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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 11:41:30 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/21/t1482316899kdk0h9vh8fuhk63.htm/, Retrieved Mon, 06 May 2024 14:11:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302119, Retrieved Mon, 06 May 2024 14:11:10 +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] [] [2016-12-21 10:41:30] [57f1f1af0ba442a9c0352eeef9ded060] [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=302119&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=302119&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302119&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	-0.324755	-3.5575	0.000269
2	-0.033174	-0.3634	0.35847
3	0.221859	2.4303	0.008282
4	-0.058108	-0.6365	0.262818
5	0.044434	0.4868	0.313661
6	0.153842	1.6853	0.047269
7	-0.09185	-1.0062	0.158179
8	0.032065	0.3513	0.363006
9	0.14958	1.6386	0.051961
10	0.018504	0.2027	0.419855
11	0.013261	0.1453	0.44237
12	-0.171769	-1.8816	0.031154
13	0.127025	1.3915	0.083326
14	0.208716	2.2864	0.011993
15	-0.115876	-1.2694	0.103386
16	-0.08371	-0.917	0.180493
17	0.126522	1.386	0.084161
18	-0.058917	-0.6454	0.259949
19	-0.058158	-0.6371	0.262642
20	0.118583	1.299	0.098216
21	-0.079943	-0.8757	0.191462

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.324755 & -3.5575 & 0.000269 \tabularnewline
2 & -0.033174 & -0.3634 & 0.35847 \tabularnewline
3 & 0.221859 & 2.4303 & 0.008282 \tabularnewline
4 & -0.058108 & -0.6365 & 0.262818 \tabularnewline
5 & 0.044434 & 0.4868 & 0.313661 \tabularnewline
6 & 0.153842 & 1.6853 & 0.047269 \tabularnewline
7 & -0.09185 & -1.0062 & 0.158179 \tabularnewline
8 & 0.032065 & 0.3513 & 0.363006 \tabularnewline
9 & 0.14958 & 1.6386 & 0.051961 \tabularnewline
10 & 0.018504 & 0.2027 & 0.419855 \tabularnewline
11 & 0.013261 & 0.1453 & 0.44237 \tabularnewline
12 & -0.171769 & -1.8816 & 0.031154 \tabularnewline
13 & 0.127025 & 1.3915 & 0.083326 \tabularnewline
14 & 0.208716 & 2.2864 & 0.011993 \tabularnewline
15 & -0.115876 & -1.2694 & 0.103386 \tabularnewline
16 & -0.08371 & -0.917 & 0.180493 \tabularnewline
17 & 0.126522 & 1.386 & 0.084161 \tabularnewline
18 & -0.058917 & -0.6454 & 0.259949 \tabularnewline
19 & -0.058158 & -0.6371 & 0.262642 \tabularnewline
20 & 0.118583 & 1.299 & 0.098216 \tabularnewline
21 & -0.079943 & -0.8757 & 0.191462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302119&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]-0.324755[/C][C]-3.5575[/C][C]0.000269[/C][/ROW]
[ROW][C]2[/C][C]-0.033174[/C][C]-0.3634[/C][C]0.35847[/C][/ROW]
[ROW][C]3[/C][C]0.221859[/C][C]2.4303[/C][C]0.008282[/C][/ROW]
[ROW][C]4[/C][C]-0.058108[/C][C]-0.6365[/C][C]0.262818[/C][/ROW]
[ROW][C]5[/C][C]0.044434[/C][C]0.4868[/C][C]0.313661[/C][/ROW]
[ROW][C]6[/C][C]0.153842[/C][C]1.6853[/C][C]0.047269[/C][/ROW]
