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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 30 Nov 2010 11:00:00 +0000

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/2010/Nov/30/t12911147193diafdcwyqlp0un.htm/, Retrieved Mon, 12 May 2025 00:37:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103325, Retrieved Mon, 12 May 2025 00:37:22 +0000

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User-defined keywords

Estimated Impact

249

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

F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Central Tendency] [Workshop 8, Robus...] [2010-11-28 19:41:12] [d946de7cca328fbcf207448a112523ab]
-         [Central Tendency] [Workshop 8, Centr...] [2010-11-29 20:08:54] [3635fb7041b1998c5a1332cf9de22bce]
- RMP         [(Partial) Autocorrelation Function] [Workshop 8 autoco...] [2010-11-30 11:00:00] [9ac5e967b06232cfb69e0c18e3cc2b37] [Current]
- R  D          [(Partial) Autocorrelation Function] [WS8 - Mini-tutori...] [2011-11-29 13:04:17] [74be16979710d4c4e7c6647856088456] 
-    D            [(Partial) Autocorrelation Function] [Paper Deel 2 - Da...] [2011-12-20 10:22:05] [95a4a8598e82ac3272c4dca488d0ba38] 

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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=103325&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=103325&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103325&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	0.541824	4.197	4.5e-05
2	0.32105	2.4868	0.007844
3	0.034801	0.2696	0.394208
4	-0.299251	-2.318	0.011938
5	-0.427385	-3.3105	0.00079
6	-0.475716	-3.6849	0.000247
7	-0.37676	-2.9184	0.002473
8	-0.314266	-2.4343	0.008957
9	0.030221	0.2341	0.407857
10	0.216941	1.6804	0.049038
11	0.360268	2.7906	0.003522
12	0.605049	4.6867	8e-06
13	0.3702	2.8676	0.00285
14	0.301899	2.3385	0.011356
15	0.097313	0.7538	0.226964
16	-0.134519	-1.042	0.150801
17	-0.29067	-2.2515	0.014013

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.541824 & 4.197 & 4.5e-05 \tabularnewline
2 & 0.32105 & 2.4868 & 0.007844 \tabularnewline
3 & 0.034801 & 0.2696 & 0.394208 \tabularnewline
4 & -0.299251 & -2.318 & 0.011938 \tabularnewline
5 & -0.427385 & -3.3105 & 0.00079 \tabularnewline
6 & -0.475716 & -3.6849 & 0.000247 \tabularnewline
7 & -0.37676 & -2.9184 & 0.002473 \tabularnewline
8 & -0.314266 & -2.4343 & 0.008957 \tabularnewline
9 & 0.030221 & 0.2341 & 0.407857 \tabularnewline
10 & 0.216941 & 1.6804 & 0.049038 \tabularnewline
11 & 0.360268 & 2.7906 & 0.003522 \tabularnewline
12 & 0.605049 & 4.6867 & 8e-06 \tabularnewline
13 & 0.3702 & 2.8676 & 0.00285 \tabularnewline
14 & 0.301899 & 2.3385 & 0.011356 \tabularnewline
15 & 0.097313 & 0.7538 & 0.226964 \tabularnewline
16 & -0.134519 & -1.042 & 0.150801 \tabularnewline
17 & -0.29067 & -2.2515 & 0.014013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103325&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]0.541824[/C][C]4.197[/C][C]4.5e-05[/C][/ROW]
[ROW][C]2[/C][C]0.32105[/C][C]2.4868[/C][C]0.007844[/C][/ROW]
[ROW][C]3[/C][C]0.034801[/C][C]0.2696[/C][C]0.394208[/C][/ROW]
[ROW][C]4[/C][C]-0.299251[/C][C]-2.318[/C][C]0.011938[/C][/ROW]
[ROW][C]5[/C][C]-0.427385[/C][C]-3.3105[/C][C]0.00079[/C][/ROW]
[ROW][C]6[/C][C]-0.475716[/C][C]-3.6849[/C][C]0.000247[/C][/ROW]
[ROW][C]7[/C][C]-0.37676[/C][C]-2.9184[/C][C]0.002473[/C][/ROW]
[ROW][C]8[/C][C]-0.314266[/C][C]-2.4343[/C][C]0.008957[/C][/ROW]
[ROW][C]9[/C][C]0.030221[/C][C]0.2341[/C][C]0.407857[/C][/ROW]
[ROW][C]10[/C][C]0.216941[/C][C]1.6804[/C][C]0.049038[/C][/ROW]
[ROW][C]11[/C][C]0.360268[/C][C]2.7906[/C][C]0.003522[/C][/ROW]
[ROW][C]12[/C][C]0.605049[/C][C]4.6867[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]0.3702[/C][C]2.8676[/C][C]0.00285[/C][/ROW]
[ROW][C]14[/C][C]0.301899[/C][C]2.3385[/C][C]0.011356[/C][/ROW]
[ROW][C]15[/C][C]0.097313[/C][C]0.7538[/C][C]0.226964[/C][/ROW]
[ROW][C]16[/C][C]-0.134519[/C][C]-1.042[/C][C]0.150801[/C][/ROW]
[ROW][C]17[/C][C]-0.29067[/C][C]-2.2515[/C][C]0.014013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103325&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103325&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	0.541824	4.197	4.5e-05
2	0.32105	2.4868	0.007844
3	0.034801	0.2696	0.394208
4	-0.299251	-2.318	0.011938
5	-0.427385	-3.3105	0.00079
6	-0.475716	-3.6849	0.000247
7	-0.37676	-2.9184	0.002473
8	-0.314266	-2.4343	0.008957
9	0.030221	0.2341	0.407857
10	0.216941	1.6804	0.049038
11	0.360268	2.7906	0.003522
12	0.605049	4.6867	8e-06
13	0.3702	2.8676	0.00285
14	0.301899	2.3385	0.011356
15	0.097313	0.7538	0.226964
16	-0.134519	-1.042	0.150801
17	-0.29067	-2.2515	0.014013

