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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 24 Dec 2014 10:41:13 +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/2014/Dec/24/t1419417716j18u11bo6z0uuk6.htm/, Retrieved Thu, 31 Oct 2024 22:44:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271432, Retrieved Thu, 31 Oct 2024 22:44:58 +0000

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IsPrivate?

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User-defined keywords

Estimated Impact

175

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

-       [(Partial) Autocorrelation Function] [] [2014-12-24 10:41:13] [517bf63cbd197750110a40d4d2cd39d6] [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	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271432&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271432&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.507216	-4.1826	4.2e-05
2	0.018437	0.152	0.439805
3	0.062576	0.516	0.30376
4	-0.076227	-0.6286	0.265863
5	0.110622	0.9122	0.18244
6	-0.183901	-1.5165	0.067016
7	0.132462	1.0923	0.139276
8	-0.075103	-0.6193	0.268888
9	0.033609	0.2771	0.391255
10	0.106232	0.876	0.192054
11	-0.443776	-3.6595	0.000247
12	0.686335	5.6597	0
13	-0.420383	-3.4666	0.000459
14	0.06289	0.5186	0.302861
15	0.037526	0.3095	0.378963
16	-0.036337	-0.2996	0.382683
17	0.054729	0.4513	0.326602
18	-0.174105	-1.4357	0.077835
19	0.159539	1.3156	0.096365
20	-0.015941	-0.1315	0.447902
21	-0.027689	-0.2283	0.410038
22	0.076052	0.6271	0.266334
23	-0.320211	-2.6405	0.005129
24	0.531239	4.3807	2.1e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.507216 & -4.1826 & 4.2e-05 \tabularnewline
2 & 0.018437 & 0.152 & 0.439805 \tabularnewline
3 & 0.062576 & 0.516 & 0.30376 \tabularnewline
4 & -0.076227 & -0.6286 & 0.265863 \tabularnewline
5 & 0.110622 & 0.9122 & 0.18244 \tabularnewline
6 & -0.183901 & -1.5165 & 0.067016 \tabularnewline
7 & 0.132462 & 1.0923 & 0.139276 \tabularnewline
8 & -0.075103 & -0.6193 & 0.268888 \tabularnewline
9 & 0.033609 & 0.2771 & 0.391255 \tabularnewline
10 & 0.106232 & 0.876 & 0.192054 \tabularnewline
11 & -0.443776 & -3.6595 & 0.000247 \tabularnewline
12 & 0.686335 & 5.6597 & 0 \tabularnewline
13 & -0.420383 & -3.4666 & 0.000459 \tabularnewline
14 & 0.06289 & 0.5186 & 0.302861 \tabularnewline
15 & 0.037526 & 0.3095 & 0.378963 \tabularnewline
16 & -0.036337 & -0.2996 & 0.382683 \tabularnewline
17 & 0.054729 & 0.4513 & 0.326602 \tabularnewline
18 & -0.174105 & -1.4357 & 0.077835 \tabularnewline
19 & 0.159539 & 1.3156 & 0.096365 \tabularnewline
20 & -0.015941 & -0.1315 & 0.447902 \tabularnewline
21 & -0.027689 & -0.2283 & 0.410038 \tabularnewline
22 & 0.076052 & 0.6271 & 0.266334 \tabularnewline
23 & -0.320211 & -2.6405 & 0.005129 \tabularnewline
24 & 0.531239 & 4.3807 & 2.1e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271432&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]-0.507216[/C][C]-4.1826[/C][C]4.2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.018437[/C][C]0.152[/C][C]0.439805[/C][/ROW]
