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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

Tue, 15 Dec 2009 03:49:33 -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/15/t1260874259uzr2zwaqgyjjerf.htm/, Retrieved Wed, 08 May 2024 08:11:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67832, Retrieved Wed, 08 May 2024 08:11:00 +0000

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

-       [(Partial) Autocorrelation Function] [Autocorrelation (...] [2009-12-15 10:49:33] [91da2e1ebdd83187f2515f461585cbee] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67832&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67832&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67832&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.523138	-5.7068	0
2	-0.059912	-0.6536	0.257327
3	0.391444	4.2701	2e-05
4	-0.349831	-3.8162	0.000108
5	0.102236	1.1153	0.133493
6	0.213784	2.3321	0.010688
7	-0.377524	-4.1183	3.5e-05
8	0.220245	2.4026	0.008913
9	0.082239	0.8971	0.185733
10	-0.220961	-2.4104	0.008733
11	0.109549	1.195	0.117224
12	0.000227	0.0025	0.499015
13	-0.137041	-1.4949	0.068788
14	0.146083	1.5936	0.056842
15	0.033021	0.3602	0.359662
16	-0.251445	-2.7429	0.003515
17	0.211742	2.3098	0.011311
18	0.014481	0.158	0.437376
19	-0.204621	-2.2321	0.013738
20	0.193436	2.1101	0.01847
21	-0.02036	-0.2221	0.412307

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.523138 & -5.7068 & 0 \tabularnewline
2 & -0.059912 & -0.6536 & 0.257327 \tabularnewline
3 & 0.391444 & 4.2701 & 2e-05 \tabularnewline
4 & -0.349831 & -3.8162 & 0.000108 \tabularnewline
5 & 0.102236 & 1.1153 & 0.133493 \tabularnewline
6 & 0.213784 & 2.3321 & 0.010688 \tabularnewline
7 & -0.377524 & -4.1183 & 3.5e-05 \tabularnewline
8 & 0.220245 & 2.4026 & 0.008913 \tabularnewline
9 & 0.082239 & 0.8971 & 0.185733 \tabularnewline
10 & -0.220961 & -2.4104 & 0.008733 \tabularnewline
11 & 0.109549 & 1.195 & 0.117224 \tabularnewline
12 & 0.000227 & 0.0025 & 0.499015 \tabularnewline
13 & -0.137041 & -1.4949 & 0.068788 \tabularnewline
14 & 0.146083 & 1.5936 & 0.056842 \tabularnewline
15 & 0.033021 & 0.3602 & 0.359662 \tabularnewline
16 & -0.251445 & -2.7429 & 0.003515 \tabularnewline
17 & 0.211742 & 2.3098 & 0.011311 \tabularnewline
18 & 0.014481 & 0.158 & 0.437376 \tabularnewline
19 & -0.204621 & -2.2321 & 0.013738 \tabularnewline
