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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 30 Jun 2025 05:45:42 +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/2025/Jun/30/t1751255377p2dxetjo5dx2tyw.htm/, Retrieved Sat, 29 Aug 2026 13:34:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=320242, Retrieved Sat, 29 Aug 2026 13:34:40 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

187

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

-       [(Partial) Autocorrelation Function] [] [2025-06-30 03:45:42] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

5.00
1.00
-3.00
-2.00
10.00
8.00
0.00
0.00
-8.00
-4.00
12.00
8.00
-6.00
13.00
-9.00
19.00
-18.00
0.00
0.00
-3.00
3.00
3.00
-6.00
0.00
4.00
-15.00
3.00
-7.00
29.00
-9.00
12.00
-18.00
4.00
-3.00
2.00
-3.00
-9.00
27.00
11.00
-8.00
-21.00
9.00
-4.00
-2.00
-8.00
-12.00
-1.00
1.00
-16.00
7.00
-7.00
13.00
16.00
17.00
-17.00
1.00
-4.00
5.00
5.00
10.00
7.00
-13.00
10.00
-6.00
15.00
11.00
-8.00
-1.00
-8.00
-11.00
15.00
-7.00
2.00
6.00
-6.00
4.00
11.00
-10.00
9.00
-15.00
-11.00
2.00
-6.00
3.00
-7.00
15.00
-4.00
2.00
11.00
4.00
10.00
-13.00
-8.00
-7.00
-4.00
-5.00
-8.00
-11.00
-6.00
8.00
5.00
13.00
12.00
-38.00
12.00
-7.00
-4.00
19.00
4.00
20.00
4.00
9.00
-20.00
20.00
-3.00
5.00
-11.00
4.00
16.00
-11.00
-8.00
-36.00
52.00
-13.00
11.00
11.00
-27.00
-2.00
9.00
-26.00
-1.00

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=320242&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=320242&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=320242&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	-0.309815	-3.546	0.000272
2	0.095351	1.0913	0.138562
3	-0.096891	-1.109	0.134738
4	-0.098995	-1.133	0.129631
5	0.061001	0.6982	0.24315
6	-0.000288	-0.0033	0.498688
7	-0.056108	-0.6422	0.260936
8	-0.060966	-0.6978	0.243274
9	0.175917	2.0135	0.023057
10	-0.140279	-1.6056	0.055389
11	0.069735	0.7982	0.213112
12	-0.133673	-1.53	0.064219
13	0.087177	0.9978	0.160111
14	0.002494	0.0286	0.488633
15	0.065332	0.7478	0.227972
16	-0.109162	-1.2494	0.106871
17	-0.000338	-0.0039	0.498462
18	0.044028	0.5039	0.307582
19	-0.113945	-1.3042	0.097232
20	-0.091271	-1.0446	0.149054
21	0.041943	0.4801	0.315994

