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R Software Module

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 06 Dec 2011 15:37:55 -0500

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/2011/Dec/06/t1323203895wuhgfxbwgw73een.htm/, Retrieved Sun, 28 Apr 2024 22:01:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151917, Retrieved Sun, 28 Apr 2024 22:01:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

102

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R  D    [(Partial) Autocorrelation Function] [WS9 - ACF] [2010-12-07 08:36:37] [1f5baf2b24e732d76900bb8178fc04e7]
- R         [(Partial) Autocorrelation Function] [Autocorrelatie] [2011-12-06 20:26:10] [19d77e37efa419fdc040c74a96874aff]
- RM            [(Partial) Autocorrelation Function] [] [2011-12-06 20:37:55] [0f9b7c3b8d01420b2751adc6f98a35df] [Current]

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Dataseries X:

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Histogram

Boxplots

2.4
2.4
2.5
2.6
2.4
2.6
2.4
2.3
2.4
2.4
2.4
2.4
2.4
2.4
2.4
2.4
2.5
2.1
2.1
2
2
2
1.9
1.9
2
1.8
1.6
1.3
1.4
1.4
1.5
1.7
1.6
1.5
1.6
1.5
1.1
1.1
1.1
1.4
1.3
1.4
1.3
1.1
1
0.9
0.8
0.8
0.8
0.8
1
1.1
1
0.9
1.1
1.2
1.2
1.4
1.5
1.7
1.9
1.9
1.9
1.7
1.7
2.1
2
2
2.5
2.4
2.5
2.5
2
1.9
2.2
2.7
3.1
2.8
2.6
2.3
2.2
2.2
2
2
2.6
2.5
2.5
2.3
2
1.9
2
2.1
2.1
2.3
2.3
2.3
2.1
2.4
2.5
2.1
1.8
1.9
1.9
2.1
2.2
2
2.2
2
1.9
1.6
1.7
2
2.5
2.4
2.3
2.3
2.1
2.4
2.2
2.4
1.9
2.1
2.1
2.1
2
2.1
2.2
2.2
2.6
2.5
2.3
2.2
2.4
2.3
2.2
2.5
2.5
2.5
2.4
2.3
1.7
1.6
1.9
1.9
1.8
1.8
1.9
1.9
1.9
1.9
1.8
1.7
2.1
2.6
3.1
3.1
3.2
3.3
3.6
3.3
3.7
4
4
3.8
3.6
3.2
2.1
1.6
1.1
1.2
0.6
0.6
0
-0.1
-0.6
-0.2
-0.3
-0.1
0.5
0.9

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151917&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151917&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151917&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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.941868	12.6365	0
2	0.859886	11.5366	0
3	0.755657	10.1382	0
4	0.652835	8.7587	0
5	0.546721	7.335	0
6	0.445576	5.978	0
7	0.345007	4.6288	4e-06
8	0.239836	3.2177	0.000766
9	0.136661	1.8335	0.03419
10	0.029079	0.3901	0.348446
11	-0.071669	-0.9615	0.168785
12	-0.171304	-2.2983	0.011348
13	-0.218232	-2.9279	0.001927
14	-0.237625	-3.1881	0.000845
15	-0.225293	-3.0226	0.001436
16	-0.204488	-2.7435	0.003347
17	-0.181149	-2.4304	0.008032
18	-0.156952	-2.1057	0.018307
19	-0.131287	-1.7614	0.039934
20	-0.110079	-1.4769	0.070729
21	-0.091958	-1.2337	0.109454
22	-0.06944	-0.9316	0.176386