[ROW][C]3[/C][C]0.062576[/C][C]0.516[/C][C]0.30376[/C][/ROW]
[ROW][C]4[/C][C]-0.076227[/C][C]-0.6286[/C][C]0.265863[/C][/ROW]
[ROW][C]5[/C][C]0.110622[/C][C]0.9122[/C][C]0.18244[/C][/ROW]
[ROW][C]6[/C][C]-0.183901[/C][C]-1.5165[/C][C]0.067016[/C][/ROW]
[ROW][C]7[/C][C]0.132462[/C][C]1.0923[/C][C]0.139276[/C][/ROW]
[ROW][C]8[/C][C]-0.075103[/C][C]-0.6193[/C][C]0.268888[/C][/ROW]
[ROW][C]9[/C][C]0.033609[/C][C]0.2771[/C][C]0.391255[/C][/ROW]
[ROW][C]10[/C][C]0.106232[/C][C]0.876[/C][C]0.192054[/C][/ROW]
[ROW][C]11[/C][C]-0.443776[/C][C]-3.6595[/C][C]0.000247[/C][/ROW]
[ROW][C]12[/C][C]0.686335[/C][C]5.6597[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.420383[/C][C]-3.4666[/C][C]0.000459[/C][/ROW]
[ROW][C]14[/C][C]0.06289[/C][C]0.5186[/C][C]0.302861[/C][/ROW]
[ROW][C]15[/C][C]0.037526[/C][C]0.3095[/C][C]0.378963[/C][/ROW]
[ROW][C]16[/C][C]-0.036337[/C][C]-0.2996[/C][C]0.382683[/C][/ROW]
[ROW][C]17[/C][C]0.054729[/C][C]0.4513[/C][C]0.326602[/C][/ROW]
[ROW][C]18[/C][C]-0.174105[/C][C]-1.4357[/C][C]0.077835[/C][/ROW]
[ROW][C]19[/C][C]0.159539[/C][C]1.3156[/C][C]0.096365[/C][/ROW]
[ROW][C]20[/C][C]-0.015941[/C][C]-0.1315[/C][C]0.447902[/C][/ROW]
[ROW][C]21[/C][C]-0.027689[/C][C]-0.2283[/C][C]0.410038[/C][/ROW]
[ROW][C]22[/C][C]0.076052[/C][C]0.6271[/C][C]0.266334[/C][/ROW]
[ROW][C]23[/C][C]-0.320211[/C][C]-2.6405[/C][C]0.005129[/C][/ROW]
[ROW][C]24[/C][C]0.531239[/C][C]4.3807[/C][C]2.1e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271432&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	-0.507216	-4.1826	4.2e-05
2	0.018437	0.152	0.439805
3	0.062576	0.516	0.30376
4	-0.076227	-0.6286	0.265863
5	0.110622	0.9122	0.18244
6	-0.183901	-1.5165	0.067016
7	0.132462	1.0923	0.139276
8	-0.075103	-0.6193	0.268888
9	0.033609	0.2771	0.391255
10	0.106232	0.876	0.192054
11	-0.443776	-3.6595	0.000247
12	0.686335	5.6597	0
13	-0.420383	-3.4666	0.000459
14	0.06289	0.5186	0.302861
15	0.037526	0.3095	0.378963
16	-0.036337	-0.2996	0.382683
17	0.054729	0.4513	0.326602
18	-0.174105	-1.4357	0.077835
19	0.159539	1.3156	0.096365
20	-0.015941	-0.1315	0.447902
21	-0.027689	-0.2283	0.410038
22	0.076052	0.6271	0.266334
23	-0.320211	-2.6405	0.005129
24	0.531239	4.3807	2.1e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.507216	-4.1826	4.2e-05
2	-0.321558	-2.6516	0.004979
3	-0.132393	-1.0917	0.1394
4	-0.139402	-1.1495	0.127181
5	0.027581	0.2274	0.410384
6	-0.169545	-1.3981	0.083313
7	-0.062013	-0.5114	0.305374
8	-0.118985	-0.9812	0.164991
9	-0.052888	-0.4361	0.332063
10	0.115258	0.9504	0.172626
11	-0.476299	-3.9277	0.000102
12	0.395457	3.261	0.000868
13	-0.046653	-0.3847	0.350827
14	0.063338	0.5223	0.301581
15	-0.063479	-0.5235	0.301178
16	0.061423	0.5065	0.30707
17	-0.106754	-0.8803	0.190894
18	-0.090095	-0.7429	0.230038
19	-0.077406	-0.6383	0.262709
20	0.104028	0.8578	0.196998
21	0.014125	0.1165	0.453808
22	-0.112467	-0.9274	0.178494
23	-0.039628	-0.3268	0.372419
24	0.051544	0.425	0.336075

