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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Oct 2014 16:43:56 +0100

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/Oct/19/t14137335013yoyam9saehplxz.htm/, Retrieved Sun, 12 May 2024 03:15:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243686, Retrieved Sun, 12 May 2024 03:15:31 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [Autocorrelatie le...] [2014-10-19 15:43:56] [8bdab0fd537d5455eaa21dec7dfb1324] [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	1 seconds
R Server	'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243686&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243686&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243686&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	1 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.601302	5.1022	1e-06
2	0.475791	4.0372	6.7e-05
3	0.171267	1.4532	0.07525
4	-0.062045	-0.5265	0.30009
5	-0.233205	-1.9788	0.025831
6	-0.194104	-1.647	0.051955
7	-0.194691	-1.652	0.051444
8	-0.00065	-0.0055	0.497807
9	0.147271	1.2496	0.107739
10	0.359345	3.0491	0.001605
11	0.406478	3.4491	0.000472
12	0.621313	5.272	1e-06
13	0.358446	3.0415	0.001641
14	0.285256	2.4205	0.009012
15	0.073176	0.6209	0.268306
16	-0.101771	-0.8636	0.195349
17	-0.233313	-1.9797	0.025779
18	-0.269674	-2.2883	0.01253
19	-0.264669	-2.2458	0.013894
20	-0.137011	-1.1626	0.124421
21	-0.013566	-0.1151	0.454339
22	0.17863	1.5157	0.066983
23	0.232329	1.9714	0.026262
24	0.387975	3.2921	0.000771

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.601302 & 5.1022 & 1e-06 \tabularnewline
2 & 0.475791 & 4.0372 & 6.7e-05 \tabularnewline
3 & 0.171267 & 1.4532 & 0.07525 \tabularnewline
4 & -0.062045 & -0.5265 & 0.30009 \tabularnewline
5 & -0.233205 & -1.9788 & 0.025831 \tabularnewline
6 & -0.194104 & -1.647 & 0.051955 \tabularnewline
7 & -0.194691 & -1.652 & 0.051444 \tabularnewline
8 & -0.00065 & -0.0055 & 0.497807 \tabularnewline
9 & 0.147271 & 1.2496 & 0.107739 \tabularnewline
10 & 0.359345 & 3.0491 & 0.001605 \tabularnewline
11 & 0.406478 & 3.4491 & 0.000472 \tabularnewline
12 & 0.621313 & 5.272 & 1e-06 \tabularnewline
13 & 0.358446 & 3.0415 & 0.001641 \tabularnewline
14 & 0.285256 & 2.4205 & 0.009012 \tabularnewline
15 & 0.073176 & 0.6209 & 0.268306 \tabularnewline
16 & -0.101771 & -0.8636 & 0.195349 \tabularnewline
17 & -0.233313 & -1.9797 & 0.025779 \tabularnewline
18 & -0.269674 & -2.2883 & 0.01253 \tabularnewline
19 & -0.264669 & -2.2458 & 0.013894 \tabularnewline
20 & -0.137011 & -1.1626 & 0.124421 \tabularnewline
21 & -0.013566 & -0.1151 & 0.454339 \tabularnewline