[ROW][C]7[/C][C]-0.09185[/C][C]-1.0062[/C][C]0.158179[/C][/ROW]
[ROW][C]8[/C][C]0.032065[/C][C]0.3513[/C][C]0.363006[/C][/ROW]
[ROW][C]9[/C][C]0.14958[/C][C]1.6386[/C][C]0.051961[/C][/ROW]
[ROW][C]10[/C][C]0.018504[/C][C]0.2027[/C][C]0.419855[/C][/ROW]
[ROW][C]11[/C][C]0.013261[/C][C]0.1453[/C][C]0.44237[/C][/ROW]
[ROW][C]12[/C][C]-0.171769[/C][C]-1.8816[/C][C]0.031154[/C][/ROW]
[ROW][C]13[/C][C]0.127025[/C][C]1.3915[/C][C]0.083326[/C][/ROW]
[ROW][C]14[/C][C]0.208716[/C][C]2.2864[/C][C]0.011993[/C][/ROW]
[ROW][C]15[/C][C]-0.115876[/C][C]-1.2694[/C][C]0.103386[/C][/ROW]
[ROW][C]16[/C][C]-0.08371[/C][C]-0.917[/C][C]0.180493[/C][/ROW]
[ROW][C]17[/C][C]0.126522[/C][C]1.386[/C][C]0.084161[/C][/ROW]
[ROW][C]18[/C][C]-0.058917[/C][C]-0.6454[/C][C]0.259949[/C][/ROW]
[ROW][C]19[/C][C]-0.058158[/C][C]-0.6371[/C][C]0.262642[/C][/ROW]
[ROW][C]20[/C][C]0.118583[/C][C]1.299[/C][C]0.098216[/C][/ROW]
[ROW][C]21[/C][C]-0.079943[/C][C]-0.8757[/C][C]0.191462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302119&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302119&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	-0.324755	-3.5575	0.000269
2	-0.033174	-0.3634	0.35847
3	0.221859	2.4303	0.008282
4	-0.058108	-0.6365	0.262818
5	0.044434	0.4868	0.313661
6	0.153842	1.6853	0.047269
7	-0.09185	-1.0062	0.158179
8	0.032065	0.3513	0.363006
9	0.14958	1.6386	0.051961
10	0.018504	0.2027	0.419855
11	0.013261	0.1453	0.44237
12	-0.171769	-1.8816	0.031154
13	0.127025	1.3915	0.083326
14	0.208716	2.2864	0.011993
15	-0.115876	-1.2694	0.103386
16	-0.08371	-0.917	0.180493
17	0.126522	1.386	0.084161
18	-0.058917	-0.6454	0.259949
19	-0.058158	-0.6371	0.262642
20	0.118583	1.299	0.098216
21	-0.079943	-0.8757	0.191462

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.324755	-3.5575	0.000269
2	-0.154986	-1.6978	0.04607
3	0.182216	1.9961	0.024095
4	0.089027	0.9752	0.1657
5	0.09175	1.0051	0.158442
6	0.180156	1.9735	0.025368
7	0.020349	0.2229	0.411993
8	-0.009608	-0.1053	0.458176
9	0.102931	1.1276	0.13088
10	0.136069	1.4906	0.06935
11	0.072605	0.7953	0.213992
12	-0.266037	-2.9143	0.002127
13	-0.080664	-0.8836	0.189333
14	0.253526	2.7772	0.003182
15	0.128446	1.4071	0.080998
16	-0.181801	-1.9915	0.024347
17	-0.078404	-0.8589	0.196062
18	0.029098	0.3188	0.375235
19	-0.133628	-1.4638	0.072928
20	-0.047062	-0.5155	0.303562
21	0.125345	1.3731	0.086142

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.324755 & -3.5575 & 0.000269 \tabularnewline
2 & -0.154986 & -1.6978 & 0.04607 \tabularnewline
3 & 0.182216 & 1.9961 & 0.024095 \tabularnewline
4 & 0.089027 & 0.9752 & 0.1657 \tabularnewline
5 & 0.09175 & 1.0051 & 0.158442 \tabularnewline
6 & 0.180156 & 1.9735 & 0.025368 \tabularnewline
7 & 0.020349 & 0.2229 & 0.411993 \tabularnewline
8 & -0.009608 & -0.1053 & 0.458176 \tabularnewline
9 & 0.102931 & 1.1276 & 0.13088 \tabularnewline
10 & 0.136069 & 1.4906 & 0.06935 \tabularnewline
