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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 12 Dec 2017 22:49:40 +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/2017/Dec/12/t151311538975nl3hhdi1rct35.htm/, Retrieved Wed, 15 May 2024 15:59:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309192, Retrieved Wed, 15 May 2024 15:59:23 +0000

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Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2017-12-12 21:49:40] [8829069b4432872c842806a35f4fa8df] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309192&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=309192&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309192&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.690529	10.0543	0
2	0.554816	8.0782	0
3	0.633976	9.2308	0
4	0.73679	10.7278	0
5	0.660758	9.6208	0
6	0.640291	9.3228	0
7	0.633818	9.2285	0
8	0.716118	10.4268	0
9	0.569444	8.2912	0
10	0.461598	6.721	0
11	0.594021	8.6491	0
12	0.804543	11.7143	0
13	0.54152	7.8846	0
14	0.418125	6.088	0
15	0.468733	6.8249	0
16	0.569251	8.2884	0
17	0.516978	7.5273	0
18	0.458636	6.6778	0
19	0.469581	6.8372	0
20	0.546473	7.9568	0
21	0.391293	5.6973	0
22	0.315164	4.5889	4e-06
23	0.45299	6.5956	0
24	0.618698	9.0084	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.690529 & 10.0543 & 0 \tabularnewline
2 & 0.554816 & 8.0782 & 0 \tabularnewline
3 & 0.633976 & 9.2308 & 0 \tabularnewline
4 & 0.73679 & 10.7278 & 0 \tabularnewline
5 & 0.660758 & 9.6208 & 0 \tabularnewline
6 & 0.640291 & 9.3228 & 0 \tabularnewline
7 & 0.633818 & 9.2285 & 0 \tabularnewline
8 & 0.716118 & 10.4268 & 0 \tabularnewline
9 & 0.569444 & 8.2912 & 0 \tabularnewline
10 & 0.461598 & 6.721 & 0 \tabularnewline
11 & 0.594021 & 8.6491 & 0 \tabularnewline
12 & 0.804543 & 11.7143 & 0 \tabularnewline
13 & 0.54152 & 7.8846 & 0 \tabularnewline
14 & 0.418125 & 6.088 & 0 \tabularnewline
15 & 0.468733 & 6.8249 & 0 \tabularnewline
16 & 0.569251 & 8.2884 & 0 \tabularnewline
17 & 0.516978 & 7.5273 & 0 \tabularnewline
18 & 0.458636 & 6.6778 & 0 \tabularnewline
19 & 0.469581 & 6.8372 & 0 \tabularnewline
20 & 0.546473 & 7.9568 & 0 \tabularnewline
21 & 0.391293 & 5.6973 & 0 \tabularnewline
22 & 0.315164 & 4.5889 & 4e-06 \tabularnewline
23 & 0.45299 & 6.5956 & 0 \tabularnewline
24 & 0.618698 & 9.0084 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309192&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]0.690529[/C][C]10.0543[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.554816[/C][C]8.0782[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.633976[/C][C]9.2308[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.73679[/C][C]10.7278[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.660758[/C][C]9.6208[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.640291[/C][C]9.3228[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.633818[/C][C]9.2285[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.716118[/C][C]10.4268[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.569444[/C][C]8.2912[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.461598[/C][C]6.721[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.594021[/C][C]8.6491[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.804543[/C][C]11.7143[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.54152[/C][C]7.8846[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.418125[/C][C]6.088[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.468733[/C][C]6.8249[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.569251[/C][C]8.2884[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.516978[/C][C]7.5273[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.458636[/C][C]6.6778[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.469581[/C][C]6.8372[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.546473[/C][C]7.9568[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.391293[/C][C]5.6973[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.315164[/C][C]4.5889[/C][C]4e-06[/C][/ROW]
[ROW][C]23[/C][C]0.45299[/C][C]6.5956[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.618698[/C][C]9.0084[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309192&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309192&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	0.690529	10.0543	0
2	0.554816	8.0782	0
3	0.633976	9.2308	0
4	0.73679	10.7278	0
5	0.660758	9.6208	0
6	0.640291	9.3228	0
7	0.633818	9.2285	0
8	0.716118	10.4268	0
9	0.569444	8.2912	0
10	0.461598	6.721	0
11	0.594021	8.6491	0
12	0.804543	11.7143	0
13	0.54152	7.8846	0
14	0.418125	6.088	0
15	0.468733	6.8249	0
16	0.569251	8.2884	0
17	0.516978	7.5273	0
18	0.458636	6.6778	0
19	0.469581	6.8372	0
20	0.546473	7.9568	0
21	0.391293	5.6973	0
22	0.315164	4.5889	4e-06
23	0.45299	6.5956	0
24	0.618698	9.0084	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.690529	10.0543	0
2	0.149064	2.1704	0.015544
3	0.400817	5.836	0
4	0.403707	5.8781	0
5	0.113604	1.6541	0.049793
6	0.226492	3.2978	0.000571
7	0.053714	0.7821	0.217517
8	0.279973	4.0765	3.2e-05
9	-0.277165	-4.0356	3.8e-05
10	-0.3012	-4.3855	9e-06
11	0.10207	1.4862	0.069361
12	0.489223	7.1232	0
13	-0.396929	-5.7794	0
14	-0.220954	-3.2171	0.000749
15	-0.145909	-2.1245	0.017394
16	0.045164	0.6576	0.255757
17	0.119872	1.7454	0.041186
18	-0.051025	-0.7429	0.229173
19	0.069106	1.0062	0.157733
20	-0.040561	-0.5906	0.277718
21	0.021943	0.3195	0.374834
22	0.157263	2.2898	0.011509
23	0.075211	1.0951	0.137361
24	0.102683	1.4951	0.06819

