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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 15 Dec 2010 16:31:24 +0000

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/2010/Dec/15/t12924305706hd2xbrzoe1w80s.htm/, Retrieved Fri, 03 May 2024 10:51:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110542, Retrieved Fri, 03 May 2024 10:51:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

182

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

-     [(Partial) Autocorrelation Function] [tutorial 2] [2010-12-13 19:20:33] [2db53827eae1799a3d605fb62e1e92dc]
- R  D    [(Partial) Autocorrelation Function] [Tutorial9] [2010-12-15 16:31:24] [6e19356a8195a048e2417405f21c29e8] [Current]
- R  D      [(Partial) Autocorrelation Function] [Workshop9] [2010-12-17 19:15:56] [8b2514d8f13517d765015fc185a22b4b] 
- R PD      [(Partial) Autocorrelation Function] [Workshop9] [2010-12-17 19:30:57] [8b2514d8f13517d765015fc185a22b4b] 
- R PD      [(Partial) Autocorrelation Function] [ACF OTR] [2010-12-17 20:24:20] [dc0ae7e1387be9b795f5d6299e383759] 
- R PD      [(Partial) Autocorrelation Function] [ACF OTR] [2010-12-17 20:24:20] [46df8573ee32a55e1a6edcfb6691f406] 

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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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110542&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110542&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110542&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' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.990176	21.9408	0
2	0.981015	21.7378	0
3	0.972838	21.5567	0
4	0.965112	21.3854	0
5	0.958127	21.2307	0
6	0.949942	21.0493	0
7	0.941492	20.8621	0
8	0.932852	20.6706	0
9	0.923266	20.4582	0
10	0.913187	20.2349	0
11	0.902438	19.9967	0
12	0.892361	19.7734	0
13	0.881145	19.5249	0
14	0.869388	19.2644	0
15	0.857295	18.9964	0
16	0.845578	18.7368	0
17	0.834653	18.4947	0
18	0.824232	18.2638	0
19	0.813963	18.0362	0
20	0.802938	17.7919	0
21	0.791685	17.5426	0
22	0.780115	17.2862	0
23	0.768375	17.0261	0
24	0.756937	16.7726	0
25	0.746513	16.5416	0
26	0.736408	16.3177	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.990176 & 21.9408 & 0 \tabularnewline
2 & 0.981015 & 21.7378 & 0 \tabularnewline
3 & 0.972838 & 21.5567 & 0 \tabularnewline
4 & 0.965112 & 21.3854 & 0 \tabularnewline
5 & 0.958127 & 21.2307 & 0 \tabularnewline
6 & 0.949942 & 21.0493 & 0 \tabularnewline
7 & 0.941492 & 20.8621 & 0 \tabularnewline
8 & 0.932852 & 20.6706 & 0 \tabularnewline
9 & 0.923266 & 20.4582 & 0 \tabularnewline
10 & 0.913187 & 20.2349 & 0 \tabularnewline
11 & 0.902438 & 19.9967 & 0 \tabularnewline
12 & 0.892361 & 19.7734 & 0 \tabularnewline
13 & 0.881145 & 19.5249 & 0 \tabularnewline
14 & 0.869388 & 19.2644 & 0 \tabularnewline
15 & 0.857295 & 18.9964 & 0 \tabularnewline
16 & 0.845578 & 18.7368 & 0 \tabularnewline
17 & 0.834653 & 18.4947 & 0 \tabularnewline
18 & 0.824232 & 18.2638 & 0 \tabularnewline
19 & 0.813963 & 18.0362 & 0 \tabularnewline
20 & 0.802938 & 17.7919 & 0 \tabularnewline
21 & 0.791685 & 17.5426 & 0 \tabularnewline
22 & 0.780115 & 17.2862 & 0 \tabularnewline
23 & 0.768375 & 17.0261 & 0 \tabularnewline
24 & 0.756937 & 16.7726 & 0 \tabularnewline
25 & 0.746513 & 16.5416 & 0 \tabularnewline
