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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, 03 Dec 2009 05:58:30 -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/2009/Dec/03/t1259845154oaznt179umahtb7.htm/, Retrieved Thu, 25 Apr 2024 02:13:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62705, Retrieved Thu, 25 Apr 2024 02:13:10 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

JSSHWWS9P4

Estimated Impact

120

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD    [(Partial) Autocorrelation Function] [Autocorrelation F...] [2009-12-03 12:58:30] [c8fd62404619100d8e91184019148412] [Current]

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Boxplots

11.1
10.9
10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3
8.1

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=62705&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=62705&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62705&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	0.396934	3.0489	0.001718
2	-0.248066	-1.9054	0.030801
3	-0.499029	-3.8331	0.000155
4	-0.334539	-2.5696	0.006364
5	0.10024	0.77	0.222199
6	0.390328	2.9982	0.001986
7	0.232838	1.7885	0.039418
8	-0.14038	-1.0783	0.142649
9	-0.327823	-2.5181	0.007267
10	-0.255465	-1.9623	0.027227
11	0.071127	0.5463	0.293448
12	0.359671	2.7627	0.003817
13	0.053927	0.4142	0.340107
14	-0.127542	-0.9797	0.165624
15	-0.096202	-0.7389	0.231436
16	-0.05339	-0.4101	0.34161
17	0.076548	0.588	0.279396

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.396934 & 3.0489 & 0.001718 \tabularnewline
2 & -0.248066 & -1.9054 & 0.030801 \tabularnewline
3 & -0.499029 & -3.8331 & 0.000155 \tabularnewline
4 & -0.334539 & -2.5696 & 0.006364 \tabularnewline
5 & 0.10024 & 0.77 & 0.222199 \tabularnewline
6 & 0.390328 & 2.9982 & 0.001986 \tabularnewline
7 & 0.232838 & 1.7885 & 0.039418 \tabularnewline
8 & -0.14038 & -1.0783 & 0.142649 \tabularnewline
9 & -0.327823 & -2.5181 & 0.007267 \tabularnewline
10 & -0.255465 & -1.9623 & 0.027227 \tabularnewline
11 & 0.071127 & 0.5463 & 0.293448 \tabularnewline
12 & 0.359671 & 2.7627 & 0.003817 \tabularnewline
13 & 0.053927 & 0.4142 & 0.340107 \tabularnewline
14 & -0.127542 & -0.9797 & 0.165624 \tabularnewline
15 & -0.096202 & -0.7389 & 0.231436 \tabularnewline
16 & -0.05339 & -0.4101 & 0.34161 \tabularnewline
17 & 0.076548 & 0.588 & 0.279396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62705&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]0.396934[/C][C]3.0489[/C][C]0.001718[/C][/ROW]
[ROW][C]2[/C][C]-0.248066[/C][C]-1.9054[/C][C]0.030801[/C][/ROW]
[ROW][C]3[/C][C]-0.499029[/C][C]-3.8331[/C][C]0.000155[/C][/ROW]
[ROW][C]4[/C][C]-0.334539[/C][C]-2.5696[/C][C]0.006364[/C][/ROW]
[ROW][C]5[/C][C]0.10024[/C][C]0.77[/C][C]0.222199[/C][/ROW]
[ROW][C]6[/C][C]0.390328[/C][C]2.9982[/C][C]0.001986[/C][/ROW]
[ROW][C]7[/C][C]0.232838[/C][C]1.7885[/C][C]0.039418[/C][/ROW]
[ROW][C]8[/C][C]-0.14038[/C][C]-1.0783[/C][C]0.142649[/C][/ROW]
[ROW][C]9[/C][C]-0.327823[/C][C]-2.5181[/C][C]0.007267[/C][/ROW]
[ROW][C]10[/C][C]-0.255465[/C][C]-1.9623[/C][C]0.027227[/C][/ROW]
[ROW][C]11[/C][C]0.071127[/C][C]0.5463[/C][C]0.293448[/C][/ROW]
[ROW][C]12[/C][C]0.359671[/C][C]2.7627[/C][C]0.003817[/C][/ROW]
[ROW][C]13[/C][C]0.053927[/C][C]0.4142[/C][C]0.340107[/C][/ROW]
[ROW][C]14[/C][C]-0.127542[/C][C]-0.9797[/C][C]0.165624[/C][/ROW]
[ROW][C]15[/C][C]-0.096202[/C][C]-0.7389[/C][C]0.231436[/C][/ROW]
[ROW][C]16[/C][C]-0.05339[/C][C]-0.4101[/C][C]0.34161[/C][/ROW]
[ROW][C]17[/C][C]0.076548[/C][C]0.588[/C][C]0.279396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62705&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62705&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	0.396934	3.0489	0.001718
2	-0.248066	-1.9054	0.030801
3	-0.499029	-3.8331	0.000155
4	-0.334539	-2.5696	0.006364
5	0.10024	0.77	0.222199
6	0.390328	2.9982	0.001986
7	0.232838	1.7885	0.039418
8	-0.14038	-1.0783	0.142649
9	-0.327823	-2.5181	0.007267
10	-0.255465	-1.9623	0.027227
11	0.071127	0.5463	0.293448
12	0.359671	2.7627	0.003817
13	0.053927	0.4142	0.340107
14	-0.127542	-0.9797	0.165624
15	-0.096202	-0.7389	0.231436
16	-0.05339	-0.4101	0.34161
17	0.076548	0.588	0.279396