11 & 0.072605 & 0.7953 & 0.213992 \tabularnewline
12 & -0.266037 & -2.9143 & 0.002127 \tabularnewline
13 & -0.080664 & -0.8836 & 0.189333 \tabularnewline
14 & 0.253526 & 2.7772 & 0.003182 \tabularnewline
15 & 0.128446 & 1.4071 & 0.080998 \tabularnewline
16 & -0.181801 & -1.9915 & 0.024347 \tabularnewline
17 & -0.078404 & -0.8589 & 0.196062 \tabularnewline
18 & 0.029098 & 0.3188 & 0.375235 \tabularnewline
19 & -0.133628 & -1.4638 & 0.072928 \tabularnewline
20 & -0.047062 & -0.5155 & 0.303562 \tabularnewline
21 & 0.125345 & 1.3731 & 0.086142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302119&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]-0.324755[/C][C]-3.5575[/C][C]0.000269[/C][/ROW]
[ROW][C]2[/C][C]-0.154986[/C][C]-1.6978[/C][C]0.04607[/C][/ROW]
[ROW][C]3[/C][C]0.182216[/C][C]1.9961[/C][C]0.024095[/C][/ROW]
[ROW][C]4[/C][C]0.089027[/C][C]0.9752[/C][C]0.1657[/C][/ROW]
[ROW][C]5[/C][C]0.09175[/C][C]1.0051[/C][C]0.158442[/C][/ROW]
[ROW][C]6[/C][C]0.180156[/C][C]1.9735[/C][C]0.025368[/C][/ROW]
[ROW][C]7[/C][C]0.020349[/C][C]0.2229[/C][C]0.411993[/C][/ROW]
[ROW][C]8[/C][C]-0.009608[/C][C]-0.1053[/C][C]0.458176[/C][/ROW]
[ROW][C]9[/C][C]0.102931[/C][C]1.1276[/C][C]0.13088[/C][/ROW]
[ROW][C]10[/C][C]0.136069[/C][C]1.4906[/C][C]0.06935[/C][/ROW]
[ROW][C]11[/C][C]0.072605[/C][C]0.7953[/C][C]0.213992[/C][/ROW]
[ROW][C]12[/C][C]-0.266037[/C][C]-2.9143[/C][C]0.002127[/C][/ROW]
[ROW][C]13[/C][C]-0.080664[/C][C]-0.8836[/C][C]0.189333[/C][/ROW]
[ROW][C]14[/C][C]0.253526[/C][C]2.7772[/C][C]0.003182[/C][/ROW]
[ROW][C]15[/C][C]0.128446[/C][C]1.4071[/C][C]0.080998[/C][/ROW]
[ROW][C]16[/C][C]-0.181801[/C][C]-1.9915[/C][C]0.024347[/C][/ROW]
[ROW][C]17[/C][C]-0.078404[/C][C]-0.8589[/C][C]0.196062[/C][/ROW]
[ROW][C]18[/C][C]0.029098[/C][C]0.3188[/C][C]0.375235[/C][/ROW]
[ROW][C]19[/C][C]-0.133628[/C][C]-1.4638[/C][C]0.072928[/C][/ROW]
[ROW][C]20[/C][C]-0.047062[/C][C]-0.5155[/C][C]0.303562[/C][/ROW]
[ROW][C]21[/C][C]0.125345[/C][C]1.3731[/C][C]0.086142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302119&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302119&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	-0.324755	-3.5575	0.000269
2	-0.154986	-1.6978	0.04607
3	0.182216	1.9961	0.024095
4	0.089027	0.9752	0.1657
5	0.09175	1.0051	0.158442
6	0.180156	1.9735	0.025368
7	0.020349	0.2229	0.411993
8	-0.009608	-0.1053	0.458176
9	0.102931	1.1276	0.13088
10	0.136069	1.4906	0.06935
11	0.072605	0.7953	0.213992
12	-0.266037	-2.9143	0.002127
13	-0.080664	-0.8836	0.189333
14	0.253526	2.7772	0.003182
15	0.128446	1.4071	0.080998
16	-0.181801	-1.9915	0.024347
17	-0.078404	-0.8589	0.196062
18	0.029098	0.3188	0.375235
19	-0.133628	-1.4638	0.072928
20	-0.047062	-0.5155	0.303562
21	0.125345	1.3731	0.086142

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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