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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

Wed, 14 Dec 2016 09:13:17 +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/14/t1481703360qruegw62i6tg1cp.htm/, Retrieved Fri, 03 May 2024 17:31:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299262, Retrieved Fri, 03 May 2024 17:31:08 +0000

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No (this computation is public)

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Estimated Impact

104

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

-       [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2016-12-14 08:13:17] [2a4be59ea15844c348dc523b08af79fc] [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=299262&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=299262&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299262&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	0.545925	5.7257	0
2	0.16065	1.6849	0.047421
3	-0.070008	-0.7342	0.232181
4	-0.011349	-0.119	0.452733
5	0.009438	0.099	0.460664
6	-0.027686	-0.2904	0.38604
7	-0.067355	-0.7064	0.24071
8	-0.059116	-0.62	0.268265
9	-0.031434	-0.3297	0.371135
10	-0.177701	-1.8637	0.032512
11	-0.335076	-3.5143	0.000321
12	-0.506731	-5.3146	0
13	-0.292911	-3.0721	0.00134
14	-0.089092	-0.9344	0.17607
15	0.010629	0.1115	0.45572
16	-0.004754	-0.0499	0.480164
17	0.000422	0.0044	0.49824
18	0.010235	0.1073	0.457355
19	0.039576	0.4151	0.339446
20	0.073945	0.7755	0.21984

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.545925 & 5.7257 & 0 \tabularnewline
2 & 0.16065 & 1.6849 & 0.047421 \tabularnewline
3 & -0.070008 & -0.7342 & 0.232181 \tabularnewline
4 & -0.011349 & -0.119 & 0.452733 \tabularnewline
5 & 0.009438 & 0.099 & 0.460664 \tabularnewline
6 & -0.027686 & -0.2904 & 0.38604 \tabularnewline
7 & -0.067355 & -0.7064 & 0.24071 \tabularnewline
8 & -0.059116 & -0.62 & 0.268265 \tabularnewline
9 & -0.031434 & -0.3297 & 0.371135 \tabularnewline
10 & -0.177701 & -1.8637 & 0.032512 \tabularnewline
11 & -0.335076 & -3.5143 & 0.000321 \tabularnewline
12 & -0.506731 & -5.3146 & 0 \tabularnewline
13 & -0.292911 & -3.0721 & 0.00134 \tabularnewline
14 & -0.089092 & -0.9344 & 0.17607 \tabularnewline
15 & 0.010629 & 0.1115 & 0.45572 \tabularnewline
16 & -0.004754 & -0.0499 & 0.480164 \tabularnewline