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.507216 & -4.1826 & 4.2e-05 \tabularnewline
2 & -0.321558 & -2.6516 & 0.004979 \tabularnewline
3 & -0.132393 & -1.0917 & 0.1394 \tabularnewline
4 & -0.139402 & -1.1495 & 0.127181 \tabularnewline
5 & 0.027581 & 0.2274 & 0.410384 \tabularnewline
6 & -0.169545 & -1.3981 & 0.083313 \tabularnewline
7 & -0.062013 & -0.5114 & 0.305374 \tabularnewline
8 & -0.118985 & -0.9812 & 0.164991 \tabularnewline
9 & -0.052888 & -0.4361 & 0.332063 \tabularnewline
10 & 0.115258 & 0.9504 & 0.172626 \tabularnewline
11 & -0.476299 & -3.9277 & 0.000102 \tabularnewline
12 & 0.395457 & 3.261 & 0.000868 \tabularnewline
13 & -0.046653 & -0.3847 & 0.350827 \tabularnewline
14 & 0.063338 & 0.5223 & 0.301581 \tabularnewline
15 & -0.063479 & -0.5235 & 0.301178 \tabularnewline
16 & 0.061423 & 0.5065 & 0.30707 \tabularnewline
17 & -0.106754 & -0.8803 & 0.190894 \tabularnewline
18 & -0.090095 & -0.7429 & 0.230038 \tabularnewline
19 & -0.077406 & -0.6383 & 0.262709 \tabularnewline
20 & 0.104028 & 0.8578 & 0.196998 \tabularnewline
21 & 0.014125 & 0.1165 & 0.453808 \tabularnewline
22 & -0.112467 & -0.9274 & 0.178494 \tabularnewline
23 & -0.039628 & -0.3268 & 0.372419 \tabularnewline
24 & 0.051544 & 0.425 & 0.336075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271432&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]-0.507216[/C][C]-4.1826[/C][C]4.2e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.321558[/C][C]-2.6516[/C][C]0.004979[/C][/ROW]
[ROW][C]3[/C][C]-0.132393[/C][C]-1.0917[/C][C]0.1394[/C][/ROW]
[ROW][C]4[/C][C]-0.139402[/C][C]-1.1495[/C][C]0.127181[/C][/ROW]
[ROW][C]5[/C][C]0.027581[/C][C]0.2274[/C][C]0.410384[/C][/ROW]
[ROW][C]6[/C][C]-0.169545[/C][C]-1.3981[/C][C]0.083313[/C][/ROW]
[ROW][C]7[/C][C]-0.062013[/C][C]-0.5114[/C][C]0.305374[/C][/ROW]
[ROW][C]8[/C][C]-0.118985[/C][C]-0.9812[/C][C]0.164991[/C][/ROW]
[ROW][C]9[/C][C]-0.052888[/C][C]-0.4361[/C][C]0.332063[/C][/ROW]
[ROW][C]10[/C][C]0.115258[/C][C]0.9504[/C][C]0.172626[/C][/ROW]
[ROW][C]11[/C][C]-0.476299[/C][C]-3.9277[/C][C]0.000102[/C][/ROW]
[ROW][C]12[/C][C]0.395457[/C][C]3.261[/C][C]0.000868[/C][/ROW]
[ROW][C]13[/C][C]-0.046653[/C][C]-0.3847[/C][C]0.350827[/C][/ROW]
[ROW][C]14[/C][C]0.063338[/C][C]0.5223[/C][C]0.301581[/C][/ROW]
[ROW][C]15[/C][C]-0.063479[/C][C]-0.5235[/C][C]0.301178[/C][/ROW]
[ROW][C]16[/C][C]0.061423[/C][C]0.5065[/C][C]0.30707[/C][/ROW]
[ROW][C]17[/C][C]-0.106754[/C][C]-0.8803[/C][C]0.190894[/C][/ROW]
[ROW][C]18[/C][C]-0.090095[/C][C]-0.7429[/C][C]0.230038[/C][/ROW]
[ROW][C]19[/C][C]-0.077406[/C][C]-0.6383[/C][C]0.262709[/C][/ROW]
[ROW][C]20[/C][C]0.104028[/C][C]0.8578[/C][C]0.196998[/C][/ROW]
[ROW][C]21[/C][C]0.014125[/C][C]0.1165[/C][C]0.453808[/C][/ROW]
[ROW][C]22[/C][C]-0.112467[/C][C]-0.9274[/C][C]0.178494[/C][/ROW]
[ROW][C]23[/C][C]-0.039628[/C][C]-0.3268[/C][C]0.372419[/C][/ROW]
[ROW][C]24[/C][C]0.051544[/C][C]0.425[/C][C]0.336075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271432&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271432&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	-0.507216	-4.1826	4.2e-05
2	-0.321558	-2.6516	0.004979
3	-0.132393	-1.0917	0.1394
4	-0.139402	-1.1495	0.127181
5	0.027581	0.2274	0.410384
6	-0.169545	-1.3981	0.083313
7	-0.062013	-0.5114	0.305374
8	-0.118985	-0.9812	0.164991
9	-0.052888	-0.4361	0.332063
10	0.115258	0.9504	0.172626
11	-0.476299	-3.9277	0.000102
12	0.395457	3.261	0.000868
13	-0.046653	-0.3847	0.350827
14	0.063338	0.5223	0.301581
15	-0.063479	-0.5235	0.301178
16	0.061423	0.5065	0.30707
17	-0.106754	-0.8803	0.190894
18	-0.090095	-0.7429	0.230038
19	-0.077406	-0.6383	0.262709
20	0.104028	0.8578	0.196998
21	0.014125	0.1165	0.453808
22	-0.112467	-0.9274	0.178494
23	-0.039628	-0.3268	0.372419
24	0.051544	0.425	0.336075

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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