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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 22:38:31 +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/2016/Dec/16/t14819247199iw08sz8lw1u29a.htm/, Retrieved Thu, 02 May 2024 15:48:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300570, Retrieved Thu, 02 May 2024 15:48:56 +0000

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

-       [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2016-12-16 21:38:31] [8dbd6448339a84ba150e9d534057ba9c] [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=300570&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=300570&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300570&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	0.693533	7.7849	0
2	0.593843	6.6659	0
3	0.543384	6.0995	0
4	0.315058	3.5365	0.000284
5	0.355337	3.9886	5.6e-05
6	0.338252	3.7969	0.000113
7	0.297867	3.3435	0.000545
8	0.263871	2.9619	0.001827
9	0.367713	4.1276	3.3e-05
10	0.35144	3.9449	6.6e-05
11	0.380495	4.271	1.9e-05
12	0.55079	6.1826	0
13	0.367118	4.1209	3.4e-05
14	0.337201	3.7851	0.000118
15	0.265641	2.9818	0.00172
16	0.076208	0.8554	0.196966
17	0.151735	1.7032	0.045496
18	0.129041	1.4485	0.074983
19	0.120345	1.3509	0.08958
20	0.144623	1.6234	0.053503
21	0.198515	2.2283	0.013816

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.693533 & 7.7849 & 0 \tabularnewline
2 & 0.593843 & 6.6659 & 0 \tabularnewline
3 & 0.543384 & 6.0995 & 0 \tabularnewline
4 & 0.315058 & 3.5365 & 0.000284 \tabularnewline
5 & 0.355337 & 3.9886 & 5.6e-05 \tabularnewline
6 & 0.338252 & 3.7969 & 0.000113 \tabularnewline
7 & 0.297867 & 3.3435 & 0.000545 \tabularnewline
8 & 0.263871 & 2.9619 & 0.001827 \tabularnewline
9 & 0.367713 & 4.1276 & 3.3e-05 \tabularnewline
10 & 0.35144 & 3.9449 & 6.6e-05 \tabularnewline
11 & 0.380495 & 4.271 & 1.9e-05 \tabularnewline
12 & 0.55079 & 6.1826 & 0 \tabularnewline
13 & 0.367118 & 4.1209 & 3.4e-05 \tabularnewline
14 & 0.337201 & 3.7851 & 0.000118 \tabularnewline
15 & 0.265641 & 2.9818 & 0.00172 \tabularnewline
16 & 0.076208 & 0.8554 & 0.196966 \tabularnewline
17 & 0.151735 & 1.7032 & 0.045496 \tabularnewline
18 & 0.129041 & 1.4485 & 0.074983 \tabularnewline
19 & 0.120345 & 1.3509 & 0.08958 \tabularnewline