17 & 0.000422 & 0.0044 & 0.49824 \tabularnewline
18 & 0.010235 & 0.1073 & 0.457355 \tabularnewline
19 & 0.039576 & 0.4151 & 0.339446 \tabularnewline
20 & 0.073945 & 0.7755 & 0.21984 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299262&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]0.545925[/C][C]5.7257[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.16065[/C][C]1.6849[/C][C]0.047421[/C][/ROW]
[ROW][C]3[/C][C]-0.070008[/C][C]-0.7342[/C][C]0.232181[/C][/ROW]
[ROW][C]4[/C][C]-0.011349[/C][C]-0.119[/C][C]0.452733[/C][/ROW]
[ROW][C]5[/C][C]0.009438[/C][C]0.099[/C][C]0.460664[/C][/ROW]
[ROW][C]6[/C][C]-0.027686[/C][C]-0.2904[/C][C]0.38604[/C][/ROW]
[ROW][C]7[/C][C]-0.067355[/C][C]-0.7064[/C][C]0.24071[/C][/ROW]
[ROW][C]8[/C][C]-0.059116[/C][C]-0.62[/C][C]0.268265[/C][/ROW]
[ROW][C]9[/C][C]-0.031434[/C][C]-0.3297[/C][C]0.371135[/C][/ROW]
[ROW][C]10[/C][C]-0.177701[/C][C]-1.8637[/C][C]0.032512[/C][/ROW]
[ROW][C]11[/C][C]-0.335076[/C][C]-3.5143[/C][C]0.000321[/C][/ROW]
[ROW][C]12[/C][C]-0.506731[/C][C]-5.3146[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.292911[/C][C]-3.0721[/C][C]0.00134[/C][/ROW]
[ROW][C]14[/C][C]-0.089092[/C][C]-0.9344[/C][C]0.17607[/C][/ROW]
[ROW][C]15[/C][C]0.010629[/C][C]0.1115[/C][C]0.45572[/C][/ROW]
[ROW][C]16[/C][C]-0.004754[/C][C]-0.0499[/C][C]0.480164[/C][/ROW]
[ROW][C]17[/C][C]0.000422[/C][C]0.0044[/C][C]0.49824[/C][/ROW]
[ROW][C]18[/C][C]0.010235[/C][C]0.1073[/C][C]0.457355[/C][/ROW]
[ROW][C]19[/C][C]0.039576[/C][C]0.4151[/C][C]0.339446[/C][/ROW]
[ROW][C]20[/C][C]0.073945[/C][C]0.7755[/C][C]0.21984[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299262&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299262&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	0.545925	5.7257	0
2	0.16065	1.6849	0.047421
3	-0.070008	-0.7342	0.232181
4	-0.011349	-0.119	0.452733
5	0.009438	0.099	0.460664
6	-0.027686	-0.2904	0.38604
7	-0.067355	-0.7064	0.24071
8	-0.059116	-0.62	0.268265
9	-0.031434	-0.3297	0.371135
10	-0.177701	-1.8637	0.032512
11	-0.335076	-3.5143	0.000321
12	-0.506731	-5.3146	0
13	-0.292911	-3.0721	0.00134
14	-0.089092	-0.9344	0.17607
15	0.010629	0.1115	0.45572
16	-0.004754	-0.0499	0.480164
17	0.000422	0.0044	0.49824
18	0.010235	0.1073	0.457355
19	0.039576	0.4151	0.339446
20	0.073945	0.7755	0.21984