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.309815 & -3.546 & 0.000272 \tabularnewline
2 & 0.095351 & 1.0913 & 0.138562 \tabularnewline
3 & -0.096891 & -1.109 & 0.134738 \tabularnewline
4 & -0.098995 & -1.133 & 0.129631 \tabularnewline
5 & 0.061001 & 0.6982 & 0.24315 \tabularnewline
6 & -0.000288 & -0.0033 & 0.498688 \tabularnewline
7 & -0.056108 & -0.6422 & 0.260936 \tabularnewline
8 & -0.060966 & -0.6978 & 0.243274 \tabularnewline
9 & 0.175917 & 2.0135 & 0.023057 \tabularnewline
10 & -0.140279 & -1.6056 & 0.055389 \tabularnewline
11 & 0.069735 & 0.7982 & 0.213112 \tabularnewline
12 & -0.133673 & -1.53 & 0.064219 \tabularnewline
13 & 0.087177 & 0.9978 & 0.160111 \tabularnewline
14 & 0.002494 & 0.0286 & 0.488633 \tabularnewline
15 & 0.065332 & 0.7478 & 0.227972 \tabularnewline
16 & -0.109162 & -1.2494 & 0.106871 \tabularnewline
17 & -0.000338 & -0.0039 & 0.498462 \tabularnewline
18 & 0.044028 & 0.5039 & 0.307582 \tabularnewline
19 & -0.113945 & -1.3042 & 0.097232 \tabularnewline
20 & -0.091271 & -1.0446 & 0.149054 \tabularnewline
21 & 0.041943 & 0.4801 & 0.315994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=320242&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]-0.309815[/C][C]-3.546[/C][C]0.000272[/C][/ROW]
[ROW][C]2[/C][C]0.095351[/C][C]1.0913[/C][C]0.138562[/C][/ROW]
[ROW][C]3[/C][C]-0.096891[/C][C]-1.109[/C][C]0.134738[/C][/ROW]
[ROW][C]4[/C][C]-0.098995[/C][C]-1.133[/C][C]0.129631[/C][/ROW]
[ROW][C]5[/C][C]0.061001[/C][C]0.6982[/C][C]0.24315[/C][/ROW]
[ROW][C]6[/C][C]-0.000288[/C][C]-0.0033[/C][C]0.498688[/C][/ROW]
[ROW][C]7[/C][C]-0.056108[/C][C]-0.6422[/C][C]0.260936[/C][/ROW]
[ROW][C]8[/C][C]-0.060966[/C][C]-0.6978[/C][C]0.243274[/C][/ROW]
[ROW][C]9[/C][C]0.175917[/C][C]2.0135[/C][C]0.023057[/C][/ROW]
[ROW][C]10[/C][C]-0.140279[/C][C]-1.6056[/C][C]0.055389[/C][/ROW]
[ROW][C]11[/C][C]0.069735[/C][C]0.7982[/C][C]0.213112[/C][/ROW]
[ROW][C]12[/C][C]-0.133673[/C][C]-1.53[/C][C]0.064219[/C][/ROW]
[ROW][C]13[/C][C]0.087177[/C][C]0.9978[/C][C]0.160111[/C][/ROW]
[ROW][C]14[/C][C]0.002494[/C][C]0.0286[/C][C]0.488633[/C][/ROW]
[ROW][C]15[/C][C]0.065332[/C][C]0.7478[/C][C]0.227972[/C][/ROW]
[ROW][C]16[/C][C]-0.109162[/C][C]-1.2494[/C][C]0.106871[/C][/ROW]
[ROW][C]17[/C][C]-0.000338[/C][C]-0.0039[/C][C]0.498462[/C][/ROW]
[ROW][C]18[/C][C]0.044028[/C][C]0.5039[/C][C]0.307582[/C][/ROW]
[ROW][C]19[/C][C]-0.113945[/C][C]-1.3042[/C][C]0.097232[/C][/ROW]
[ROW][C]20[/C][C]-0.091271[/C][C]-1.0446[/C][C]0.149054[/C][/ROW]
[ROW][C]21[/C][C]0.041943[/C][C]0.4801[/C][C]0.315994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=320242&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=320242&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	-0.309815	-3.546	0.000272
2	0.095351	1.0913	0.138562
3	-0.096891	-1.109	0.134738
4	-0.098995	-1.133	0.129631
5	0.061001	0.6982	0.24315
6	-0.000288	-0.0033	0.498688
7	-0.056108	-0.6422	0.260936
8	-0.060966	-0.6978	0.243274
9	0.175917	2.0135	0.023057
10	-0.140279	-1.6056	0.055389
11	0.069735	0.7982	0.213112
12	-0.133673	-1.53	0.064219
13	0.087177	0.9978	0.160111
14	0.002494	0.0286	0.488633
15	0.065332	0.7478	0.227972
16	-0.109162	-1.2494	0.106871
17	-0.000338	-0.0039	0.498462
18	0.044028	0.5039	0.307582
19	-0.113945	-1.3042	0.097232
20	-0.091271	-1.0446	0.149054
21	0.041943	0.4801	0.315994

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.309815	-3.546	0.000272
2	-0.000701	-0.008	0.496806
3	-0.074718	-0.8552	0.197005
4	-0.166761	-1.9087	0.029247
5	-0.015146	-0.1734	0.431319
6	0.018288	0.2093	0.417265
7	-0.088086	-1.0082	0.157611
8	-0.133888	-1.5324	0.063916
9	0.156405	1.7901	0.03787
10	-0.05875	-0.6724	0.251251
11	-0.052428	-0.6001	0.274749
12	-0.115013	-1.3164	0.095172
13	0.059956	0.6862	0.246893
14	0.004318	0.0494	0.48033
15	0.036587	0.4188	0.338041
16	-0.086599	-0.9912	0.161715
17	-0.027835	-0.3186	0.375275
18	0.019117	0.2188	0.41357
19	-0.113792	-1.3024	0.097531
20	-0.256883	-2.9402	0.00194
21	0.006843	0.0783	0.468846