20 & 0.144623 & 1.6234 & 0.053503 \tabularnewline
21 & 0.198515 & 2.2283 & 0.013816 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300570&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]0.693533[/C][C]7.7849[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.593843[/C][C]6.6659[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.543384[/C][C]6.0995[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.315058[/C][C]3.5365[/C][C]0.000284[/C][/ROW]
[ROW][C]5[/C][C]0.355337[/C][C]3.9886[/C][C]5.6e-05[/C][/ROW]
[ROW][C]6[/C][C]0.338252[/C][C]3.7969[/C][C]0.000113[/C][/ROW]
[ROW][C]7[/C][C]0.297867[/C][C]3.3435[/C][C]0.000545[/C][/ROW]
[ROW][C]8[/C][C]0.263871[/C][C]2.9619[/C][C]0.001827[/C][/ROW]
[ROW][C]9[/C][C]0.367713[/C][C]4.1276[/C][C]3.3e-05[/C][/ROW]
[ROW][C]10[/C][C]0.35144[/C][C]3.9449[/C][C]6.6e-05[/C][/ROW]
[ROW][C]11[/C][C]0.380495[/C][C]4.271[/C][C]1.9e-05[/C][/ROW]
[ROW][C]12[/C][C]0.55079[/C][C]6.1826[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.367118[/C][C]4.1209[/C][C]3.4e-05[/C][/ROW]
[ROW][C]14[/C][C]0.337201[/C][C]3.7851[/C][C]0.000118[/C][/ROW]
[ROW][C]15[/C][C]0.265641[/C][C]2.9818[/C][C]0.00172[/C][/ROW]
[ROW][C]16[/C][C]0.076208[/C][C]0.8554[/C][C]0.196966[/C][/ROW]
[ROW][C]17[/C][C]0.151735[/C][C]1.7032[/C][C]0.045496[/C][/ROW]
[ROW][C]18[/C][C]0.129041[/C][C]1.4485[/C][C]0.074983[/C][/ROW]
[ROW][C]19[/C][C]0.120345[/C][C]1.3509[/C][C]0.08958[/C][/ROW]
[ROW][C]20[/C][C]0.144623[/C][C]1.6234[/C][C]0.053503[/C][/ROW]
[ROW][C]21[/C][C]0.198515[/C][C]2.2283[/C][C]0.013816[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300570&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300570&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	0.693533	7.7849	0
2	0.593843	6.6659	0
3	0.543384	6.0995	0
4	0.315058	3.5365	0.000284
5	0.355337	3.9886	5.6e-05
6	0.338252	3.7969	0.000113
7	0.297867	3.3435	0.000545
8	0.263871	2.9619	0.001827
9	0.367713	4.1276	3.3e-05
10	0.35144	3.9449	6.6e-05
11	0.380495	4.271	1.9e-05
12	0.55079	6.1826	0
13	0.367118	4.1209	3.4e-05
14	0.337201	3.7851	0.000118
15	0.265641	2.9818	0.00172
16	0.076208	0.8554	0.196966
17	0.151735	1.7032	0.045496
18	0.129041	1.4485	0.074983
19	0.120345	1.3509	0.08958
20	0.144623	1.6234	0.053503
21	0.198515	2.2283	0.013816