22 & 0.17863 & 1.5157 & 0.066983 \tabularnewline
23 & 0.232329 & 1.9714 & 0.026262 \tabularnewline
24 & 0.387975 & 3.2921 & 0.000771 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243686&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]0.601302[/C][C]5.1022[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.475791[/C][C]4.0372[/C][C]6.7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.171267[/C][C]1.4532[/C][C]0.07525[/C][/ROW]
[ROW][C]4[/C][C]-0.062045[/C][C]-0.5265[/C][C]0.30009[/C][/ROW]
[ROW][C]5[/C][C]-0.233205[/C][C]-1.9788[/C][C]0.025831[/C][/ROW]
[ROW][C]6[/C][C]-0.194104[/C][C]-1.647[/C][C]0.051955[/C][/ROW]
[ROW][C]7[/C][C]-0.194691[/C][C]-1.652[/C][C]0.051444[/C][/ROW]
[ROW][C]8[/C][C]-0.00065[/C][C]-0.0055[/C][C]0.497807[/C][/ROW]
[ROW][C]9[/C][C]0.147271[/C][C]1.2496[/C][C]0.107739[/C][/ROW]
[ROW][C]10[/C][C]0.359345[/C][C]3.0491[/C][C]0.001605[/C][/ROW]
[ROW][C]11[/C][C]0.406478[/C][C]3.4491[/C][C]0.000472[/C][/ROW]
[ROW][C]12[/C][C]0.621313[/C][C]5.272[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.358446[/C][C]3.0415[/C][C]0.001641[/C][/ROW]
[ROW][C]14[/C][C]0.285256[/C][C]2.4205[/C][C]0.009012[/C][/ROW]
[ROW][C]15[/C][C]0.073176[/C][C]0.6209[/C][C]0.268306[/C][/ROW]
[ROW][C]16[/C][C]-0.101771[/C][C]-0.8636[/C][C]0.195349[/C][/ROW]
[ROW][C]17[/C][C]-0.233313[/C][C]-1.9797[/C][C]0.025779[/C][/ROW]
[ROW][C]18[/C][C]-0.269674[/C][C]-2.2883[/C][C]0.01253[/C][/ROW]
[ROW][C]19[/C][C]-0.264669[/C][C]-2.2458[/C][C]0.013894[/C][/ROW]
[ROW][C]20[/C][C]-0.137011[/C][C]-1.1626[/C][C]0.124421[/C][/ROW]
[ROW][C]21[/C][C]-0.013566[/C][C]-0.1151[/C][C]0.454339[/C][/ROW]
[ROW][C]22[/C][C]0.17863[/C][C]1.5157[/C][C]0.066983[/C][/ROW]
[ROW][C]23[/C][C]0.232329[/C][C]1.9714[/C][C]0.026262[/C][/ROW]
[ROW][C]24[/C][C]0.387975[/C][C]3.2921[/C][C]0.000771[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243686&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243686&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	0.601302	5.1022	1e-06
2	0.475791	4.0372	6.7e-05
3	0.171267	1.4532	0.07525
4	-0.062045	-0.5265	0.30009
5	-0.233205	-1.9788	0.025831
6	-0.194104	-1.647	0.051955
7	-0.194691	-1.652	0.051444
8	-0.00065	-0.0055	0.497807
9	0.147271	1.2496	0.107739
10	0.359345	3.0491	0.001605
11	0.406478	3.4491	0.000472
12	0.621313	5.272	1e-06
13	0.358446	3.0415	0.001641
14	0.285256	2.4205	0.009012
15	0.073176	0.6209	0.268306
16	-0.101771	-0.8636	0.195349
17	-0.233313	-1.9797	0.025779
18	-0.269674	-2.2883	0.01253
19	-0.264669	-2.2458	0.013894
20	-0.137011	-1.1626	0.124421
21	-0.013566	-0.1151	0.454339
22	0.17863	1.5157	0.066983
23	0.232329	1.9714	0.026262
24	0.387975	3.2921	0.000771

