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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 18:16:28 +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/19/t14821678353wy08xbd3yy5dq9.htm/, Retrieved Sun, 19 May 2024 19:10:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301428, Retrieved Sun, 19 May 2024 19:10:18 +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] [N1993 autocorrela...] [2016-12-19 17:16:28] [1eb03b74c4069f30e782d39ada1a3213] [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=301428&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=301428&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301428&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	0.870221	9.2914	0
2	0.757939	8.0926	0
3	0.700503	7.4793	0
4	0.632091	6.7489	0
5	0.586775	6.265	0
6	0.531129	5.6709	0
7	0.438518	4.6821	4e-06
8	0.335975	3.5872	0.000247
9	0.23254	2.4828	0.007245
10	0.135137	1.4429	0.0759
11	0.044099	0.4709	0.319324
12	-0.091825	-0.9804	0.164476
13	-0.122988	-1.3132	0.095884
14	-0.155792	-1.6634	0.049489
15	-0.23495	-2.5086	0.006764
16	-0.288664	-3.0821	0.001289
17	-0.34995	-3.7364	0.000147
18	-0.420025	-4.4846	9e-06
19	-0.456705	-4.8763	2e-06
20	-0.451249	-4.818	2e-06
21	-0.469905	-5.0172	1e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.870221 & 9.2914 & 0 \tabularnewline
2 & 0.757939 & 8.0926 & 0 \tabularnewline
3 & 0.700503 & 7.4793 & 0 \tabularnewline
4 & 0.632091 & 6.7489 & 0 \tabularnewline
5 & 0.586775 & 6.265 & 0 \tabularnewline
6 & 0.531129 & 5.6709 & 0 \tabularnewline
7 & 0.438518 & 4.6821 & 4e-06 \tabularnewline
8 & 0.335975 & 3.5872 & 0.000247 \tabularnewline
9 & 0.23254 & 2.4828 & 0.007245 \tabularnewline
10 & 0.135137 & 1.4429 & 0.0759 \tabularnewline
11 & 0.044099 & 0.4709 & 0.319324 \tabularnewline
12 & -0.091825 & -0.9804 & 0.164476 \tabularnewline
13 & -0.122988 & -1.3132 & 0.095884 \tabularnewline
14 & -0.155792 & -1.6634 & 0.049489 \tabularnewline
15 & -0.23495 & -2.5086 & 0.006764 \tabularnewline
16 & -0.288664 & -3.0821 & 0.001289 \tabularnewline
17 & -0.34995 & -3.7364 & 0.000147 \tabularnewline
18 & -0.420025 & -4.4846 & 9e-06 \tabularnewline
19 & -0.456705 & -4.8763 & 2e-06 \tabularnewline
20 & -0.451249 & -4.818 & 2e-06 \tabularnewline
21 & -0.469905 & -5.0172 & 1e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301428&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]0.870221[/C][C]9.2914[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.757939[/C][C]8.0926[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.700503[/C][C]7.4793[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.632091[/C][C]6.7489[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.586775[/C][C]6.265[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.531129[/C][C]5.6709[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.438518[/C][C]4.6821[/C][C]4e-06[/C][/ROW]