20 & 0.193436 & 2.1101 & 0.01847 \tabularnewline
21 & -0.02036 & -0.2221 & 0.412307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67832&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]-0.523138[/C][C]-5.7068[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.059912[/C][C]-0.6536[/C][C]0.257327[/C][/ROW]
[ROW][C]3[/C][C]0.391444[/C][C]4.2701[/C][C]2e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.349831[/C][C]-3.8162[/C][C]0.000108[/C][/ROW]
[ROW][C]5[/C][C]0.102236[/C][C]1.1153[/C][C]0.133493[/C][/ROW]
[ROW][C]6[/C][C]0.213784[/C][C]2.3321[/C][C]0.010688[/C][/ROW]
[ROW][C]7[/C][C]-0.377524[/C][C]-4.1183[/C][C]3.5e-05[/C][/ROW]
[ROW][C]8[/C][C]0.220245[/C][C]2.4026[/C][C]0.008913[/C][/ROW]
[ROW][C]9[/C][C]0.082239[/C][C]0.8971[/C][C]0.185733[/C][/ROW]
[ROW][C]10[/C][C]-0.220961[/C][C]-2.4104[/C][C]0.008733[/C][/ROW]
[ROW][C]11[/C][C]0.109549[/C][C]1.195[/C][C]0.117224[/C][/ROW]
[ROW][C]12[/C][C]0.000227[/C][C]0.0025[/C][C]0.499015[/C][/ROW]
[ROW][C]13[/C][C]-0.137041[/C][C]-1.4949[/C][C]0.068788[/C][/ROW]
[ROW][C]14[/C][C]0.146083[/C][C]1.5936[/C][C]0.056842[/C][/ROW]
[ROW][C]15[/C][C]0.033021[/C][C]0.3602[/C][C]0.359662[/C][/ROW]
[ROW][C]16[/C][C]-0.251445[/C][C]-2.7429[/C][C]0.003515[/C][/ROW]
[ROW][C]17[/C][C]0.211742[/C][C]2.3098[/C][C]0.011311[/C][/ROW]
[ROW][C]18[/C][C]0.014481[/C][C]0.158[/C][C]0.437376[/C][/ROW]
[ROW][C]19[/C][C]-0.204621[/C][C]-2.2321[/C][C]0.013738[/C][/ROW]
[ROW][C]20[/C][C]0.193436[/C][C]2.1101[/C][C]0.01847[/C][/ROW]
[ROW][C]21[/C][C]-0.02036[/C][C]-0.2221[/C][C]0.412307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67832&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67832&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	-0.523138	-5.7068	0
2	-0.059912	-0.6536	0.257327
3	0.391444	4.2701	2e-05
4	-0.349831	-3.8162	0.000108
5	0.102236	1.1153	0.133493
6	0.213784	2.3321	0.010688
7	-0.377524	-4.1183	3.5e-05
8	0.220245	2.4026	0.008913
9	0.082239	0.8971	0.185733
10	-0.220961	-2.4104	0.008733
11	0.109549	1.195	0.117224
12	0.000227	0.0025	0.499015
13	-0.137041	-1.4949	0.068788
14	0.146083	1.5936	0.056842
15	0.033021	0.3602	0.359662
16	-0.251445	-2.7429	0.003515
17	0.211742	2.3098	0.011311
18	0.014481	0.158	0.437376
19	-0.204621	-2.2321	0.013738
20	0.193436	2.1101	0.01847
21	-0.02036	-0.2221	0.412307

