[/C][C]2.6419[/C][C]0.004672[/C][/ROW]
[ROW][C]4[/C][C]0.176549[/C][C]1.934[/C][C]0.027734[/C][/ROW]
[ROW][C]5[/C][C]0.088188[/C][C]0.9661[/C][C]0.16798[/C][/ROW]
[ROW][C]6[/C][C]0.278948[/C][C]3.0557[/C][C]0.001384[/C][/ROW]
[ROW][C]7[/C][C]0.081123[/C][C]0.8887[/C][C]0.187982[/C][/ROW]
[ROW][C]8[/C][C]0.16009[/C][C]1.7537[/C][C]0.041018[/C][/ROW]
[ROW][C]9[/C][C]0.202692[/C][C]2.2204[/C][C]0.014135[/C][/ROW]
[ROW][C]10[/C][C]-0.15939[/C][C]-1.746[/C][C]0.041683[/C][/ROW]
[ROW][C]11[/C][C]0.169566[/C][C]1.8575[/C][C]0.032845[/C][/ROW]
[ROW][C]12[/C][C]0.752979[/C][C]8.2485[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.116753[/C][C]1.279[/C][C]0.101689[/C][/ROW]
[ROW][C]14[/C][C]-0.183727[/C][C]-2.0126[/C][C]0.023196[/C][/ROW]
[ROW][C]15[/C][C]0.18105[/C][C]1.9833[/C][C]0.024809[/C][/ROW]
[ROW][C]16[/C][C]0.103008[/C][C]1.1284[/C][C]0.130701[/C][/ROW]
[ROW][C]17[/C][C]0.031289[/C][C]0.3428[/C][C]0.36619[/C][/ROW]
[ROW][C]18[/C][C]0.193454[/C][C]2.1192[/C][C]0.018068[/C][/ROW]
[ROW][C]19[/C][C]-0.006142[/C][C]-0.0673[/C][C]0.473234[/C][/ROW]
[ROW][C]20[/C][C]0.059745[/C][C]0.6545[/C][C]0.257031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160098&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160098&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	0.215268	2.3581	0.009992
2	-0.153239	-1.6787	0.047911
3	0.241168	2.6419	0.004672
4	0.176549	1.934	0.027734
5	0.088188	0.9661	0.16798
6	0.278948	3.0557	0.001384
7	0.081123	0.8887	0.187982
8	0.16009	1.7537	0.041018
9	0.202692	2.2204	0.014135
10	-0.15939	-1.746	0.041683
11	0.169566	1.8575	0.032845
12	0.752979	8.2485	0
13	0.116753	1.279	0.101689
14	-0.183727	-2.0126	0.023196
15	0.18105	1.9833	0.024809
16	0.103008	1.1284	0.130701
17	0.031289	0.3428	0.36619
18	0.193454	2.1192	0.018068
19	-0.006142	-0.0673	0.473234
20	0.059745	0.6545	0.257031

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.215268	2.3581	0.009992
2	-0.209278	-2.2925	0.011809
3	0.357619	3.9175	7.5e-05
4	-0.034705	-0.3802	0.352242
5	0.209405	2.2939	0.011767
6	0.19769	2.1656	0.016161
7	-0.067491	-0.7393	0.230576
8	0.309687	3.3925	0.000469
9	-0.118937	-1.3029	0.097553
10	-0.194797	-2.1339	0.017444
11	0.341917	3.7455	0.000139
12	0.566393	6.2045	0
13	-0.182675	-2.0011	0.023819
14	-0.071686	-0.7853	0.21692
15	-0.106203	-1.1634	0.123489
16	-0.088411	-0.9685	0.167374
17	-0.049072	-0.5376	0.29594
18	-0.07135	-0.7816	0.217996
19	-0.103911	-1.1383	0.128634
20	-0.071351	-0.7816	0.217991

