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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 01 Dec 2007 06:14:05 -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/2007/Dec/01/t119651419234z44bw98frca86.htm/, Retrieved Sun, 19 May 2024 20:22:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2249, Retrieved Sun, 19 May 2024 20:22:34 +0000

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No (this computation is public)

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Estimated Impact

202

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-       [(Partial) Autocorrelation Function] [autocorrelatie au...] [2007-12-01 13:14:05] [bd02e85be52eb1cb060a2c60779eb820] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2249&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2249&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2249&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	10.3923	0
1	0.4043	4.2016	2.7e-05
2	0.359399	3.735	0.000151
3	0.239721	2.4913	0.007125
4	0.150185	1.5608	0.060752
5	0.125772	1.3071	0.096984
6	0.037442	0.3891	0.34898
7	0.062054	0.6449	0.260184
8	0.029426	0.3058	0.380172
9	-0.083378	-0.8665	0.805928
10	-0.055488	-0.5766	0.717311
11	-0.129188	-1.3426	0.908885
12	-0.105735	-1.0988	0.862857
13	-0.025283	-0.2627	0.603377
14	0.016499	0.1715	0.432088
15	0.090105	0.9364	0.175579
16	0.042732	0.4441	0.328936
17	0.036599	0.3803	0.352217
18	-0.045307	-0.4708	0.680648
19	-0.015526	-0.1614	0.563942

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 10.3923 & 0 \tabularnewline
1 & 0.4043 & 4.2016 & 2.7e-05 \tabularnewline
2 & 0.359399 & 3.735 & 0.000151 \tabularnewline
3 & 0.239721 & 2.4913 & 0.007125 \tabularnewline
4 & 0.150185 & 1.5608 & 0.060752 \tabularnewline
5 & 0.125772 & 1.3071 & 0.096984 \tabularnewline
6 & 0.037442 & 0.3891 & 0.34898 \tabularnewline
7 & 0.062054 & 0.6449 & 0.260184 \tabularnewline
8 & 0.029426 & 0.3058 & 0.380172 \tabularnewline
9 & -0.083378 & -0.8665 & 0.805928 \tabularnewline
10 & -0.055488 & -0.5766 & 0.717311 \tabularnewline
11 & -0.129188 & -1.3426 & 0.908885 \tabularnewline
12 & -0.105735 & -1.0988 & 0.862857 \tabularnewline
13 & -0.025283 & -0.2627 & 0.603377 \tabularnewline
14 & 0.016499 & 0.1715 & 0.432088 \tabularnewline
15 & 0.090105 & 0.9364 & 0.175579 \tabularnewline