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.523138	-5.7068	0
2	-0.459277	-5.0101	1e-06
3	0.183978	2.007	0.02351
4	-0.012521	-0.1366	0.445792
5	-0.007464	-0.0814	0.467621
6	0.17664	1.9269	0.028187
7	-0.124864	-1.3621	0.087869
8	-0.084364	-0.9203	0.179637
9	0.049558	0.5406	0.29489
10	0.078167	0.8527	0.197769
11	-0.105743	-1.1535	0.125505
12	-0.118765	-1.2956	0.098815
13	-0.110942	-1.2102	0.114294
14	-0.05534	-0.6037	0.2736
15	0.171987	1.8762	0.031542
16	-0.099027	-1.0803	0.141107
17	-0.092095	-1.0046	0.158555
18	0.029295	0.3196	0.374927
19	-0.036521	-0.3984	0.345525
20	-0.041413	-0.4518	0.326132
21	0.090088	0.9827	0.163865

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.523138 & -5.7068 & 0 \tabularnewline
2 & -0.459277 & -5.0101 & 1e-06 \tabularnewline
3 & 0.183978 & 2.007 & 0.02351 \tabularnewline
4 & -0.012521 & -0.1366 & 0.445792 \tabularnewline
5 & -0.007464 & -0.0814 & 0.467621 \tabularnewline
6 & 0.17664 & 1.9269 & 0.028187 \tabularnewline
7 & -0.124864 & -1.3621 & 0.087869 \tabularnewline
8 & -0.084364 & -0.9203 & 0.179637 \tabularnewline
9 & 0.049558 & 0.5406 & 0.29489 \tabularnewline
10 & 0.078167 & 0.8527 & 0.197769 \tabularnewline
11 & -0.105743 & -1.1535 & 0.125505 \tabularnewline
12 & -0.118765 & -1.2956 & 0.098815 \tabularnewline
13 & -0.110942 & -1.2102 & 0.114294 \tabularnewline
14 & -0.05534 & -0.6037 & 0.2736 \tabularnewline
15 & 0.171987 & 1.8762 & 0.031542 \tabularnewline
16 & -0.099027 & -1.0803 & 0.141107 \tabularnewline
17 & -0.092095 & -1.0046 & 0.158555 \tabularnewline
18 & 0.029295 & 0.3196 & 0.374927 \tabularnewline
19 & -0.036521 & -0.3984 & 0.345525 \tabularnewline
20 & -0.041413 & -0.4518 & 0.326132 \tabularnewline
21 & 0.090088 & 0.9827 & 0.163865 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67832&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]-0.523138[/C][C]-5.7068[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.459277[/C][C]-5.0101[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.183978[/C][C]2.007[/C][C]0.02351[/C][/ROW]
[ROW][C]4[/C][C]-0.012521[/C][C]-0.1366[/C][C]0.445792[/C][/ROW]
[ROW][C]5[/C][C]-0.007464[/C][C]-0.0814[/C][C]0.467621[/C][/ROW]
[ROW][C]6[/C][C]0.17664[/C][C]1.9269[/C][C]0.028187[/C][/ROW]
[ROW][C]7[/C][C]-0.124864[/C][C]-1.3621[/C][C]0.087869[/C][/ROW]
[ROW][C]8[/C][C]-0.084364[/C][C]-0.9203[/C][C]0.179637[/C][/ROW]
[ROW][C]9[/C][C]0.049558[/C][C]0.5406[/C][C]0.29489[/C][/ROW]
[ROW][C]10[/C][C]0.078167[/C][C]0.8527[/C][C]0.197769[/C][/ROW]
[ROW][C]11[/C][C]-0.105743[/C][C]-1.1535[/C][C]0.125505[/C][/ROW]
[ROW][C]12[/C][C]-0.118765[/C][C]-1.2956[/C][C]0.098815[/C][/ROW]
[ROW][C]13[/C][C]-0.110942[/C][C]-1.2102[/C][C]0.114294[/C][/ROW]
[ROW][C]14[/C][C]-0.05534[/C][C]-0.6037[/C][C]0.2736[/C][/ROW]
[ROW][C]15[/C][C]0.171987[/C][C]1.8762[/C][C]0.031542[/C][/ROW]
[ROW][C]16[/C][C]-0.099027[/C][C]-1.0803[/C][C]0.141107[/C][/ROW]
[ROW][C]17[/C][C]-0.092095[/C][C]-1.0046[/C][C]0.158555[/C][/ROW]
[ROW][C]18[/C][C]0.029295[/C][C]0.3196[/C][C]0.374927[/C][/ROW]
[ROW][C]19[/C][C]-0.036521[/C][C]-0.3984[/C][C]0.345525[/C][/ROW]
[ROW][C]20[/C][C]-0.041413[/C][C]-0.4518[/C][C]0.326132[/C][/ROW]
[ROW][C]21[/C][C]0.090088[/C][C]0.9827[/C][C]0.163865[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67832&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67832&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	-0.523138	-5.7068	0
2	-0.459277	-5.0101	1e-06
3	0.183978	2.007	0.02351
4	-0.012521	-0.1366	0.445792
5	-0.007464	-0.0814	0.467621
6	0.17664	1.9269	0.028187
7	-0.124864	-1.3621	0.087869
8	-0.084364	-0.9203	0.179637
9	0.049558	0.5406	0.29489
10	0.078167	0.8527	0.197769
11	-0.105743	-1.1535	0.125505
12	-0.118765	-1.2956	0.098815
13	-0.110942	-1.2102	0.114294
14	-0.05534	-0.6037	0.2736
15	0.171987	1.8762	0.031542
16	-0.099027	-1.0803	0.141107
17	-0.092095	-1.0046	0.158555
18	0.029295	0.3196	0.374927
19	-0.036521	-0.3984	0.345525
20	-0.041413	-0.4518	0.326132
21	0.090088	0.9827	0.163865

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; 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