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.396934	3.0489	0.001718
2	-0.481483	-3.6983	0.000239
3	-0.250387	-1.9233	0.029639
4	-0.139757	-1.0735	0.143711
5	0.108268	0.8316	0.204487
6	0.108366	0.8324	0.204277
7	-0.082347	-0.6325	0.264745
8	-0.116812	-0.8973	0.186616
9	-0.044054	-0.3384	0.368137
10	-0.099681	-0.7657	0.223464
11	0.06245	0.4797	0.316611
12	0.116526	0.8951	0.187197
13	-0.399154	-3.066	0.001636
14	0.22439	1.7236	0.045011
15	0.113491	0.8717	0.193442
16	-0.11814	-0.9075	0.18393
17	0.026111	0.2006	0.420866

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.396934 & 3.0489 & 0.001718 \tabularnewline
2 & -0.481483 & -3.6983 & 0.000239 \tabularnewline
3 & -0.250387 & -1.9233 & 0.029639 \tabularnewline
4 & -0.139757 & -1.0735 & 0.143711 \tabularnewline
5 & 0.108268 & 0.8316 & 0.204487 \tabularnewline
6 & 0.108366 & 0.8324 & 0.204277 \tabularnewline
7 & -0.082347 & -0.6325 & 0.264745 \tabularnewline
8 & -0.116812 & -0.8973 & 0.186616 \tabularnewline
9 & -0.044054 & -0.3384 & 0.368137 \tabularnewline
10 & -0.099681 & -0.7657 & 0.223464 \tabularnewline
11 & 0.06245 & 0.4797 & 0.316611 \tabularnewline
12 & 0.116526 & 0.8951 & 0.187197 \tabularnewline
13 & -0.399154 & -3.066 & 0.001636 \tabularnewline
14 & 0.22439 & 1.7236 & 0.045011 \tabularnewline
15 & 0.113491 & 0.8717 & 0.193442 \tabularnewline
16 & -0.11814 & -0.9075 & 0.18393 \tabularnewline
17 & 0.026111 & 0.2006 & 0.420866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62705&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]0.396934[/C][C]3.0489[/C][C]0.001718[/C][/ROW]
[ROW][C]2[/C][C]-0.481483[/C][C]-3.6983[/C][C]0.000239[/C][/ROW]
[ROW][C]3[/C][C]-0.250387[/C][C]-1.9233[/C][C]0.029639[/C][/ROW]
[ROW][C]4[/C][C]-0.139757[/C][C]-1.0735[/C][C]0.143711[/C][/ROW]
[ROW][C]5[/C][C]0.108268[/C][C]0.8316[/C][C]0.204487[/C][/ROW]
[ROW][C]6[/C][C]0.108366[/C][C]0.8324[/C][C]0.204277[/C][/ROW]
[ROW][C]7[/C][C]-0.082347[/C][C]-0.6325[/C][C]0.264745[/C][/ROW]
[ROW][C]8[/C][C]-0.116812[/C][C]-0.8973[/C][C]0.186616[/C][/ROW]
[ROW][C]9[/C][C]-0.044054[/C][C]-0.3384[/C][C]0.368137[/C][/ROW]
[ROW][C]10[/C][C]-0.099681[/C][C]-0.7657[/C][C]0.223464[/C][/ROW]
[ROW][C]11[/C][C]0.06245[/C][C]0.4797[/C][C]0.316611[/C][/ROW]
[ROW][C]12[/C][C]0.116526[/C][C]0.8951[/C][C]0.187197[/C][/ROW]
[ROW][C]13[/C][C]-0.399154[/C][C]-3.066[/C][C]0.001636[/C][/ROW]
[ROW][C]14[/C][C]0.22439[/C][C]1.7236[/C][C]0.045011[/C][/ROW]
[ROW][C]15[/C][C]0.113491[/C][C]0.8717[/C][C]0.193442[/C][/ROW]
[ROW][C]16[/C][C]-0.11814[/C][C]-0.9075[/C][C]0.18393[/C][/ROW]
[ROW][C]17[/C][C]0.026111[/C][C]0.2006[/C][C]0.420866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62705&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62705&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	0.396934	3.0489	0.001718
2	-0.481483	-3.6983	0.000239
3	-0.250387	-1.9233	0.029639
4	-0.139757	-1.0735	0.143711
5	0.108268	0.8316	0.204487
6	0.108366	0.8324	0.204277
7	-0.082347	-0.6325	0.264745
8	-0.116812	-0.8973	0.186616
9	-0.044054	-0.3384	0.368137
10	-0.099681	-0.7657	0.223464
11	0.06245	0.4797	0.316611
12	0.116526	0.8951	0.187197
13	-0.399154	-3.066	0.001636
14	0.22439	1.7236	0.045011
15	0.113491	0.8717	0.193442
16	-0.11814	-0.9075	0.18393
17	0.026111	0.2006	0.420866

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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