16 & 0.042732 & 0.4441 & 0.328936 \tabularnewline
17 & 0.036599 & 0.3803 & 0.352217 \tabularnewline
18 & -0.045307 & -0.4708 & 0.680648 \tabularnewline
19 & -0.015526 & -0.1614 & 0.563942 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2249&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]0[/C][C]1[/C][C]10.3923[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.4043[/C][C]4.2016[/C][C]2.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.359399[/C][C]3.735[/C][C]0.000151[/C][/ROW]
[ROW][C]3[/C][C]0.239721[/C][C]2.4913[/C][C]0.007125[/C][/ROW]
[ROW][C]4[/C][C]0.150185[/C][C]1.5608[/C][C]0.060752[/C][/ROW]
[ROW][C]5[/C][C]0.125772[/C][C]1.3071[/C][C]0.096984[/C][/ROW]
[ROW][C]6[/C][C]0.037442[/C][C]0.3891[/C][C]0.34898[/C][/ROW]
[ROW][C]7[/C][C]0.062054[/C][C]0.6449[/C][C]0.260184[/C][/ROW]
[ROW][C]8[/C][C]0.029426[/C][C]0.3058[/C][C]0.380172[/C][/ROW]
[ROW][C]9[/C][C]-0.083378[/C][C]-0.8665[/C][C]0.805928[/C][/ROW]
[ROW][C]10[/C][C]-0.055488[/C][C]-0.5766[/C][C]0.717311[/C][/ROW]
[ROW][C]11[/C][C]-0.129188[/C][C]-1.3426[/C][C]0.908885[/C][/ROW]
[ROW][C]12[/C][C]-0.105735[/C][C]-1.0988[/C][C]0.862857[/C][/ROW]
[ROW][C]13[/C][C]-0.025283[/C][C]-0.2627[/C][C]0.603377[/C][/ROW]
[ROW][C]14[/C][C]0.016499[/C][C]0.1715[/C][C]0.432088[/C][/ROW]
[ROW][C]15[/C][C]0.090105[/C][C]0.9364[/C][C]0.175579[/C][/ROW]
[ROW][C]16[/C][C]0.042732[/C][C]0.4441[/C][C]0.328936[/C][/ROW]
[ROW][C]17[/C][C]0.036599[/C][C]0.3803[/C][C]0.352217[/C][/ROW]
[ROW][C]18[/C][C]-0.045307[/C][C]-0.4708[/C][C]0.680648[/C][/ROW]
[ROW][C]19[/C][C]-0.015526[/C][C]-0.1614[/C][C]0.563942[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2249&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2249&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
0	1	10.3923	0
1	0.4043	4.2016	2.7e-05
2	0.359399	3.735	0.000151
3	0.239721	2.4913	0.007125
4	0.150185	1.5608	0.060752
5	0.125772	1.3071	0.096984
6	0.037442	0.3891	0.34898
7	0.062054	0.6449	0.260184
8	0.029426	0.3058	0.380172
9	-0.083378	-0.8665	0.805928
10	-0.055488	-0.5766	0.717311
11	-0.129188	-1.3426	0.908885
12	-0.105735	-1.0988	0.862857
13	-0.025283	-0.2627	0.603377
14	0.016499	0.1715	0.432088
15	0.090105	0.9364	0.175579
16	0.042732	0.4441	0.328936
17	0.036599	0.3803	0.352217
18	-0.045307	-0.4708	0.680648
19	-0.015526	-0.1614	0.563942

