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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2007 09:21:56 -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/04/t1196784598okme05bs5qz0rtz.htm/, Retrieved Wed, 01 May 2024 23:18:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2415, Retrieved Wed, 01 May 2024 23:18:43 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

177

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

-       [(Partial) Autocorrelation Function] [Autocorrelation_I...] [2007-12-04 16:21:56] [ca5e0f9f346e091f4d0fe7e17f7dba21] [Current]

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Dataseries X:

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Histogram

Boxplots

25,1
-32,7
-4,1
3,6
8,1
8,9
-4,5
2,5
5,5
-27,8
-16,7
31,8
-0,7
-2,5
8,6
-16,5
6,8
29
-13,9
-12
23,9
-44,1
3,6
30,2
-0,7
-8,9
5,9
-10,9
7,3
22,6
-17,8
-8,2
27,1
-43
0,5
30,1
-14,2
7,4
1,8
-10,1
9,9
23,2
-30,5
22,6
9,3
-46
-0,5
31,9
0,9
1
-4,3
-1,9
0,9
23,7
-19,1
6
17,3
-38,2
-9,3

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 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 & 4 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=2415&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]4 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=2415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2415&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	4 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	7.6811	0
1	-0.316212	-2.4289	0.990894
2	-0.390017	-2.9958	0.998001
3	0.432745	3.324	0.000764
4	-0.253966	-1.9508	0.972079
5	-0.175394	-1.3472	0.908471
6	0.44341	3.4059	0.000596
7	-0.235407	-1.8082	0.962163
8	-0.133828	-1.028	0.845916
9	0.406976	3.126	0.001374
10	-0.456368	-3.5054	0.999561
11	-0.145248	-1.1157	0.865457
12	0.665003	5.108	2e-06
13	-0.244375	-1.8771	0.967273
14	-0.226542	-1.7401	0.956473
15	0.326231	2.5058	0.007497
16	-0.265383	-2.0384	0.977002

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & -0.316212 & -2.4289 & 0.990894 \tabularnewline
2 & -0.390017 & -2.9958 & 0.998001 \tabularnewline
3 & 0.432745 & 3.324 & 0.000764 \tabularnewline
4 & -0.253966 & -1.9508 & 0.972079 \tabularnewline
5 & -0.175394 & -1.3472 & 0.908471 \tabularnewline
6 & 0.44341 & 3.4059 & 0.000596 \tabularnewline
7 & -0.235407 & -1.8082 & 0.962163 \tabularnewline
8 & -0.133828 & -1.028 & 0.845916 \tabularnewline
9 & 0.406976 & 3.126 & 0.001374 \tabularnewline
10 & -0.456368 & -3.5054 & 0.999561 \tabularnewline
11 & -0.145248 & -1.1157 & 0.865457 \tabularnewline
12 & 0.665003 & 5.108 & 2e-06 \tabularnewline
13 & -0.244375 & -1.8771 & 0.967273 \tabularnewline
14 & -0.226542 & -1.7401 & 0.956473 \tabularnewline
15 & 0.326231 & 2.5058 & 0.007497 \tabularnewline
16 & -0.265383 & -2.0384 & 0.977002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2415&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.316212[/C][C]-2.4289[/C][C]0.990894[/C][/ROW]
[ROW][C]2[/C][C]-0.390017[/C][C]-2.9958[/C][C]0.998001[/C][/ROW]
[ROW][C]3[/C][C]0.432745[/C][C]3.324[/C][C]0.000764[/C][/ROW]
[ROW][C]4[/C][C]-0.253966[/C][C]-1.9508[/C][C]0.972079[/C][/ROW]
[ROW][C]5[/C][C]-0.175394[/C][C]-1.3472[/C][C]0.908471[/C][/ROW]
[ROW][C]6[/C][C]0.44341[/C][C]3.4059[/C][C]0.000596[/C][/ROW]
[ROW][C]7[/C][C]-0.235407[/C][C]-1.8082[/C][C]0.962163[/C][/ROW]
[ROW][C]8[/C][C]-0.133828[/C][C]-1.028[/C][C]0.845916[/C][/ROW]
[ROW][C]9[/C][C]0.406976[/C][C]3.126[/C][C]0.001374[/C][/ROW]
[ROW][C]10[/C][C]-0.456368[/C][C]-3.5054[/C][C]0.999561[/C][/ROW]
[ROW][C]11[/C][C]-0.145248[/C][C]-1.1157[/C][C]0.865457[/C][/ROW]
[ROW][C]12[/C][C]0.665003[/C][C]5.108[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.244375[/C][C]-1.8771[/C][C]0.967273[/C][/ROW]
[ROW][C]14[/C][C]-0.226542[/C][C]-1.7401[/C][C]0.956473[/C][/ROW]
[ROW][C]15[/C][C]0.326231[/C][C]2.5058[/C][C]0.007497[/C][/ROW]
[ROW][C]16[/C][C]-0.265383[/C][C]-2.0384[/C][C]0.977002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2415&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	7.6811	0
1	-0.316212	-2.4289	0.990894
2	-0.390017	-2.9958	0.998001
3	0.432745	3.324	0.000764
4	-0.253966	-1.9508	0.972079
5	-0.175394	-1.3472	0.908471
6	0.44341	3.4059	0.000596
7	-0.235407	-1.8082	0.962163
8	-0.133828	-1.028	0.845916
9	0.406976	3.126	0.001374
10	-0.456368	-3.5054	0.999561
11	-0.145248	-1.1157	0.865457
12	0.665003	5.108	2e-06
13	-0.244375	-1.8771	0.967273
14	-0.226542	-1.7401	0.956473
15	0.326231	2.5058	0.007497
16	-0.265383	-2.0384	0.977002