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.693533	7.7849	0
2	0.217442	2.4408	0.008023
3	0.14214	1.5955	0.056551
4	-0.299189	-3.3584	0.000519
5	0.257966	2.8957	0.002231
6	0.070931	0.7962	0.213707
7	0.091566	1.0278	0.153002
8	-0.212366	-2.3838	0.009314
9	0.454366	5.1003	1e-06
10	-0.119259	-1.3387	0.091544
11	0.275853	3.0964	0.001207
12	0.075081	0.8428	0.200474
13	-0.185329	-2.0803	0.019762
14	-0.128907	-1.447	0.075194
15	-0.153669	-1.7249	0.043496
16	-0.013997	-0.1571	0.437704
17	0.13553	1.5213	0.065342
18	-0.034389	-0.386	0.350067
19	0.028382	0.3186	0.375285
20	-0.012266	-0.1377	0.445352
21	0.12285	1.379	0.085172

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.693533 & 7.7849 & 0 \tabularnewline
2 & 0.217442 & 2.4408 & 0.008023 \tabularnewline
3 & 0.14214 & 1.5955 & 0.056551 \tabularnewline
4 & -0.299189 & -3.3584 & 0.000519 \tabularnewline
5 & 0.257966 & 2.8957 & 0.002231 \tabularnewline
6 & 0.070931 & 0.7962 & 0.213707 \tabularnewline
7 & 0.091566 & 1.0278 & 0.153002 \tabularnewline
8 & -0.212366 & -2.3838 & 0.009314 \tabularnewline
9 & 0.454366 & 5.1003 & 1e-06 \tabularnewline
10 & -0.119259 & -1.3387 & 0.091544 \tabularnewline
11 & 0.275853 & 3.0964 & 0.001207 \tabularnewline
12 & 0.075081 & 0.8428 & 0.200474 \tabularnewline
13 & -0.185329 & -2.0803 & 0.019762 \tabularnewline
14 & -0.128907 & -1.447 & 0.075194 \tabularnewline
15 & -0.153669 & -1.7249 & 0.043496 \tabularnewline
16 & -0.013997 & -0.1571 & 0.437704 \tabularnewline
17 & 0.13553 & 1.5213 & 0.065342 \tabularnewline
18 & -0.034389 & -0.386 & 0.350067 \tabularnewline
19 & 0.028382 & 0.3186 & 0.375285 \tabularnewline
20 & -0.012266 & -0.1377 & 0.445352 \tabularnewline
21 & 0.12285 & 1.379 & 0.085172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300570&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]0.693533[/C][C]7.7849[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.217442[/C][C]2.4408[/C][C]0.008023[/C][/ROW]
[ROW][C]3[/C][C]0.14214[/C][C]1.5955[/C][C]0.056551[/C][/ROW]
[ROW][C]4[/C][C]-0.299189[/C][C]-3.3584[/C][C]0.000519[/C][/ROW]
[ROW][C]5[/C][C]0.257966[/C][C]2.8957[/C][C]0.002231[/C][/ROW]
[ROW][C]6[/C][C]0.070931[/C][C]0.7962[/C][C]0.213707[/C][/ROW]
[ROW][C]7[/C][C]0.091566[/C][C]1.0278[/C][C]0.153002[/C][/ROW]
[ROW][C]8[/C][C]-0.212366[/C][C]-2.3838[/C][C]0.009314[/C][/ROW]
[ROW][C]9[/C][C]0.454366[/C][C]5.1003[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]-0.119259[/C][C]-1.3387[/C][C]0.091544[/C][/ROW]
[ROW][C]11[/C][C]0.275853[/C][C]3.0964[/C][C]0.001207[/C][/ROW]
[ROW][C]12[/C][C]0.075081[/C][C]0.8428[/C][C]0.200474[/C][/ROW]
[ROW][C]13[/C][C]-0.185329[/C][C]-2.0803[/C][C]0.019762[/C][/ROW]
[ROW][C]14[/C][C]-0.128907[/C][C]-1.447[/C][C]0.075194[/C][/ROW]
[ROW][C]15[/C][C]-0.153669[/C][C]-1.7249[/C][C]0.043496[/C][/ROW]
[ROW][C]16[/C][C]-0.013997[/C][C]-0.1571[/C][C]0.437704[/C][/ROW]
[ROW][C]17[/C][C]0.13553[/C][C]1.5213[/C][C]0.065342[/C][/ROW]
[ROW][C]18[/C][C]-0.034389[/C][C]-0.386[/C][C]0.350067[/C][/ROW]
[ROW][C]19[/C][C]0.028382[/C][C]0.3186[/C][C]0.375285[/C][/ROW]
[ROW][C]20[/C][C]-0.012266[/C][C]-0.1377[/C][C]0.445352[/C][/ROW]
[ROW][C]21[/C][C]0.12285[/C][C]1.379[/C][C]0.085172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300570&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300570&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	0.693533	7.7849	0
2	0.217442	2.4408	0.008023
3	0.14214	1.5955	0.056551
4	-0.299189	-3.3584	0.000519
5	0.257966	2.8957	0.002231
6	0.070931	0.7962	0.213707
7	0.091566	1.0278	0.153002
8	-0.212366	-2.3838	0.009314
9	0.454366	5.1003	1e-06
10	-0.119259	-1.3387	0.091544
11	0.275853	3.0964	0.001207
12	0.075081	0.8428	0.200474
13	-0.185329	-2.0803	0.019762
14	-0.128907	-1.447	0.075194
15	-0.153669	-1.7249	0.043496
16	-0.013997	-0.1571	0.437704
17	0.13553	1.5213	0.065342
18	-0.034389	-0.386	0.350067
19	0.028382	0.3186	0.375285
20	-0.012266	-0.1377	0.445352
21	0.12285	1.379	0.085172

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; 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