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.4043	4.2016	2.7e-05
1	0.234228	2.4342	0.008283
2	0.042689	0.4436	0.329095
3	-0.023222	-0.2413	0.595121
4	0.022772	0.2366	0.406689
5	-0.054912	-0.5707	0.715295
6	0.03551	0.369	0.356415
7	0.001114	0.0116	0.495394
8	-0.136883	-1.4225	0.921122
9	-0.011733	-0.1219	0.548409
10	-0.071864	-0.7468	0.771607
11	-0.015746	-0.1636	0.56484
12	0.098151	1.02	0.155
13	0.081026	0.842	0.200811
14	0.079413	0.8253	0.205515
15	-0.024458	-0.2542	0.60008
16	-0.032558	-0.3384	0.632123
17	-0.118288	-1.2293	0.889182
18	0.018473	0.192	0.424059
19	0.098524	1.0239	0.154087

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.4043 & 4.2016 & 2.7e-05 \tabularnewline
1 & 0.234228 & 2.4342 & 0.008283 \tabularnewline
2 & 0.042689 & 0.4436 & 0.329095 \tabularnewline
3 & -0.023222 & -0.2413 & 0.595121 \tabularnewline
4 & 0.022772 & 0.2366 & 0.406689 \tabularnewline
5 & -0.054912 & -0.5707 & 0.715295 \tabularnewline
6 & 0.03551 & 0.369 & 0.356415 \tabularnewline
7 & 0.001114 & 0.0116 & 0.495394 \tabularnewline
8 & -0.136883 & -1.4225 & 0.921122 \tabularnewline
9 & -0.011733 & -0.1219 & 0.548409 \tabularnewline
10 & -0.071864 & -0.7468 & 0.771607 \tabularnewline
11 & -0.015746 & -0.1636 & 0.56484 \tabularnewline
12 & 0.098151 & 1.02 & 0.155 \tabularnewline
13 & 0.081026 & 0.842 & 0.200811 \tabularnewline
14 & 0.079413 & 0.8253 & 0.205515 \tabularnewline
15 & -0.024458 & -0.2542 & 0.60008 \tabularnewline
16 & -0.032558 & -0.3384 & 0.632123 \tabularnewline
17 & -0.118288 & -1.2293 & 0.889182 \tabularnewline
18 & 0.018473 & 0.192 & 0.424059 \tabularnewline
19 & 0.098524 & 1.0239 & 0.154087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2249&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]0[/C][C]0.4043[/C][C]4.2016[/C][C]2.7e-05[/C][/ROW]
[ROW][C]1[/C][C]0.234228[/C][C]2.4342[/C][C]0.008283[/C][/ROW]
[ROW][C]2[/C][C]0.042689[/C][C]0.4436[/C][C]0.329095[/C][/ROW]
[ROW][C]3[/C][C]-0.023222[/C][C]-0.2413[/C][C]0.595121[/C][/ROW]
[ROW][C]4[/C][C]0.022772[/C][C]0.2366[/C][C]0.406689[/C][/ROW]
[ROW][C]5[/C][C]-0.054912[/C][C]-0.5707[/C][C]0.715295[/C][/ROW]
[ROW][C]6[/C][C]0.03551[/C][C]0.369[/C][C]0.356415[/C][/ROW]
[ROW][C]7[/C][C]0.001114[/C][C]0.0116[/C][C]0.495394[/C][/ROW]
[ROW][C]8[/C][C]-0.136883[/C][C]-1.4225[/C][C]0.921122[/C][/ROW]
[ROW][C]9[/C][C]-0.011733[/C][C]-0.1219[/C][C]0.548409[/C][/ROW]
[ROW][C]10[/C][C]-0.071864[/C][C]-0.7468[/C][C]0.771607[/C][/ROW]
[ROW][C]11[/C][C]-0.015746[/C][C]-0.1636[/C][C]0.56484[/C][/ROW]
[ROW][C]12[/C][C]0.098151[/C][C]1.02[/C][C]0.155[/C][/ROW]
[ROW][C]13[/C][C]0.081026[/C][C]0.842[/C][C]0.200811[/C][/ROW]
[ROW][C]14[/C][C]0.079413[/C][C]0.8253[/C][C]0.205515[/C][/ROW]
[ROW][C]15[/C][C]-0.024458[/C][C]-0.2542[/C][C]0.60008[/C][/ROW]
[ROW][C]16[/C][C]-0.032558[/C][C]-0.3384[/C][C]0.632123[/C][/ROW]
[ROW][C]17[/C][C]-0.118288[/C][C]-1.2293[/C][C]0.889182[/C][/ROW]
[ROW][C]18[/C][C]0.018473[/C][C]0.192[/C][C]0.424059[/C][/ROW]
[ROW][C]19[/C][C]0.098524[/C][C]1.0239[/C][C]0.154087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2249&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2249&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
0	0.4043	4.2016	2.7e-05
1	0.234228	2.4342	0.008283
2	0.042689	0.4436	0.329095
3	-0.023222	-0.2413	0.595121
4	0.022772	0.2366	0.406689
5	-0.054912	-0.5707	0.715295
6	0.03551	0.369	0.356415
7	0.001114	0.0116	0.495394
8	-0.136883	-1.4225	0.921122
9	-0.011733	-0.1219	0.548409
10	-0.071864	-0.7468	0.771607
11	-0.015746	-0.1636	0.56484
12	0.098151	1.02	0.155
13	0.081026	0.842	0.200811
14	0.079413	0.8253	0.205515
15	-0.024458	-0.2542	0.60008
16	-0.032558	-0.3384	0.632123
17	-0.118288	-1.2293	0.889182
18	0.018473	0.192	0.424059
19	0.098524	1.0239	0.154087

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(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