[ROW][C]8[/C][C]0.335975[/C][C]3.5872[/C][C]0.000247[/C][/ROW]
[ROW][C]9[/C][C]0.23254[/C][C]2.4828[/C][C]0.007245[/C][/ROW]
[ROW][C]10[/C][C]0.135137[/C][C]1.4429[/C][C]0.0759[/C][/ROW]
[ROW][C]11[/C][C]0.044099[/C][C]0.4709[/C][C]0.319324[/C][/ROW]
[ROW][C]12[/C][C]-0.091825[/C][C]-0.9804[/C][C]0.164476[/C][/ROW]
[ROW][C]13[/C][C]-0.122988[/C][C]-1.3132[/C][C]0.095884[/C][/ROW]
[ROW][C]14[/C][C]-0.155792[/C][C]-1.6634[/C][C]0.049489[/C][/ROW]
[ROW][C]15[/C][C]-0.23495[/C][C]-2.5086[/C][C]0.006764[/C][/ROW]
[ROW][C]16[/C][C]-0.288664[/C][C]-3.0821[/C][C]0.001289[/C][/ROW]
[ROW][C]17[/C][C]-0.34995[/C][C]-3.7364[/C][C]0.000147[/C][/ROW]
[ROW][C]18[/C][C]-0.420025[/C][C]-4.4846[/C][C]9e-06[/C][/ROW]
[ROW][C]19[/C][C]-0.456705[/C][C]-4.8763[/C][C]2e-06[/C][/ROW]
[ROW][C]20[/C][C]-0.451249[/C][C]-4.818[/C][C]2e-06[/C][/ROW]
[ROW][C]21[/C][C]-0.469905[/C][C]-5.0172[/C][C]1e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301428&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301428&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	0.870221	9.2914	0
2	0.757939	8.0926	0
3	0.700503	7.4793	0
4	0.632091	6.7489	0
5	0.586775	6.265	0
6	0.531129	5.6709	0
7	0.438518	4.6821	4e-06
8	0.335975	3.5872	0.000247
9	0.23254	2.4828	0.007245
10	0.135137	1.4429	0.0759
11	0.044099	0.4709	0.319324
12	-0.091825	-0.9804	0.164476
13	-0.122988	-1.3132	0.095884
14	-0.155792	-1.6634	0.049489
15	-0.23495	-2.5086	0.006764
16	-0.288664	-3.0821	0.001289
17	-0.34995	-3.7364	0.000147
18	-0.420025	-4.4846	9e-06
19	-0.456705	-4.8763	2e-06
20	-0.451249	-4.818	2e-06
21	-0.469905	-5.0172	1e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.870221	9.2914	0
2	0.002698	0.0288	0.488536
3	0.16629	1.7755	0.039243
4	-0.054711	-0.5841	0.280137
5	0.097621	1.0423	0.149738
6	-0.074219	-0.7924	0.214873
7	-0.149485	-1.5961	0.056621
8	-0.144729	-1.5453	0.062524
9	-0.133334	-1.4236	0.078644
10	-0.097399	-1.0399	0.150285
11	-0.101425	-1.0829	0.140563
12	-0.303409	-3.2395	0.000785
13	0.352471	3.7634	0.000133
14	-0.105652	-1.128	0.130834
15	-0.022937	-0.2449	0.403486
16	-0.03376	-0.3605	0.359584
17	-0.043756	-0.4672	0.320629
18	-0.102052	-1.0896	0.139089
19	-0.079705	-0.851	0.198272
20	0.079794	0.852	0.198008
21	-0.145187	-1.5502	0.061936

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.870221 & 9.2914 & 0 \tabularnewline
2 & 0.002698 & 0.0288 & 0.488536 \tabularnewline
3 & 0.16629 & 1.7755 & 0.039243 \tabularnewline
4 & -0.054711 & -0.5841 & 0.280137 \tabularnewline
5 & 0.097621 & 1.0423 & 0.149738 \tabularnewline
6 & -0.074219 & -0.7924 & 0.214873 \tabularnewline
7 & -0.149485 & -1.5961 & 0.056621 \tabularnewline
8 & -0.144729 & -1.5453 & 0.062524 \tabularnewline
9 & -0.133334 & -1.4236 & 0.078644 \tabularnewline
10 & -0.097399 & -1.0399 & 0.150285 \tabularnewline
11 & -0.101425 & -1.0829 & 0.140563 \tabularnewline
12 & -0.303409 & -3.2395 & 0.000785 \tabularnewline
13 & 0.352471 & 3.7634 & 0.000133 \tabularnewline
