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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 06 Oct 2023 22:13:35 +0200

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/2023/Oct/06/t1696623281z6fuf04x3zi1bfq.htm/, Retrieved Sat, 30 May 2026 17:02:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319957, Retrieved Sat, 30 May 2026 17:02:44 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

212

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

-       [(Partial) Autocorrelation Function] [] [2023-10-06 20:13:35] [d41d8cd98f00b204e9800998ecf8427e] [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=319957&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=319957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319957&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	-0.110497	-0.4688	0.32242
2	-0.299284	-1.2698	0.110172
3	0.275811	1.1702	0.128597
4	-0.101824	-0.432	0.335435
5	-0.312847	-1.3273	0.1005
6	-0.12989	-0.5511	0.294178
7	0.152376	0.6465	0.263065
8	-0.184602	-0.7832	0.221847
9	-0.049474	-0.2099	0.418052
10	0.489174	2.0754	0.02628
11	-0.055632	-0.236	0.408038
12	-0.113827	-0.4829	0.317485
13	0.116202	0.493	0.313985
14	-0.021104	-0.0895	0.464822
15	-0.094101	-0.3992	0.347208
16	-0.053085	-0.2252	0.412173
17	-0.007398	-0.0314	0.487654
18	NA	NA	NA
19	NA	NA	NA
20	NA	NA	NA
21	NA	NA	NA
22	NA	NA	NA
23	NA	NA	NA
24	NA	NA	NA

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.110497 & -0.4688 & 0.32242 \tabularnewline
2 & -0.299284 & -1.2698 & 0.110172 \tabularnewline
3 & 0.275811 & 1.1702 & 0.128597 \tabularnewline
4 & -0.101824 & -0.432 & 0.335435 \tabularnewline
5 & -0.312847 & -1.3273 & 0.1005 \tabularnewline
6 & -0.12989 & -0.5511 & 0.294178 \tabularnewline
7 & 0.152376 & 0.6465 & 0.263065 \tabularnewline
8 & -0.184602 & -0.7832 & 0.221847 \tabularnewline
9 & -0.049474 & -0.2099 & 0.418052 \tabularnewline
10 & 0.489174 & 2.0754 & 0.02628 \tabularnewline
11 & -0.055632 & -0.236 & 0.408038 \tabularnewline
12 & -0.113827 & -0.4829 & 0.317485 \tabularnewline
13 & 0.116202 & 0.493 & 0.313985 \tabularnewline
14 & -0.021104 & -0.0895 & 0.464822 \tabularnewline
15 & -0.094101 & -0.3992 & 0.347208 \tabularnewline
16 & -0.053085 & -0.2252 & 0.412173 \tabularnewline
17 & -0.007398 & -0.0314 & 0.487654 \tabularnewline
18 & NA & NA & NA \tabularnewline
19 & NA & NA & NA \tabularnewline
20 & NA & NA & NA \tabularnewline
21 & NA & NA & NA \tabularnewline
22 & NA & NA & NA \tabularnewline
23 & NA & NA & NA \tabularnewline
24 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319957&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]-0.110497[/C][C]-0.4688[/C][C]0.32242[/C][/ROW]
[ROW][C]2[/C][C]-0.299284[/C][C]-1.2698[/C][C]0.110172[/C][/ROW]
[ROW][C]3[/C][C]0.275811[/C][C]1.1702[/C][C]0.128597[/C][/ROW]
[ROW][C]4[/C][C]-0.101824[/C][C]-0.432[/C][C]0.335435[/C][/ROW]
[ROW][C]5[/C][C]-0.312847[/C][C]-1.3273[/C][C]0.1005[/C][/ROW]
[ROW][C]6[/C][C]-0.12989[/C][C]-0.5511[/C][C]0.294178[/C][/ROW]
[ROW][C]7[/C][C]0.152376[/C][C]0.6465[/C][C]0.263065[/C][/ROW]
[ROW][C]8[/C][C]-0.184602[/C][C]-0.7832[/C][C]0.221847[/C][/ROW]
[ROW][C]9[/C][C]-0.049474[/C][C]-0.2099[/C][C]0.418052[/C][/ROW]
[ROW][C]10[/C][C]0.489174[/C][C]2.0754[/C][C]0.02628[/C][/ROW]
[ROW][C]11[/C][C]-0.055632[/C][C]-0.236[/C][C]0.408038[/C][/ROW]
[ROW][C]12[/C][C]-0.113827[/C][C]-0.4829[/C][C]0.317485[/C][/ROW]
[ROW][C]13[/C][C]0.116202[/C][C]0.493[/C][C]0.313985[/C][/ROW]
[ROW][C]14[/C][C]-0.021104[/C][C]-0.0895[/C][C]0.464822[/C][/ROW]
[ROW][C]15[/C][C]-0.094101[/C][C]-0.3992[/C][C]0.347208[/C][/ROW]
[ROW][C]16[/C][C]-0.053085[/C][C]-0.2252[/C][C]0.412173[/C][/ROW]
[ROW][C]17[/C][C]-0.007398[/C][C]-0.0314[/C][C]0.487654[/C][/ROW]
[ROW][C]18[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]19[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]20[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]21[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]22[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]23[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]24[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319957&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	-0.110497	-0.4688	0.32242
2	-0.299284	-1.2698	0.110172
3	0.275811	1.1702	0.128597
4	-0.101824	-0.432	0.335435
5	-0.312847	-1.3273	0.1005
6	-0.12989	-0.5511	0.294178
7	0.152376	0.6465	0.263065
8	-0.184602	-0.7832	0.221847
9	-0.049474	-0.2099	0.418052
10	0.489174	2.0754	0.02628
11	-0.055632	-0.236	0.408038
12	-0.113827	-0.4829	0.317485
13	0.116202	0.493	0.313985
14	-0.021104	-0.0895	0.464822
15	-0.094101	-0.3992	0.347208
16	-0.053085	-0.2252	0.412173
17	-0.007398	-0.0314	0.487654
18	NA	NA	NA
19	NA	NA	NA
20	NA	NA	NA
21	NA	NA	NA
22	NA	NA	NA
23	NA	NA	NA
24	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.110497	-0.4688	0.32242
2	-0.315343	-1.3379	0.098796
3	0.221984	0.9418	0.179383
4	-0.167	-0.7085	0.243848
5	-0.220657	-0.9362	0.180789
6	-0.379567	-1.6104	0.062357
7	0.004198	0.0178	0.492993
8	-0.329112	-1.3963	0.089803
9	-0.072523	-0.3077	0.380925
10	0.213798	0.9071	0.188178
11	-0.023757	-0.1008	0.460415
12	0.028839	0.1224	0.451988
13	-0.185357	-0.7864	0.220931
14	0.006275	0.0266	0.489527
15	0.07159	0.3037	0.382408
16	0.154141	0.654	0.260701
17	-0.098875	-0.4195	0.339911
18	NA	NA	NA
19	NA	NA	NA
20	NA	NA	NA
21	NA	NA	NA
22	NA	NA	NA
23	NA	NA	NA
24	NA	NA	NA