26 & 0.736408 & 16.3177 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110542&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]0.990176[/C][C]21.9408[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.981015[/C][C]21.7378[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.972838[/C][C]21.5567[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.965112[/C][C]21.3854[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.958127[/C][C]21.2307[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.949942[/C][C]21.0493[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.941492[/C][C]20.8621[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.932852[/C][C]20.6706[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.923266[/C][C]20.4582[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.913187[/C][C]20.2349[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.902438[/C][C]19.9967[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.892361[/C][C]19.7734[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.881145[/C][C]19.5249[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.869388[/C][C]19.2644[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.857295[/C][C]18.9964[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.845578[/C][C]18.7368[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.834653[/C][C]18.4947[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.824232[/C][C]18.2638[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.813963[/C][C]18.0362[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.802938[/C][C]17.7919[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.791685[/C][C]17.5426[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.780115[/C][C]17.2862[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.768375[/C][C]17.0261[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.756937[/C][C]16.7726[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.746513[/C][C]16.5416[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]0.736408[/C][C]16.3177[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110542&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110542&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	0.990176	21.9408	0
2	0.981015	21.7378	0
3	0.972838	21.5567	0
4	0.965112	21.3854	0
5	0.958127	21.2307	0
6	0.949942	21.0493	0
7	0.941492	20.8621	0
8	0.932852	20.6706	0
9	0.923266	20.4582	0
10	0.913187	20.2349	0
11	0.902438	19.9967	0
12	0.892361	19.7734	0
13	0.881145	19.5249	0
14	0.869388	19.2644	0
15	0.857295	18.9964	0
16	0.845578	18.7368	0
17	0.834653	18.4947	0
18	0.824232	18.2638	0
19	0.813963	18.0362	0
20	0.802938	17.7919	0
21	0.791685	17.5426	0
22	0.780115	17.2862	0
23	0.768375	17.0261	0
24	0.756937	16.7726	0
25	0.746513	16.5416	0
26	0.736408	16.3177	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.990176	21.9408	0
2	0.028971	0.642	0.260601
3	0.046889	1.039	0.149659
4	0.022419	0.4968	0.309783
5	0.038508	0.8533	0.196958
6	-0.059854	-1.3263	0.092683
7	-0.017272	-0.3827	0.35105
8	-0.019268	-0.4269	0.334805
9	-0.056911	-1.2611	0.103941
10	-0.040713	-0.9021	0.18371
11	-0.045973	-1.0187	0.154425
12	0.021103	0.4676	0.320136
13	-0.069953	-1.5501	0.060886
14	-0.033588	-0.7443	0.228536
15	-0.029111	-0.6451	0.259597
16	0.0141	0.3124	0.377419
17	0.028711	0.6362	0.262476
18	0.03282	0.7272	0.233715
19	0.018256	0.4045	0.343
20	-0.032309	-0.7159	0.237189
21	-0.008992	-0.1993	0.421072
22	-0.0241	-0.534	0.296788
23	-0.01442	-0.3195	0.374733
24	-0.003157	-0.0699	0.472132
25	0.045942	1.018	0.154587
26	0.010902	0.2416	0.404603

