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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 26 Nov 2010 17:48:27 +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/26/t1290793649orld5mq3665mupv.htm/, Retrieved Sat, 04 May 2024 00:27:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102123, Retrieved Sat, 04 May 2024 00:27:07 +0000

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No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

119

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

-       [(Partial) Autocorrelation Function] [] [2010-11-26 17:48:27] [465c6c9df074117d1de4b3f3c25f0c87] [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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102123&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102123&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102123&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.004857	0.053	0.478919
2	0.038748	0.4227	0.336641
3	-0.025782	-0.2813	0.389503
4	-0.104057	-1.1351	0.129302
5	0.039723	0.4333	0.33278
6	-0.039873	-0.435	0.332188
7	0.046565	0.508	0.306208
8	-0.051746	-0.5645	0.286743
9	-0.024655	-0.269	0.394214
10	0.065192	0.7112	0.239189
11	-0.142182	-1.551	0.061776
12	0.462541	5.0457	1e-06
13	-0.158412	-1.7281	0.043284
14	0.070231	0.7661	0.222557
15	-0.014525	-0.1584	0.437187
16	-0.101196	-1.1039	0.135927
17	0.02495	0.2722	0.392982
18	0.017255	0.1882	0.425507
19	0.067039	0.7313	0.233014
20	-0.088036	-0.9604	0.16941

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.004857 & 0.053 & 0.478919 \tabularnewline
2 & 0.038748 & 0.4227 & 0.336641 \tabularnewline
3 & -0.025782 & -0.2813 & 0.389503 \tabularnewline
4 & -0.104057 & -1.1351 & 0.129302 \tabularnewline
5 & 0.039723 & 0.4333 & 0.33278 \tabularnewline
6 & -0.039873 & -0.435 & 0.332188 \tabularnewline
7 & 0.046565 & 0.508 & 0.306208 \tabularnewline
8 & -0.051746 & -0.5645 & 0.286743 \tabularnewline
9 & -0.024655 & -0.269 & 0.394214 \tabularnewline
10 & 0.065192 & 0.7112 & 0.239189 \tabularnewline
11 & -0.142182 & -1.551 & 0.061776 \tabularnewline
12 & 0.462541 & 5.0457 & 1e-06 \tabularnewline
13 & -0.158412 & -1.7281 & 0.043284 \tabularnewline
14 & 0.070231 & 0.7661 & 0.222557 \tabularnewline
15 & -0.014525 & -0.1584 & 0.437187 \tabularnewline
16 & -0.101196 & -1.1039 & 0.135927 \tabularnewline