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.110497 & -0.4688 & 0.32242 \tabularnewline
2 & -0.315343 & -1.3379 & 0.098796 \tabularnewline
3 & 0.221984 & 0.9418 & 0.179383 \tabularnewline
4 & -0.167 & -0.7085 & 0.243848 \tabularnewline
5 & -0.220657 & -0.9362 & 0.180789 \tabularnewline
6 & -0.379567 & -1.6104 & 0.062357 \tabularnewline
7 & 0.004198 & 0.0178 & 0.492993 \tabularnewline
8 & -0.329112 & -1.3963 & 0.089803 \tabularnewline
9 & -0.072523 & -0.3077 & 0.380925 \tabularnewline
10 & 0.213798 & 0.9071 & 0.188178 \tabularnewline
11 & -0.023757 & -0.1008 & 0.460415 \tabularnewline
12 & 0.028839 & 0.1224 & 0.451988 \tabularnewline
13 & -0.185357 & -0.7864 & 0.220931 \tabularnewline
14 & 0.006275 & 0.0266 & 0.489527 \tabularnewline
15 & 0.07159 & 0.3037 & 0.382408 \tabularnewline
16 & 0.154141 & 0.654 & 0.260701 \tabularnewline
17 & -0.098875 & -0.4195 & 0.339911 \tabularnewline
18 & NA & NA & NA \tabularnewline
19 & NA & NA & NA \tabularnewline
20 & NA & NA & NA \tabularnewline
21 & NA & NA & NA \tabularnewline
22 & NA & NA & NA \tabularnewline
23 & NA & NA & NA \tabularnewline
24 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319957&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]-0.110497[/C][C]-0.4688[/C][C]0.32242[/C][/ROW]
[ROW][C]2[/C][C]-0.315343[/C][C]-1.3379[/C][C]0.098796[/C][/ROW]
[ROW][C]3[/C][C]0.221984[/C][C]0.9418[/C][C]0.179383[/C][/ROW]
[ROW][C]4[/C][C]-0.167[/C][C]-0.7085[/C][C]0.243848[/C][/ROW]
[ROW][C]5[/C][C]-0.220657[/C][C]-0.9362[/C][C]0.180789[/C][/ROW]
[ROW][C]6[/C][C]-0.379567[/C][C]-1.6104[/C][C]0.062357[/C][/ROW]
[ROW][C]7[/C][C]0.004198[/C][C]0.0178[/C][C]0.492993[/C][/ROW]
[ROW][C]8[/C][C]-0.329112[/C][C]-1.3963[/C][C]0.089803[/C][/ROW]
[ROW][C]9[/C][C]-0.072523[/C][C]-0.3077[/C][C]0.380925[/C][/ROW]
[ROW][C]10[/C][C]0.213798[/C][C]0.9071[/C][C]0.188178[/C][/ROW]
[ROW][C]11[/C][C]-0.023757[/C][C]-0.1008[/C][C]0.460415[/C][/ROW]
[ROW][C]12[/C][C]0.028839[/C][C]0.1224[/C][C]0.451988[/C][/ROW]
[ROW][C]13[/C][C]-0.185357[/C][C]-0.7864[/C][C]0.220931[/C][/ROW]
[ROW][C]14[/C][C]0.006275[/C][C]0.0266[/C][C]0.489527[/C][/ROW]
[ROW][C]15[/C][C]0.07159[/C][C]0.3037[/C][C]0.382408[/C][/ROW]
[ROW][C]16[/C][C]0.154141[/C][C]0.654[/C][C]0.260701[/C][/ROW]
[ROW][C]17[/C][C]-0.098875[/C][C]-0.4195[/C][C]0.339911[/C][/ROW]
[ROW][C]18[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]19[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]20[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]21[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]22[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]23[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]24[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319957&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319957&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	-0.110497	-0.4688	0.32242
2	-0.315343	-1.3379	0.098796
3	0.221984	0.9418	0.179383
4	-0.167	-0.7085	0.243848
5	-0.220657	-0.9362	0.180789
6	-0.379567	-1.6104	0.062357
7	0.004198	0.0178	0.492993
8	-0.329112	-1.3963	0.089803
9	-0.072523	-0.3077	0.380925
10	0.213798	0.9071	0.188178
11	-0.023757	-0.1008	0.460415
12	0.028839	0.1224	0.451988
13	-0.185357	-0.7864	0.220931
14	0.006275	0.0266	0.489527
15	0.07159	0.3037	0.382408
16	0.154141	0.654	0.260701
17	-0.098875	-0.4195	0.339911
18	NA	NA	NA
19	NA	NA	NA
20	NA	NA	NA
21	NA	NA	NA
22	NA	NA	NA
23	NA	NA	NA
24	NA	NA	NA