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.316212	-2.4289	0.990894
1	-0.544446	-4.182	0.999951
2	0.11072	0.8505	0.199254
3	-0.359661	-2.7626	0.996183
4	-0.213142	-1.6372	0.946541
5	0.058594	0.4501	0.327154
6	-0.140497	-1.0792	0.857549
7	-0.027645	-0.2123	0.583715
8	0.170536	1.3099	0.097652
9	-0.38171	-2.932	0.997606
10	-0.347033	-2.6656	0.995051
11	0.17679	1.358	0.089825
12	0.165487	1.2711	0.104335
13	0.073606	0.5654	0.286979
14	-0.051316	-0.3942	0.652561
15	-0.020488	-0.1574	0.562256
16	0.087591	0.6728	0.251851

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.316212 & -2.4289 & 0.990894 \tabularnewline
1 & -0.544446 & -4.182 & 0.999951 \tabularnewline
2 & 0.11072 & 0.8505 & 0.199254 \tabularnewline
3 & -0.359661 & -2.7626 & 0.996183 \tabularnewline
4 & -0.213142 & -1.6372 & 0.946541 \tabularnewline
5 & 0.058594 & 0.4501 & 0.327154 \tabularnewline
6 & -0.140497 & -1.0792 & 0.857549 \tabularnewline
7 & -0.027645 & -0.2123 & 0.583715 \tabularnewline
8 & 0.170536 & 1.3099 & 0.097652 \tabularnewline
9 & -0.38171 & -2.932 & 0.997606 \tabularnewline
10 & -0.347033 & -2.6656 & 0.995051 \tabularnewline
11 & 0.17679 & 1.358 & 0.089825 \tabularnewline
12 & 0.165487 & 1.2711 & 0.104335 \tabularnewline
13 & 0.073606 & 0.5654 & 0.286979 \tabularnewline
14 & -0.051316 & -0.3942 & 0.652561 \tabularnewline
15 & -0.020488 & -0.1574 & 0.562256 \tabularnewline
16 & 0.087591 & 0.6728 & 0.251851 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2415&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]-0.316212[/C][C]-2.4289[/C][C]0.990894[/C][/ROW]
[ROW][C]1[/C][C]-0.544446[/C][C]-4.182[/C][C]0.999951[/C][/ROW]
[ROW][C]2[/C][C]0.11072[/C][C]0.8505[/C][C]0.199254[/C][/ROW]
[ROW][C]3[/C][C]-0.359661[/C][C]-2.7626[/C][C]0.996183[/C][/ROW]
[ROW][C]4[/C][C]-0.213142[/C][C]-1.6372[/C][C]0.946541[/C][/ROW]
[ROW][C]5[/C][C]0.058594[/C][C]0.4501[/C][C]0.327154[/C][/ROW]
[ROW][C]6[/C][C]-0.140497[/C][C]-1.0792[/C][C]0.857549[/C][/ROW]
[ROW][C]7[/C][C]-0.027645[/C][C]-0.2123[/C][C]0.583715[/C][/ROW]
[ROW][C]8[/C][C]0.170536[/C][C]1.3099[/C][C]0.097652[/C][/ROW]
[ROW][C]9[/C][C]-0.38171[/C][C]-2.932[/C][C]0.997606[/C][/ROW]
[ROW][C]10[/C][C]-0.347033[/C][C]-2.6656[/C][C]0.995051[/C][/ROW]
[ROW][C]11[/C][C]0.17679[/C][C]1.358[/C][C]0.089825[/C][/ROW]
[ROW][C]12[/C][C]0.165487[/C][C]1.2711[/C][C]0.104335[/C][/ROW]
[ROW][C]13[/C][C]0.073606[/C][C]0.5654[/C][C]0.286979[/C][/ROW]
[ROW][C]14[/C][C]-0.051316[/C][C]-0.3942[/C][C]0.652561[/C][/ROW]
[ROW][C]15[/C][C]-0.020488[/C][C]-0.1574[/C][C]0.562256[/C][/ROW]
[ROW][C]16[/C][C]0.087591[/C][C]0.6728[/C][C]0.251851[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2415&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2415&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	-0.316212	-2.4289	0.990894
1	-0.544446	-4.182	0.999951
2	0.11072	0.8505	0.199254
3	-0.359661	-2.7626	0.996183
4	-0.213142	-1.6372	0.946541
5	0.058594	0.4501	0.327154
6	-0.140497	-1.0792	0.857549
7	-0.027645	-0.2123	0.583715
8	0.170536	1.3099	0.097652
9	-0.38171	-2.932	0.997606
10	-0.347033	-2.6656	0.995051
11	0.17679	1.358	0.089825
12	0.165487	1.2711	0.104335
13	0.073606	0.5654	0.286979
14	-0.051316	-0.3942	0.652561
15	-0.020488	-0.1574	0.562256
16	0.087591	0.6728	0.251851

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 ;

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