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.309815 & -3.546 & 0.000272 \tabularnewline
2 & -0.000701 & -0.008 & 0.496806 \tabularnewline
3 & -0.074718 & -0.8552 & 0.197005 \tabularnewline
4 & -0.166761 & -1.9087 & 0.029247 \tabularnewline
5 & -0.015146 & -0.1734 & 0.431319 \tabularnewline
6 & 0.018288 & 0.2093 & 0.417265 \tabularnewline
7 & -0.088086 & -1.0082 & 0.157611 \tabularnewline
8 & -0.133888 & -1.5324 & 0.063916 \tabularnewline
9 & 0.156405 & 1.7901 & 0.03787 \tabularnewline
10 & -0.05875 & -0.6724 & 0.251251 \tabularnewline
11 & -0.052428 & -0.6001 & 0.274749 \tabularnewline
12 & -0.115013 & -1.3164 & 0.095172 \tabularnewline
13 & 0.059956 & 0.6862 & 0.246893 \tabularnewline
14 & 0.004318 & 0.0494 & 0.48033 \tabularnewline
15 & 0.036587 & 0.4188 & 0.338041 \tabularnewline
16 & -0.086599 & -0.9912 & 0.161715 \tabularnewline
17 & -0.027835 & -0.3186 & 0.375275 \tabularnewline
18 & 0.019117 & 0.2188 & 0.41357 \tabularnewline
19 & -0.113792 & -1.3024 & 0.097531 \tabularnewline
20 & -0.256883 & -2.9402 & 0.00194 \tabularnewline
21 & 0.006843 & 0.0783 & 0.468846 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=320242&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]-0.309815[/C][C]-3.546[/C][C]0.000272[/C][/ROW]
[ROW][C]2[/C][C]-0.000701[/C][C]-0.008[/C][C]0.496806[/C][/ROW]
[ROW][C]3[/C][C]-0.074718[/C][C]-0.8552[/C][C]0.197005[/C][/ROW]
[ROW][C]4[/C][C]-0.166761[/C][C]-1.9087[/C][C]0.029247[/C][/ROW]
[ROW][C]5[/C][C]-0.015146[/C][C]-0.1734[/C][C]0.431319[/C][/ROW]
[ROW][C]6[/C][C]0.018288[/C][C]0.2093[/C][C]0.417265[/C][/ROW]
[ROW][C]7[/C][C]-0.088086[/C][C]-1.0082[/C][C]0.157611[/C][/ROW]
[ROW][C]8[/C][C]-0.133888[/C][C]-1.5324[/C][C]0.063916[/C][/ROW]
[ROW][C]9[/C][C]0.156405[/C][C]1.7901[/C][C]0.03787[/C][/ROW]
[ROW][C]10[/C][C]-0.05875[/C][C]-0.6724[/C][C]0.251251[/C][/ROW]
[ROW][C]11[/C][C]-0.052428[/C][C]-0.6001[/C][C]0.274749[/C][/ROW]
[ROW][C]12[/C][C]-0.115013[/C][C]-1.3164[/C][C]0.095172[/C][/ROW]
[ROW][C]13[/C][C]0.059956[/C][C]0.6862[/C][C]0.246893[/C][/ROW]
[ROW][C]14[/C][C]0.004318[/C][C]0.0494[/C][C]0.48033[/C][/ROW]
[ROW][C]15[/C][C]0.036587[/C][C]0.4188[/C][C]0.338041[/C][/ROW]
[ROW][C]16[/C][C]-0.086599[/C][C]-0.9912[/C][C]0.161715[/C][/ROW]
[ROW][C]17[/C][C]-0.027835[/C][C]-0.3186[/C][C]0.375275[/C][/ROW]
[ROW][C]18[/C][C]0.019117[/C][C]0.2188[/C][C]0.41357[/C][/ROW]
[ROW][C]19[/C][C]-0.113792[/C][C]-1.3024[/C][C]0.097531[/C][/ROW]
[ROW][C]20[/C][C]-0.256883[/C][C]-2.9402[/C][C]0.00194[/C][/ROW]
[ROW][C]21[/C][C]0.006843[/C][C]0.0783[/C][C]0.468846[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=320242&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=320242&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	-0.309815	-3.546	0.000272
2	-0.000701	-0.008	0.496806
3	-0.074718	-0.8552	0.197005
4	-0.166761	-1.9087	0.029247
5	-0.015146	-0.1734	0.431319
6	0.018288	0.2093	0.417265
7	-0.088086	-1.0082	0.157611
8	-0.133888	-1.5324	0.063916
9	0.156405	1.7901	0.03787
10	-0.05875	-0.6724	0.251251
11	-0.052428	-0.6001	0.274749
12	-0.115013	-1.3164	0.095172
13	0.059956	0.6862	0.246893
14	0.004318	0.0494	0.48033
15	0.036587	0.4188	0.338041
16	-0.086599	-0.9912	0.161715
17	-0.027835	-0.3186	0.375275
18	0.019117	0.2188	0.41357
19	-0.113792	-1.3024	0.097531
20	-0.256883	-2.9402	0.00194
21	0.006843	0.0783	0.468846

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 = 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 &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