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 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; 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 &lt;- as.numeric(par1)
}
par2 &lt;- as.numeric(par2)
par3 &lt;- as.numeric(par3)
par4 &lt;- as.numeric(par4)
par5 &lt;- as.numeric(par5)
if (par6 == 'White Noise') par6 &lt;- 'white' else par6 &lt;- 'ma'
par7 &lt;- as.numeric(par7)
if (par8 != '') par8 &lt;- as.numeric(par8)
x &lt;- na.omit(x)
ox &lt;- x
if (par8 == '') {
if (par2 == 0) {
x &lt;- log(x)
} else {
x &lt;- (x ^ par2 - 1) / par2
}
} else {
x &lt;- log(x,base=par8)
}
if (par3 &gt; 0) x &lt;- diff(x,lag=1,difference=par3)
if (par4 &gt; 0) x &lt;- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op &lt;- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle &lt;- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub &lt;- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle &lt;- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub &lt;- 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 &lt;- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf &lt;- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf &lt;- c(racf$acf))
(mypacf &lt;- c(rpacf$acf))
lengthx &lt;- length(x)
sqrtn &lt;- sqrt(lengthx)
load(file='createtable')
a&lt;-table.start()
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Autocorrelation Function',4,TRUE)
a&lt;-table.row.end(a)
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Time lag k',header=TRUE)
a&lt;-table.element(a,'ACF(k)',header=TRUE)
a&lt;-table.element(a,'T-STAT',header=TRUE)
a&lt;-table.element(a,'P-value',header=TRUE)
a&lt;-table.row.end(a)
for (i in 2:(par1+1)) {
a&lt;-table.row.start(a)
a&lt;-table.element(a,i-1,header=TRUE)
a&lt;-table.element(a,round(myacf[i],6))
mytstat &lt;- myacf[i]*sqrtn
a&lt;-table.element(a,round(mytstat,4))
a&lt;-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a&lt;-table.row.end(a)
}
a&lt;-table.end(a)
table.save(a,file='mytable.tab')
a&lt;-table.start()
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a&lt;-table.row.end(a)
a&lt;-table.row.start(a)
a&lt;-table.element(a,'Time lag k',header=TRUE)
a&lt;-table.element(a,'PACF(k)',header=TRUE)
a&lt;-table.element(a,'T-STAT',header=TRUE)
a&lt;-table.element(a,'P-value',header=TRUE)
a&lt;-table.row.end(a)
for (i in 1:par1) {
a&lt;-table.row.start(a)
a&lt;-table.element(a,i,header=TRUE)
a&lt;-table.element(a,round(mypacf[i],6))
mytstat &lt;- mypacf[i]*sqrtn
a&lt;-table.element(a,round(mytstat,4))
a&lt;-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a&lt;-table.row.end(a)
}
a&lt;-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