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.541824	4.197	4.5e-05
2	0.038895	0.3013	0.382122
3	-0.217563	-1.6852	0.048569
4	-0.370029	-2.8662	0.00286
5	-0.160174	-1.2407	0.109773
6	-0.116476	-0.9022	0.185273
7	-0.025439	-0.1971	0.422227
8	-0.221641	-1.7168	0.045585
9	0.223176	1.7287	0.044502
10	0.075401	0.5841	0.280686
11	0.07145	0.5535	0.291006
12	0.348415	2.6988	0.004513
13	-0.182277	-1.4119	0.081571
14	0.158401	1.227	0.112313
15	0.0756	0.5856	0.280172
16	0.001403	0.0109	0.495682
17	0.027394	0.2122	0.416336

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.541824 & 4.197 & 4.5e-05 \tabularnewline
2 & 0.038895 & 0.3013 & 0.382122 \tabularnewline
3 & -0.217563 & -1.6852 & 0.048569 \tabularnewline
4 & -0.370029 & -2.8662 & 0.00286 \tabularnewline
5 & -0.160174 & -1.2407 & 0.109773 \tabularnewline
6 & -0.116476 & -0.9022 & 0.185273 \tabularnewline
7 & -0.025439 & -0.1971 & 0.422227 \tabularnewline
8 & -0.221641 & -1.7168 & 0.045585 \tabularnewline
9 & 0.223176 & 1.7287 & 0.044502 \tabularnewline
10 & 0.075401 & 0.5841 & 0.280686 \tabularnewline
11 & 0.07145 & 0.5535 & 0.291006 \tabularnewline
12 & 0.348415 & 2.6988 & 0.004513 \tabularnewline
13 & -0.182277 & -1.4119 & 0.081571 \tabularnewline
14 & 0.158401 & 1.227 & 0.112313 \tabularnewline
15 & 0.0756 & 0.5856 & 0.280172 \tabularnewline
16 & 0.001403 & 0.0109 & 0.495682 \tabularnewline
17 & 0.027394 & 0.2122 & 0.416336 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103325&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]0.541824[/C][C]4.197[/C][C]4.5e-05[/C][/ROW]
[ROW][C]2[/C][C]0.038895[/C][C]0.3013[/C][C]0.382122[/C][/ROW]
[ROW][C]3[/C][C]-0.217563[/C][C]-1.6852[/C][C]0.048569[/C][/ROW]
[ROW][C]4[/C][C]-0.370029[/C][C]-2.8662[/C][C]0.00286[/C][/ROW]
[ROW][C]5[/C][C]-0.160174[/C][C]-1.2407[/C][C]0.109773[/C][/ROW]
[ROW][C]6[/C][C]-0.116476[/C][C]-0.9022[/C][C]0.185273[/C][/ROW]
[ROW][C]7[/C][C]-0.025439[/C][C]-0.1971[/C][C]0.422227[/C][/ROW]
[ROW][C]8[/C][C]-0.221641[/C][C]-1.7168[/C][C]0.045585[/C][/ROW]
[ROW][C]9[/C][C]0.223176[/C][C]1.7287[/C][C]0.044502[/C][/ROW]
[ROW][C]10[/C][C]0.075401[/C][C]0.5841[/C][C]0.280686[/C][/ROW]
[ROW][C]11[/C][C]0.07145[/C][C]0.5535[/C][C]0.291006[/C][/ROW]
[ROW][C]12[/C][C]0.348415[/C][C]2.6988[/C][C]0.004513[/C][/ROW]
[ROW][C]13[/C][C]-0.182277[/C][C]-1.4119[/C][C]0.081571[/C][/ROW]
[ROW][C]14[/C][C]0.158401[/C][C]1.227[/C][C]0.112313[/C][/ROW]
[ROW][C]15[/C][C]0.0756[/C][C]0.5856[/C][C]0.280172[/C][/ROW]
[ROW][C]16[/C][C]0.001403[/C][C]0.0109[/C][C]0.495682[/C][/ROW]
[ROW][C]17[/C][C]0.027394[/C][C]0.2122[/C][C]0.416336[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103325&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103325&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	0.541824	4.197	4.5e-05
2	0.038895	0.3013	0.382122
3	-0.217563	-1.6852	0.048569
4	-0.370029	-2.8662	0.00286
5	-0.160174	-1.2407	0.109773
6	-0.116476	-0.9022	0.185273
7	-0.025439	-0.1971	0.422227
8	-0.221641	-1.7168	0.045585
9	0.223176	1.7287	0.044502
10	0.075401	0.5841	0.280686
11	0.07145	0.5535	0.291006
12	0.348415	2.6988	0.004513
13	-0.182277	-1.4119	0.081571
14	0.158401	1.227	0.112313
15	0.0756	0.5856	0.280172
16	0.001403	0.0109	0.495682
17	0.027394	0.2122	0.416336

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code