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.215268 & 2.3581 & 0.009992 \tabularnewline
2 & -0.209278 & -2.2925 & 0.011809 \tabularnewline
3 & 0.357619 & 3.9175 & 7.5e-05 \tabularnewline
4 & -0.034705 & -0.3802 & 0.352242 \tabularnewline
5 & 0.209405 & 2.2939 & 0.011767 \tabularnewline
6 & 0.19769 & 2.1656 & 0.016161 \tabularnewline
7 & -0.067491 & -0.7393 & 0.230576 \tabularnewline
8 & 0.309687 & 3.3925 & 0.000469 \tabularnewline
9 & -0.118937 & -1.3029 & 0.097553 \tabularnewline
10 & -0.194797 & -2.1339 & 0.017444 \tabularnewline
11 & 0.341917 & 3.7455 & 0.000139 \tabularnewline
12 & 0.566393 & 6.2045 & 0 \tabularnewline
13 & -0.182675 & -2.0011 & 0.023819 \tabularnewline
14 & -0.071686 & -0.7853 & 0.21692 \tabularnewline
15 & -0.106203 & -1.1634 & 0.123489 \tabularnewline
16 & -0.088411 & -0.9685 & 0.167374 \tabularnewline
17 & -0.049072 & -0.5376 & 0.29594 \tabularnewline
18 & -0.07135 & -0.7816 & 0.217996 \tabularnewline
19 & -0.103911 & -1.1383 & 0.128634 \tabularnewline
20 & -0.071351 & -0.7816 & 0.217991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160098&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]0.215268[/C][C]2.3581[/C][C]0.009992[/C][/ROW]
[ROW][C]2[/C][C]-0.209278[/C][C]-2.2925[/C][C]0.011809[/C][/ROW]
[ROW][C]3[/C][C]0.357619[/C][C]3.9175[/C][C]7.5e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.034705[/C][C]-0.3802[/C][C]0.352242[/C][/ROW]
[ROW][C]5[/C][C]0.209405[/C][C]2.2939[/C][C]0.011767[/C][/ROW]
[ROW][C]6[/C][C]0.19769[/C][C]2.1656[/C][C]0.016161[/C][/ROW]
[ROW][C]7[/C][C]-0.067491[/C][C]-0.7393[/C][C]0.230576[/C][/ROW]
[ROW][C]8[/C][C]0.309687[/C][C]3.3925[/C][C]0.000469[/C][/ROW]
[ROW][C]9[/C][C]-0.118937[/C][C]-1.3029[/C][C]0.097553[/C][/ROW]
[ROW][C]10[/C][C]-0.194797[/C][C]-2.1339[/C][C]0.017444[/C][/ROW]
[ROW][C]11[/C][C]0.341917[/C][C]3.7455[/C][C]0.000139[/C][/ROW]
[ROW][C]12[/C][C]0.566393[/C][C]6.2045[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.182675[/C][C]-2.0011[/C][C]0.023819[/C][/ROW]
[ROW][C]14[/C][C]-0.071686[/C][C]-0.7853[/C][C]0.21692[/C][/ROW]
[ROW][C]15[/C][C]-0.106203[/C][C]-1.1634[/C][C]0.123489[/C][/ROW]
[ROW][C]16[/C][C]-0.088411[/C][C]-0.9685[/C][C]0.167374[/C][/ROW]
[ROW][C]17[/C][C]-0.049072[/C][C]-0.5376[/C][C]0.29594[/C][/ROW]
[ROW][C]18[/C][C]-0.07135[/C][C]-0.7816[/C][C]0.217996[/C][/ROW]
[ROW][C]19[/C][C]-0.103911[/C][C]-1.1383[/C][C]0.128634[/C][/ROW]
[ROW][C]20[/C][C]-0.071351[/C][C]-0.7816[/C][C]0.217991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160098&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160098&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	0.215268	2.3581	0.009992
2	-0.209278	-2.2925	0.011809
3	0.357619	3.9175	7.5e-05
4	-0.034705	-0.3802	0.352242
5	0.209405	2.2939	0.011767
6	0.19769	2.1656	0.016161
7	-0.067491	-0.7393	0.230576
8	0.309687	3.3925	0.000469
9	-0.118937	-1.3029	0.097553
10	-0.194797	-2.1339	0.017444
11	0.341917	3.7455	0.000139
12	0.566393	6.2045	0
13	-0.182675	-2.0011	0.023819
14	-0.071686	-0.7853	0.21692
15	-0.106203	-1.1634	0.123489
16	-0.088411	-0.9685	0.167374
17	-0.049072	-0.5376	0.29594
18	-0.07135	-0.7816	0.217996
19	-0.103911	-1.1383	0.128634
20	-0.071351	-0.7816	0.217991

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 = multiplicative ; par2 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; 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