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.941868 & 12.6365 & 0 \tabularnewline
2 & 0.859886 & 11.5366 & 0 \tabularnewline
3 & 0.755657 & 10.1382 & 0 \tabularnewline
4 & 0.652835 & 8.7587 & 0 \tabularnewline
5 & 0.546721 & 7.335 & 0 \tabularnewline
6 & 0.445576 & 5.978 & 0 \tabularnewline
7 & 0.345007 & 4.6288 & 4e-06 \tabularnewline
8 & 0.239836 & 3.2177 & 0.000766 \tabularnewline
9 & 0.136661 & 1.8335 & 0.03419 \tabularnewline
10 & 0.029079 & 0.3901 & 0.348446 \tabularnewline
11 & -0.071669 & -0.9615 & 0.168785 \tabularnewline
12 & -0.171304 & -2.2983 & 0.011348 \tabularnewline
13 & -0.218232 & -2.9279 & 0.001927 \tabularnewline
14 & -0.237625 & -3.1881 & 0.000845 \tabularnewline
15 & -0.225293 & -3.0226 & 0.001436 \tabularnewline
16 & -0.204488 & -2.7435 & 0.003347 \tabularnewline
17 & -0.181149 & -2.4304 & 0.008032 \tabularnewline
18 & -0.156952 & -2.1057 & 0.018307 \tabularnewline
19 & -0.131287 & -1.7614 & 0.039934 \tabularnewline
20 & -0.110079 & -1.4769 & 0.070729 \tabularnewline
21 & -0.091958 & -1.2337 & 0.109454 \tabularnewline
22 & -0.06944 & -0.9316 & 0.176386 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151917&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]0.941868[/C][C]12.6365[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.859886[/C][C]11.5366[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.755657[/C][C]10.1382[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.652835[/C][C]8.7587[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.546721[/C][C]7.335[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.445576[/C][C]5.978[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.345007[/C][C]4.6288[/C][C]4e-06[/C][/ROW]
[ROW][C]8[/C][C]0.239836[/C][C]3.2177[/C][C]0.000766[/C][/ROW]
[ROW][C]9[/C][C]0.136661[/C][C]1.8335[/C][C]0.03419[/C][/ROW]
[ROW][C]10[/C][C]0.029079[/C][C]0.3901[/C][C]0.348446[/C][/ROW]
[ROW][C]11[/C][C]-0.071669[/C][C]-0.9615[/C][C]0.168785[/C][/ROW]
[ROW][C]12[/C][C]-0.171304[/C][C]-2.2983[/C][C]0.011348[/C][/ROW]
[ROW][C]13[/C][C]-0.218232[/C][C]-2.9279[/C][C]0.001927[/C][/ROW]
[ROW][C]14[/C][C]-0.237625[/C][C]-3.1881[/C][C]0.000845[/C][/ROW]
[ROW][C]15[/C][C]-0.225293[/C][C]-3.0226[/C][C]0.001436[/C][/ROW]
[ROW][C]16[/C][C]-0.204488[/C][C]-2.7435[/C][C]0.003347[/C][/ROW]
[ROW][C]17[/C][C]-0.181149[/C][C]-2.4304[/C][C]0.008032[/C][/ROW]
[ROW][C]18[/C][C]-0.156952[/C][C]-2.1057[/C][C]0.018307[/C][/ROW]
[ROW][C]19[/C][C]-0.131287[/C][C]-1.7614[/C][C]0.039934[/C][/ROW]
[ROW][C]20[/C][C]-0.110079[/C][C]-1.4769[/C][C]0.070729[/C][/ROW]
[ROW][C]21[/C][C]-0.091958[/C][C]-1.2337[/C][C]0.109454[/C][/ROW]
[ROW][C]22[/C][C]-0.06944[/C][C]-0.9316[/C][C]0.176386[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151917&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151917&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	0.941868	12.6365	0
2	0.859886	11.5366	0
3	0.755657	10.1382	0
4	0.652835	8.7587	0
5	0.546721	7.335	0
6	0.445576	5.978	0
7	0.345007	4.6288	4e-06
8	0.239836	3.2177	0.000766
9	0.136661	1.8335	0.03419
10	0.029079	0.3901	0.348446
11	-0.071669	-0.9615	0.168785
12	-0.171304	-2.2983	0.011348
13	-0.218232	-2.9279	0.001927
14	-0.237625	-3.1881	0.000845
15	-0.225293	-3.0226	0.001436
16	-0.204488	-2.7435	0.003347
17	-0.181149	-2.4304	0.008032
18	-0.156952	-2.1057	0.018307
19	-0.131287	-1.7614	0.039934
20	-0.110079	-1.4769	0.070729
21	-0.091958	-1.2337	0.109454
22	-0.06944	-0.9316	0.176386

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.941868	12.6365	0
2	-0.241214	-3.2362	0.000721
3	-0.210775	-2.8278	0.002609
4	0.018726	0.2512	0.400961
5	-0.079847	-1.0713	0.142743
6	-0.031273	-0.4196	0.33765
7	-0.069385	-0.9309	0.176577
8	-0.139944	-1.8775	0.031031
9	-0.045306	-0.6078	0.272027
10	-0.129875	-1.7425	0.041568
11	-0.038098	-0.5111	0.304942
12	-0.100088	-1.3428	0.090511
13	0.393359	5.2775	0
14	0.064418	0.8643	0.1943
15	0.060483	0.8115	0.209085
16	-0.026416	-0.3544	0.361726
17	-0.094129	-1.2629	0.104135
18	0.015484	0.2077	0.417835
19	-0.002218	-0.0298	0.488149
20	-0.142641	-1.9137	0.028621
21	-0.046582	-0.625	0.266392
22	-0.016675	-0.2237	0.411614