14 & -0.105652 & -1.128 & 0.130834 \tabularnewline
15 & -0.022937 & -0.2449 & 0.403486 \tabularnewline
16 & -0.03376 & -0.3605 & 0.359584 \tabularnewline
17 & -0.043756 & -0.4672 & 0.320629 \tabularnewline
18 & -0.102052 & -1.0896 & 0.139089 \tabularnewline
19 & -0.079705 & -0.851 & 0.198272 \tabularnewline
20 & 0.079794 & 0.852 & 0.198008 \tabularnewline
21 & -0.145187 & -1.5502 & 0.061936 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301428&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]0.870221[/C][C]9.2914[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.002698[/C][C]0.0288[/C][C]0.488536[/C][/ROW]
[ROW][C]3[/C][C]0.16629[/C][C]1.7755[/C][C]0.039243[/C][/ROW]
[ROW][C]4[/C][C]-0.054711[/C][C]-0.5841[/C][C]0.280137[/C][/ROW]
[ROW][C]5[/C][C]0.097621[/C][C]1.0423[/C][C]0.149738[/C][/ROW]
[ROW][C]6[/C][C]-0.074219[/C][C]-0.7924[/C][C]0.214873[/C][/ROW]
[ROW][C]7[/C][C]-0.149485[/C][C]-1.5961[/C][C]0.056621[/C][/ROW]
[ROW][C]8[/C][C]-0.144729[/C][C]-1.5453[/C][C]0.062524[/C][/ROW]
[ROW][C]9[/C][C]-0.133334[/C][C]-1.4236[/C][C]0.078644[/C][/ROW]
[ROW][C]10[/C][C]-0.097399[/C][C]-1.0399[/C][C]0.150285[/C][/ROW]
[ROW][C]11[/C][C]-0.101425[/C][C]-1.0829[/C][C]0.140563[/C][/ROW]
[ROW][C]12[/C][C]-0.303409[/C][C]-3.2395[/C][C]0.000785[/C][/ROW]
[ROW][C]13[/C][C]0.352471[/C][C]3.7634[/C][C]0.000133[/C][/ROW]
[ROW][C]14[/C][C]-0.105652[/C][C]-1.128[/C][C]0.130834[/C][/ROW]
[ROW][C]15[/C][C]-0.022937[/C][C]-0.2449[/C][C]0.403486[/C][/ROW]
[ROW][C]16[/C][C]-0.03376[/C][C]-0.3605[/C][C]0.359584[/C][/ROW]
[ROW][C]17[/C][C]-0.043756[/C][C]-0.4672[/C][C]0.320629[/C][/ROW]
[ROW][C]18[/C][C]-0.102052[/C][C]-1.0896[/C][C]0.139089[/C][/ROW]
[ROW][C]19[/C][C]-0.079705[/C][C]-0.851[/C][C]0.198272[/C][/ROW]
[ROW][C]20[/C][C]0.079794[/C][C]0.852[/C][C]0.198008[/C][/ROW]
[ROW][C]21[/C][C]-0.145187[/C][C]-1.5502[/C][C]0.061936[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301428&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301428&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	0.870221	9.2914	0
2	0.002698	0.0288	0.488536
3	0.16629	1.7755	0.039243
4	-0.054711	-0.5841	0.280137
5	0.097621	1.0423	0.149738
6	-0.074219	-0.7924	0.214873
7	-0.149485	-1.5961	0.056621
8	-0.144729	-1.5453	0.062524
9	-0.133334	-1.4236	0.078644
10	-0.097399	-1.0399	0.150285
11	-0.101425	-1.0829	0.140563
12	-0.303409	-3.2395	0.000785
13	0.352471	3.7634	0.000133
14	-0.105652	-1.128	0.130834
15	-0.022937	-0.2449	0.403486
16	-0.03376	-0.3605	0.359584
17	-0.043756	-0.4672	0.320629
18	-0.102052	-1.0896	0.139089
19	-0.079705	-0.851	0.198272
20	0.079794	0.852	0.198008
21	-0.145187	-1.5502	0.061936

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 = Default ; par2 = 1.8 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1.8 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1.8'
par1 <- 'Default'
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