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.545925	5.7257	0
2	-0.195714	-2.0527	0.021239
3	-0.100773	-1.0569	0.146432
4	0.162905	1.7086	0.045176
5	-0.072227	-0.7575	0.225177
6	-0.068658	-0.7201	0.236497
7	0.008017	0.0841	0.466572
8	-0.012038	-0.1263	0.449882
9	-0.015266	-0.1601	0.436544
10	-0.255218	-2.6767	0.004286
11	-0.185747	-1.9481	0.026974
12	-0.32209	-3.3781	0.000505
13	0.136457	1.4312	0.077608
14	-0.050975	-0.5346	0.296992
15	-0.09944	-1.0429	0.149634
16	0.041952	0.44	0.330403
17	-0.019236	-0.2017	0.420243
18	-0.080841	-0.8479	0.199177
19	0.020631	0.2164	0.414546
20	0.032004	0.3357	0.368881

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.545925 & 5.7257 & 0 \tabularnewline
2 & -0.195714 & -2.0527 & 0.021239 \tabularnewline
3 & -0.100773 & -1.0569 & 0.146432 \tabularnewline
4 & 0.162905 & 1.7086 & 0.045176 \tabularnewline
5 & -0.072227 & -0.7575 & 0.225177 \tabularnewline
6 & -0.068658 & -0.7201 & 0.236497 \tabularnewline
7 & 0.008017 & 0.0841 & 0.466572 \tabularnewline
8 & -0.012038 & -0.1263 & 0.449882 \tabularnewline
9 & -0.015266 & -0.1601 & 0.436544 \tabularnewline
10 & -0.255218 & -2.6767 & 0.004286 \tabularnewline
11 & -0.185747 & -1.9481 & 0.026974 \tabularnewline
12 & -0.32209 & -3.3781 & 0.000505 \tabularnewline
13 & 0.136457 & 1.4312 & 0.077608 \tabularnewline
14 & -0.050975 & -0.5346 & 0.296992 \tabularnewline
15 & -0.09944 & -1.0429 & 0.149634 \tabularnewline
16 & 0.041952 & 0.44 & 0.330403 \tabularnewline
17 & -0.019236 & -0.2017 & 0.420243 \tabularnewline
18 & -0.080841 & -0.8479 & 0.199177 \tabularnewline
19 & 0.020631 & 0.2164 & 0.414546 \tabularnewline
20 & 0.032004 & 0.3357 & 0.368881 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299262&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]0.545925[/C][C]5.7257[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.195714[/C][C]-2.0527[/C][C]0.021239[/C][/ROW]
[ROW][C]3[/C][C]-0.100773[/C][C]-1.0569[/C][C]0.146432[/C][/ROW]
[ROW][C]4[/C][C]0.162905[/C][C]1.7086[/C][C]0.045176[/C][/ROW]
[ROW][C]5[/C][C]-0.072227[/C][C]-0.7575[/C][C]0.225177[/C][/ROW]
[ROW][C]6[/C][C]-0.068658[/C][C]-0.7201[/C][C]0.236497[/C][/ROW]
[ROW][C]7[/C][C]0.008017[/C][C]0.0841[/C][C]0.466572[/C][/ROW]
[ROW][C]8[/C][C]-0.012038[/C][C]-0.1263[/C][C]0.449882[/C][/ROW]
[ROW][C]9[/C][C]-0.015266[/C][C]-0.1601[/C][C]0.436544[/C][/ROW]
[ROW][C]10[/C][C]-0.255218[/C][C]-2.6767[/C][C]0.004286[/C][/ROW]
[ROW][C]11[/C][C]-0.185747[/C][C]-1.9481[/C][C]0.026974[/C][/ROW]
[ROW][C]12[/C][C]-0.32209[/C][C]-3.3781[/C][C]0.000505[/C][/ROW]
[ROW][C]13[/C][C]0.136457[/C][C]1.4312[/C][C]0.077608[/C][/ROW]
[ROW][C]14[/C][C]-0.050975[/C][C]-0.5346[/C][C]0.296992[/C][/ROW]
[ROW][C]15[/C][C]-0.09944[/C][C]-1.0429[/C][C]0.149634[/C][/ROW]
[ROW][C]16[/C][C]0.041952[/C][C]0.44[/C][C]0.330403[/C][/ROW]
[ROW][C]17[/C][C]-0.019236[/C][C]-0.2017[/C][C]0.420243[/C][/ROW]
[ROW][C]18[/C][C]-0.080841[/C][C]-0.8479[/C][C]0.199177[/C][/ROW]
[ROW][C]19[/C][C]0.020631[/C][C]0.2164[/C][C]0.414546[/C][/ROW]
[ROW][C]20[/C][C]0.032004[/C][C]0.3357[/C][C]0.368881[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299262&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299262&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	0.545925	5.7257	0
2	-0.195714	-2.0527	0.021239
3	-0.100773	-1.0569	0.146432
4	0.162905	1.7086	0.045176
5	-0.072227	-0.7575	0.225177
6	-0.068658	-0.7201	0.236497
7	0.008017	0.0841	0.466572
8	-0.012038	-0.1263	0.449882
9	-0.015266	-0.1601	0.436544
10	-0.255218	-2.6767	0.004286
11	-0.185747	-1.9481	0.026974
12	-0.32209	-3.3781	0.000505
13	0.136457	1.4312	0.077608
14	-0.050975	-0.5346	0.296992
15	-0.09944	-1.0429	0.149634
16	0.041952	0.44	0.330403
17	-0.019236	-0.2017	0.420243
18	-0.080841	-0.8479	0.199177
19	0.020631	0.2164	0.414546
20	0.032004	0.3357	0.368881

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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