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.941868 & 12.6365 & 0 \tabularnewline
2 & -0.241214 & -3.2362 & 0.000721 \tabularnewline
3 & -0.210775 & -2.8278 & 0.002609 \tabularnewline
4 & 0.018726 & 0.2512 & 0.400961 \tabularnewline
5 & -0.079847 & -1.0713 & 0.142743 \tabularnewline
6 & -0.031273 & -0.4196 & 0.33765 \tabularnewline
7 & -0.069385 & -0.9309 & 0.176577 \tabularnewline
8 & -0.139944 & -1.8775 & 0.031031 \tabularnewline
9 & -0.045306 & -0.6078 & 0.272027 \tabularnewline
10 & -0.129875 & -1.7425 & 0.041568 \tabularnewline
11 & -0.038098 & -0.5111 & 0.304942 \tabularnewline
12 & -0.100088 & -1.3428 & 0.090511 \tabularnewline
13 & 0.393359 & 5.2775 & 0 \tabularnewline
14 & 0.064418 & 0.8643 & 0.1943 \tabularnewline
15 & 0.060483 & 0.8115 & 0.209085 \tabularnewline
16 & -0.026416 & -0.3544 & 0.361726 \tabularnewline
17 & -0.094129 & -1.2629 & 0.104135 \tabularnewline
18 & 0.015484 & 0.2077 & 0.417835 \tabularnewline
19 & -0.002218 & -0.0298 & 0.488149 \tabularnewline
20 & -0.142641 & -1.9137 & 0.028621 \tabularnewline
21 & -0.046582 & -0.625 & 0.266392 \tabularnewline
22 & -0.016675 & -0.2237 & 0.411614 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151917&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]0.941868[/C][C]12.6365[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.241214[/C][C]-3.2362[/C][C]0.000721[/C][/ROW]
[ROW][C]3[/C][C]-0.210775[/C][C]-2.8278[/C][C]0.002609[/C][/ROW]
[ROW][C]4[/C][C]0.018726[/C][C]0.2512[/C][C]0.400961[/C][/ROW]
[ROW][C]5[/C][C]-0.079847[/C][C]-1.0713[/C][C]0.142743[/C][/ROW]
[ROW][C]6[/C][C]-0.031273[/C][C]-0.4196[/C][C]0.33765[/C][/ROW]
[ROW][C]7[/C][C]-0.069385[/C][C]-0.9309[/C][C]0.176577[/C][/ROW]
[ROW][C]8[/C][C]-0.139944[/C][C]-1.8775[/C][C]0.031031[/C][/ROW]
[ROW][C]9[/C][C]-0.045306[/C][C]-0.6078[/C][C]0.272027[/C][/ROW]
[ROW][C]10[/C][C]-0.129875[/C][C]-1.7425[/C][C]0.041568[/C][/ROW]
[ROW][C]11[/C][C]-0.038098[/C][C]-0.5111[/C][C]0.304942[/C][/ROW]
[ROW][C]12[/C][C]-0.100088[/C][C]-1.3428[/C][C]0.090511[/C][/ROW]
[ROW][C]13[/C][C]0.393359[/C][C]5.2775[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.064418[/C][C]0.8643[/C][C]0.1943[/C][/ROW]
[ROW][C]15[/C][C]0.060483[/C][C]0.8115[/C][C]0.209085[/C][/ROW]
[ROW][C]16[/C][C]-0.026416[/C][C]-0.3544[/C][C]0.361726[/C][/ROW]
[ROW][C]17[/C][C]-0.094129[/C][C]-1.2629[/C][C]0.104135[/C][/ROW]
[ROW][C]18[/C][C]0.015484[/C][C]0.2077[/C][C]0.417835[/C][/ROW]
[ROW][C]19[/C][C]-0.002218[/C][C]-0.0298[/C][C]0.488149[/C][/ROW]
[ROW][C]20[/C][C]-0.142641[/C][C]-1.9137[/C][C]0.028621[/C][/ROW]
[ROW][C]21[/C][C]-0.046582[/C][C]-0.625[/C][C]0.266392[/C][/ROW]
[ROW][C]22[/C][C]-0.016675[/C][C]-0.2237[/C][C]0.411614[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151917&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151917&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	0.941868	12.6365	0
2	-0.241214	-3.2362	0.000721
3	-0.210775	-2.8278	0.002609
4	0.018726	0.2512	0.400961
5	-0.079847	-1.0713	0.142743
6	-0.031273	-0.4196	0.33765
7	-0.069385	-0.9309	0.176577
8	-0.139944	-1.8775	0.031031
9	-0.045306	-0.6078	0.272027
10	-0.129875	-1.7425	0.041568
11	-0.038098	-0.5111	0.304942
12	-0.100088	-1.3428	0.090511
13	0.393359	5.2775	0
14	0.064418	0.8643	0.1943
15	0.060483	0.8115	0.209085
16	-0.026416	-0.3544	0.361726
17	-0.094129	-1.2629	0.104135
18	0.015484	0.2077	0.417835
19	-0.002218	-0.0298	0.488149
20	-0.142641	-1.9137	0.028621
21	-0.046582	-0.625	0.266392
22	-0.016675	-0.2237	0.411614

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 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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)
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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