17 & 0.02495 & 0.2722 & 0.392982 \tabularnewline
18 & 0.017255 & 0.1882 & 0.425507 \tabularnewline
19 & 0.067039 & 0.7313 & 0.233014 \tabularnewline
20 & -0.088036 & -0.9604 & 0.16941 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102123&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]0.004857[/C][C]0.053[/C][C]0.478919[/C][/ROW]
[ROW][C]2[/C][C]0.038748[/C][C]0.4227[/C][C]0.336641[/C][/ROW]
[ROW][C]3[/C][C]-0.025782[/C][C]-0.2813[/C][C]0.389503[/C][/ROW]
[ROW][C]4[/C][C]-0.104057[/C][C]-1.1351[/C][C]0.129302[/C][/ROW]
[ROW][C]5[/C][C]0.039723[/C][C]0.4333[/C][C]0.33278[/C][/ROW]
[ROW][C]6[/C][C]-0.039873[/C][C]-0.435[/C][C]0.332188[/C][/ROW]
[ROW][C]7[/C][C]0.046565[/C][C]0.508[/C][C]0.306208[/C][/ROW]
[ROW][C]8[/C][C]-0.051746[/C][C]-0.5645[/C][C]0.286743[/C][/ROW]
[ROW][C]9[/C][C]-0.024655[/C][C]-0.269[/C][C]0.394214[/C][/ROW]
[ROW][C]10[/C][C]0.065192[/C][C]0.7112[/C][C]0.239189[/C][/ROW]
[ROW][C]11[/C][C]-0.142182[/C][C]-1.551[/C][C]0.061776[/C][/ROW]
[ROW][C]12[/C][C]0.462541[/C][C]5.0457[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.158412[/C][C]-1.7281[/C][C]0.043284[/C][/ROW]
[ROW][C]14[/C][C]0.070231[/C][C]0.7661[/C][C]0.222557[/C][/ROW]
[ROW][C]15[/C][C]-0.014525[/C][C]-0.1584[/C][C]0.437187[/C][/ROW]
[ROW][C]16[/C][C]-0.101196[/C][C]-1.1039[/C][C]0.135927[/C][/ROW]
[ROW][C]17[/C][C]0.02495[/C][C]0.2722[/C][C]0.392982[/C][/ROW]
[ROW][C]18[/C][C]0.017255[/C][C]0.1882[/C][C]0.425507[/C][/ROW]
[ROW][C]19[/C][C]0.067039[/C][C]0.7313[/C][C]0.233014[/C][/ROW]
[ROW][C]20[/C][C]-0.088036[/C][C]-0.9604[/C][C]0.16941[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102123&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102123&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	0.004857	0.053	0.478919
2	0.038748	0.4227	0.336641
3	-0.025782	-0.2813	0.389503
4	-0.104057	-1.1351	0.129302
5	0.039723	0.4333	0.33278
6	-0.039873	-0.435	0.332188
7	0.046565	0.508	0.306208
8	-0.051746	-0.5645	0.286743
9	-0.024655	-0.269	0.394214
10	0.065192	0.7112	0.239189
11	-0.142182	-1.551	0.061776
12	0.462541	5.0457	1e-06
13	-0.158412	-1.7281	0.043284
14	0.070231	0.7661	0.222557
15	-0.014525	-0.1584	0.437187
16	-0.101196	-1.1039	0.135927
17	0.02495	0.2722	0.392982
18	0.017255	0.1882	0.425507
19	0.067039	0.7313	0.233014
20	-0.088036	-0.9604	0.16941