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.690529 & 10.0543 & 0 \tabularnewline
2 & 0.149064 & 2.1704 & 0.015544 \tabularnewline
3 & 0.400817 & 5.836 & 0 \tabularnewline
4 & 0.403707 & 5.8781 & 0 \tabularnewline
5 & 0.113604 & 1.6541 & 0.049793 \tabularnewline
6 & 0.226492 & 3.2978 & 0.000571 \tabularnewline
7 & 0.053714 & 0.7821 & 0.217517 \tabularnewline
8 & 0.279973 & 4.0765 & 3.2e-05 \tabularnewline
9 & -0.277165 & -4.0356 & 3.8e-05 \tabularnewline
10 & -0.3012 & -4.3855 & 9e-06 \tabularnewline
11 & 0.10207 & 1.4862 & 0.069361 \tabularnewline
12 & 0.489223 & 7.1232 & 0 \tabularnewline
13 & -0.396929 & -5.7794 & 0 \tabularnewline
14 & -0.220954 & -3.2171 & 0.000749 \tabularnewline
15 & -0.145909 & -2.1245 & 0.017394 \tabularnewline
16 & 0.045164 & 0.6576 & 0.255757 \tabularnewline
17 & 0.119872 & 1.7454 & 0.041186 \tabularnewline
18 & -0.051025 & -0.7429 & 0.229173 \tabularnewline
19 & 0.069106 & 1.0062 & 0.157733 \tabularnewline
20 & -0.040561 & -0.5906 & 0.277718 \tabularnewline
21 & 0.021943 & 0.3195 & 0.374834 \tabularnewline
22 & 0.157263 & 2.2898 & 0.011509 \tabularnewline
23 & 0.075211 & 1.0951 & 0.137361 \tabularnewline
24 & 0.102683 & 1.4951 & 0.06819 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309192&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]0.690529[/C][C]10.0543[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.149064[/C][C]2.1704[/C][C]0.015544[/C][/ROW]
[ROW][C]3[/C][C]0.400817[/C][C]5.836[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.403707[/C][C]5.8781[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.113604[/C][C]1.6541[/C][C]0.049793[/C][/ROW]
[ROW][C]6[/C][C]0.226492[/C][C]3.2978[/C][C]0.000571[/C][/ROW]
[ROW][C]7[/C][C]0.053714[/C][C]0.7821[/C][C]0.217517[/C][/ROW]
[ROW][C]8[/C][C]0.279973[/C][C]4.0765[/C][C]3.2e-05[/C][/ROW]
[ROW][C]9[/C][C]-0.277165[/C][C]-4.0356[/C][C]3.8e-05[/C][/ROW]
[ROW][C]10[/C][C]-0.3012[/C][C]-4.3855[/C][C]9e-06[/C][/ROW]
[ROW][C]11[/C][C]0.10207[/C][C]1.4862[/C][C]0.069361[/C][/ROW]
[ROW][C]12[/C][C]0.489223[/C][C]7.1232[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.396929[/C][C]-5.7794[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.220954[/C][C]-3.2171[/C][C]0.000749[/C][/ROW]
[ROW][C]15[/C][C]-0.145909[/C][C]-2.1245[/C][C]0.017394[/C][/ROW]
[ROW][C]16[/C][C]0.045164[/C][C]0.6576[/C][C]0.255757[/C][/ROW]
[ROW][C]17[/C][C]0.119872[/C][C]1.7454[/C][C]0.041186[/C][/ROW]
[ROW][C]18[/C][C]-0.051025[/C][C]-0.7429[/C][C]0.229173[/C][/ROW]
[ROW][C]19[/C][C]0.069106[/C][C]1.0062[/C][C]0.157733[/C][/ROW]
[ROW][C]20[/C][C]-0.040561[/C][C]-0.5906[/C][C]0.277718[/C][/ROW]
[ROW][C]21[/C][C]0.021943[/C][C]0.3195[/C][C]0.374834[/C][/ROW]
[ROW][C]22[/C][C]0.157263[/C][C]2.2898[/C][C]0.011509[/C][/ROW]
[ROW][C]23[/C][C]0.075211[/C][C]1.0951[/C][C]0.137361[/C][/ROW]
[ROW][C]24[/C][C]0.102683[/C][C]1.4951[/C][C]0.06819[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309192&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309192&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	0.690529	10.0543	0
2	0.149064	2.1704	0.015544
3	0.400817	5.836	0
4	0.403707	5.8781	0
5	0.113604	1.6541	0.049793
6	0.226492	3.2978	0.000571
7	0.053714	0.7821	0.217517
8	0.279973	4.0765	3.2e-05
9	-0.277165	-4.0356	3.8e-05
10	-0.3012	-4.3855	9e-06
11	0.10207	1.4862	0.069361
12	0.489223	7.1232	0
13	-0.396929	-5.7794	0
14	-0.220954	-3.2171	0.000749
15	-0.145909	-2.1245	0.017394
16	0.045164	0.6576	0.255757
17	0.119872	1.7454	0.041186
18	-0.051025	-0.7429	0.229173
19	0.069106	1.0062	0.157733
20	-0.040561	-0.5906	0.277718
21	0.021943	0.3195	0.374834
22	0.157263	2.2898	0.011509
23	0.075211	1.0951	0.137361
24	0.102683	1.4951	0.06819

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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