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.601302	5.1022	1e-06
2	0.178918	1.5182	0.066676
3	-0.27706	-2.3509	0.010734
4	-0.243106	-2.0628	0.021369
5	-0.10381	-0.8809	0.190663
6	0.201208	1.7073	0.046037
7	0.012781	0.1085	0.45697
8	0.138102	1.1718	0.122563
9	0.1325	1.1243	0.13231
10	0.231474	1.9641	0.026689
11	0.040992	0.3478	0.364492
12	0.410365	3.4821	0.000425
13	-0.282399	-2.3962	0.009582
14	-0.041286	-0.3503	0.36356
15	0.06397	0.5428	0.294469
16	-0.009293	-0.0789	0.468683
17	-0.062998	-0.5346	0.297301
18	-0.245057	-2.0794	0.020572
19	0.009446	0.0801	0.468171
20	-0.064811	-0.5499	0.292031
21	0.0174	0.1476	0.441517
22	-0.001	-0.0085	0.496627
23	-0.041135	-0.349	0.36404
24	0.033153	0.2813	0.389637

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.601302 & 5.1022 & 1e-06 \tabularnewline
2 & 0.178918 & 1.5182 & 0.066676 \tabularnewline
3 & -0.27706 & -2.3509 & 0.010734 \tabularnewline
4 & -0.243106 & -2.0628 & 0.021369 \tabularnewline
5 & -0.10381 & -0.8809 & 0.190663 \tabularnewline
6 & 0.201208 & 1.7073 & 0.046037 \tabularnewline
7 & 0.012781 & 0.1085 & 0.45697 \tabularnewline
8 & 0.138102 & 1.1718 & 0.122563 \tabularnewline
9 & 0.1325 & 1.1243 & 0.13231 \tabularnewline
10 & 0.231474 & 1.9641 & 0.026689 \tabularnewline
11 & 0.040992 & 0.3478 & 0.364492 \tabularnewline
12 & 0.410365 & 3.4821 & 0.000425 \tabularnewline
13 & -0.282399 & -2.3962 & 0.009582 \tabularnewline
14 & -0.041286 & -0.3503 & 0.36356 \tabularnewline
15 & 0.06397 & 0.5428 & 0.294469 \tabularnewline
16 & -0.009293 & -0.0789 & 0.468683 \tabularnewline
17 & -0.062998 & -0.5346 & 0.297301 \tabularnewline
18 & -0.245057 & -2.0794 & 0.020572 \tabularnewline
19 & 0.009446 & 0.0801 & 0.468171 \tabularnewline
20 & -0.064811 & -0.5499 & 0.292031 \tabularnewline
21 & 0.0174 & 0.1476 & 0.441517 \tabularnewline
22 & -0.001 & -0.0085 & 0.496627 \tabularnewline
23 & -0.041135 & -0.349 & 0.36404 \tabularnewline
24 & 0.033153 & 0.2813 & 0.389637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243686&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]0.601302[/C][C]5.1022[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.178918[/C][C]1.5182[/C][C]0.066676[/C][/ROW]
[ROW][C]3[/C][C]-0.27706[/C][C]-2.3509[/C][C]0.010734[/C][/ROW]
[ROW][C]4[/C][C]-0.243106[/C][C]-2.0628[/C][C]0.021369[/C][/ROW]
[ROW][C]5[/C][C]-0.10381[/C][C]-0.8809[/C][C]0.190663[/C][/ROW]
[ROW][C]6[/C][C]0.201208[/C][C]1.7073[/C][C]0.046037[/C][/ROW]
[ROW][C]7[/C][C]0.012781[/C][C]0.1085[/C][C]0.45697[/C][/ROW]
[ROW][C]8[/C][C]0.138102[/C][C]1.1718[/C][C]0.122563[/C][/ROW]
[ROW][C]9[/C][C]0.1325[/C][C]1.1243[/C][C]0.13231[/C][/ROW]
[ROW][C]10[/C][C]0.231474[/C][C]1.9641[/C][C]0.026689[/C][/ROW]
[ROW][C]11[/C][C]0.040992[/C][C]0.3478[/C][C]0.364492[/C][/ROW]
[ROW][C]12[/C][C]0.410365[/C][C]3.4821[/C][C]0.000425[/C][/ROW]
[ROW][C]13[/C][C]-0.282399[/C][C]-2.3962[/C][C]0.009582[/C][/ROW]
[ROW][C]14[/C][C]-0.041286[/C][C]-0.3503[/C][C]0.36356[/C][/ROW]
[ROW][C]15[/C][C]0.06397[/C][C]0.5428[/C][C]0.294469[/C][/ROW]
[ROW][C]16[/C][C]-0.009293[/C][C]-0.0789[/C][C]0.468683[/C][/ROW]
[ROW][C]17[/C][C]-0.062998[/C][C]-0.5346[/C][C]0.297301[/C][/ROW]
[ROW][C]18[/C][C]-0.245057[/C][C]-2.0794[/C][C]0.020572[/C][/ROW]
[ROW][C]19[/C][C]0.009446[/C][C]0.0801[/C][C]0.468171[/C][/ROW]
[ROW][C]20[/C][C]-0.064811[/C][C]-0.5499[/C][C]0.292031[/C][/ROW]
[ROW][C]21[/C][C]0.0174[/C][C]0.1476[/C][C]0.441517[/C][/ROW]
[ROW][C]22[/C][C]-0.001[/C][C]-0.0085[/C][C]0.496627[/C][/ROW]
[ROW][C]23[/C][C]-0.041135[/C][C]-0.349[/C][C]0.36404[/C][/ROW]
[ROW][C]24[/C][C]0.033153[/C][C]0.2813[/C][C]0.389637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243686&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243686&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	0.601302	5.1022	1e-06
2	0.178918	1.5182	0.066676
3	-0.27706	-2.3509	0.010734
4	-0.243106	-2.0628	0.021369
5	-0.10381	-0.8809	0.190663
6	0.201208	1.7073	0.046037
7	0.012781	0.1085	0.45697
8	0.138102	1.1718	0.122563
9	0.1325	1.1243	0.13231
10	0.231474	1.9641	0.026689
11	0.040992	0.3478	0.364492
12	0.410365	3.4821	0.000425
13	-0.282399	-2.3962	0.009582
14	-0.041286	-0.3503	0.36356
15	0.06397	0.5428	0.294469
16	-0.009293	-0.0789	0.468683
17	-0.062998	-0.5346	0.297301
18	-0.245057	-2.0794	0.020572
19	0.009446	0.0801	0.468171
20	-0.064811	-0.5499	0.292031
21	0.0174	0.1476	0.441517
22	-0.001	-0.0085	0.496627
23	-0.041135	-0.349	0.36404
24	0.033153	0.2813	0.389637

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 0 ; 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