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.004857	0.053	0.478919
2	0.038726	0.4224	0.336731
3	-0.026191	-0.2857	0.387798
4	-0.105521	-1.1511	0.125999
5	0.043214	0.4714	0.319107
6	-0.032909	-0.359	0.360118
7	0.038777	0.423	0.336527
8	-0.059302	-0.6469	0.25947
9	-0.020522	-0.2239	0.41162
10	0.064168	0.7	0.242649
11	-0.136157	-1.4853	0.070055
12	0.464908	5.0715	1e-06
13	-0.252264	-2.7519	0.003427
14	0.143707	1.5677	0.059808
15	-0.081375	-0.8877	0.188248
16	0.013064	0.1425	0.44346
17	-0.050714	-0.5532	0.290574
18	0.115271	1.2575	0.105525
19	-0.022944	-0.2503	0.401396
20	-0.083741	-0.9135	0.181411

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.004857 & 0.053 & 0.478919 \tabularnewline
2 & 0.038726 & 0.4224 & 0.336731 \tabularnewline
3 & -0.026191 & -0.2857 & 0.387798 \tabularnewline
4 & -0.105521 & -1.1511 & 0.125999 \tabularnewline
5 & 0.043214 & 0.4714 & 0.319107 \tabularnewline
6 & -0.032909 & -0.359 & 0.360118 \tabularnewline
7 & 0.038777 & 0.423 & 0.336527 \tabularnewline
8 & -0.059302 & -0.6469 & 0.25947 \tabularnewline
9 & -0.020522 & -0.2239 & 0.41162 \tabularnewline
10 & 0.064168 & 0.7 & 0.242649 \tabularnewline
11 & -0.136157 & -1.4853 & 0.070055 \tabularnewline
12 & 0.464908 & 5.0715 & 1e-06 \tabularnewline
13 & -0.252264 & -2.7519 & 0.003427 \tabularnewline
14 & 0.143707 & 1.5677 & 0.059808 \tabularnewline
15 & -0.081375 & -0.8877 & 0.188248 \tabularnewline
16 & 0.013064 & 0.1425 & 0.44346 \tabularnewline
17 & -0.050714 & -0.5532 & 0.290574 \tabularnewline
18 & 0.115271 & 1.2575 & 0.105525 \tabularnewline
19 & -0.022944 & -0.2503 & 0.401396 \tabularnewline
20 & -0.083741 & -0.9135 & 0.181411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102123&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]0.004857[/C][C]0.053[/C][C]0.478919[/C][/ROW]
[ROW][C]2[/C][C]0.038726[/C][C]0.4224[/C][C]0.336731[/C][/ROW]
[ROW][C]3[/C][C]-0.026191[/C][C]-0.2857[/C][C]0.387798[/C][/ROW]
[ROW][C]4[/C][C]-0.105521[/C][C]-1.1511[/C][C]0.125999[/C][/ROW]
[ROW][C]5[/C][C]0.043214[/C][C]0.4714[/C][C]0.319107[/C][/ROW]
[ROW][C]6[/C][C]-0.032909[/C][C]-0.359[/C][C]0.360118[/C][/ROW]
[ROW][C]7[/C][C]0.038777[/C][C]0.423[/C][C]0.336527[/C][/ROW]
[ROW][C]8[/C][C]-0.059302[/C][C]-0.6469[/C][C]0.25947[/C][/ROW]
[ROW][C]9[/C][C]-0.020522[/C][C]-0.2239[/C][C]0.41162[/C][/ROW]
[ROW][C]10[/C][C]0.064168[/C][C]0.7[/C][C]0.242649[/C][/ROW]
[ROW][C]11[/C][C]-0.136157[/C][C]-1.4853[/C][C]0.070055[/C][/ROW]
[ROW][C]12[/C][C]0.464908[/C][C]5.0715[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.252264[/C][C]-2.7519[/C][C]0.003427[/C][/ROW]
[ROW][C]14[/C][C]0.143707[/C][C]1.5677[/C][C]0.059808[/C][/ROW]
[ROW][C]15[/C][C]-0.081375[/C][C]-0.8877[/C][C]0.188248[/C][/ROW]
[ROW][C]16[/C][C]0.013064[/C][C]0.1425[/C][C]0.44346[/C][/ROW]
[ROW][C]17[/C][C]-0.050714[/C][C]-0.5532[/C][C]0.290574[/C][/ROW]
[ROW][C]18[/C][C]0.115271[/C][C]1.2575[/C][C]0.105525[/C][/ROW]
[ROW][C]19[/C][C]-0.022944[/C][C]-0.2503[/C][C]0.401396[/C][/ROW]
[ROW][C]20[/C][C]-0.083741[/C][C]-0.9135[/C][C]0.181411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102123&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102123&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	0.004857	0.053	0.478919
2	0.038726	0.4224	0.336731
3	-0.026191	-0.2857	0.387798
4	-0.105521	-1.1511	0.125999
5	0.043214	0.4714	0.319107
6	-0.032909	-0.359	0.360118
7	0.038777	0.423	0.336527
8	-0.059302	-0.6469	0.25947
9	-0.020522	-0.2239	0.41162
10	0.064168	0.7	0.242649
11	-0.136157	-1.4853	0.070055
12	0.464908	5.0715	1e-06
13	-0.252264	-2.7519	0.003427
14	0.143707	1.5677	0.059808
15	-0.081375	-0.8877	0.188248
16	0.013064	0.1425	0.44346
17	-0.050714	-0.5532	0.290574
18	0.115271	1.2575	0.105525
19	-0.022944	-0.2503	0.401396
20	-0.083741	-0.9135	0.181411

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