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.990176 & 21.9408 & 0 \tabularnewline
2 & 0.028971 & 0.642 & 0.260601 \tabularnewline
3 & 0.046889 & 1.039 & 0.149659 \tabularnewline
4 & 0.022419 & 0.4968 & 0.309783 \tabularnewline
5 & 0.038508 & 0.8533 & 0.196958 \tabularnewline
6 & -0.059854 & -1.3263 & 0.092683 \tabularnewline
7 & -0.017272 & -0.3827 & 0.35105 \tabularnewline
8 & -0.019268 & -0.4269 & 0.334805 \tabularnewline
9 & -0.056911 & -1.2611 & 0.103941 \tabularnewline
10 & -0.040713 & -0.9021 & 0.18371 \tabularnewline
11 & -0.045973 & -1.0187 & 0.154425 \tabularnewline
12 & 0.021103 & 0.4676 & 0.320136 \tabularnewline
13 & -0.069953 & -1.5501 & 0.060886 \tabularnewline
14 & -0.033588 & -0.7443 & 0.228536 \tabularnewline
15 & -0.029111 & -0.6451 & 0.259597 \tabularnewline
16 & 0.0141 & 0.3124 & 0.377419 \tabularnewline
17 & 0.028711 & 0.6362 & 0.262476 \tabularnewline
18 & 0.03282 & 0.7272 & 0.233715 \tabularnewline
19 & 0.018256 & 0.4045 & 0.343 \tabularnewline
20 & -0.032309 & -0.7159 & 0.237189 \tabularnewline
21 & -0.008992 & -0.1993 & 0.421072 \tabularnewline
22 & -0.0241 & -0.534 & 0.296788 \tabularnewline
23 & -0.01442 & -0.3195 & 0.374733 \tabularnewline
24 & -0.003157 & -0.0699 & 0.472132 \tabularnewline
25 & 0.045942 & 1.018 & 0.154587 \tabularnewline
26 & 0.010902 & 0.2416 & 0.404603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110542&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]0.990176[/C][C]21.9408[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.028971[/C][C]0.642[/C][C]0.260601[/C][/ROW]
[ROW][C]3[/C][C]0.046889[/C][C]1.039[/C][C]0.149659[/C][/ROW]
[ROW][C]4[/C][C]0.022419[/C][C]0.4968[/C][C]0.309783[/C][/ROW]
[ROW][C]5[/C][C]0.038508[/C][C]0.8533[/C][C]0.196958[/C][/ROW]
[ROW][C]6[/C][C]-0.059854[/C][C]-1.3263[/C][C]0.092683[/C][/ROW]
[ROW][C]7[/C][C]-0.017272[/C][C]-0.3827[/C][C]0.35105[/C][/ROW]
[ROW][C]8[/C][C]-0.019268[/C][C]-0.4269[/C][C]0.334805[/C][/ROW]
[ROW][C]9[/C][C]-0.056911[/C][C]-1.2611[/C][C]0.103941[/C][/ROW]
[ROW][C]10[/C][C]-0.040713[/C][C]-0.9021[/C][C]0.18371[/C][/ROW]
[ROW][C]11[/C][C]-0.045973[/C][C]-1.0187[/C][C]0.154425[/C][/ROW]
[ROW][C]12[/C][C]0.021103[/C][C]0.4676[/C][C]0.320136[/C][/ROW]
[ROW][C]13[/C][C]-0.069953[/C][C]-1.5501[/C][C]0.060886[/C][/ROW]
[ROW][C]14[/C][C]-0.033588[/C][C]-0.7443[/C][C]0.228536[/C][/ROW]
[ROW][C]15[/C][C]-0.029111[/C][C]-0.6451[/C][C]0.259597[/C][/ROW]
[ROW][C]16[/C][C]0.0141[/C][C]0.3124[/C][C]0.377419[/C][/ROW]
[ROW][C]17[/C][C]0.028711[/C][C]0.6362[/C][C]0.262476[/C][/ROW]
[ROW][C]18[/C][C]0.03282[/C][C]0.7272[/C][C]0.233715[/C][/ROW]
[ROW][C]19[/C][C]0.018256[/C][C]0.4045[/C][C]0.343[/C][/ROW]
[ROW][C]20[/C][C]-0.032309[/C][C]-0.7159[/C][C]0.237189[/C][/ROW]
[ROW][C]21[/C][C]-0.008992[/C][C]-0.1993[/C][C]0.421072[/C][/ROW]
[ROW][C]22[/C][C]-0.0241[/C][C]-0.534[/C][C]0.296788[/C][/ROW]
[ROW][C]23[/C][C]-0.01442[/C][C]-0.3195[/C][C]0.374733[/C][/ROW]
[ROW][C]24[/C][C]-0.003157[/C][C]-0.0699[/C][C]0.472132[/C][/ROW]
[ROW][C]25[/C][C]0.045942[/C][C]1.018[/C][C]0.154587[/C][/ROW]
[ROW][C]26[/C][C]0.010902[/C][C]0.2416[/C][C]0.404603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110542&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110542&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	0.990176	21.9408	0
2	0.028971	0.642	0.260601
3	0.046889	1.039	0.149659
4	0.022419	0.4968	0.309783
5	0.038508	0.8533	0.196958
6	-0.059854	-1.3263	0.092683
7	-0.017272	-0.3827	0.35105
8	-0.019268	-0.4269	0.334805
9	-0.056911	-1.2611	0.103941
10	-0.040713	-0.9021	0.18371
11	-0.045973	-1.0187	0.154425
12	0.021103	0.4676	0.320136
13	-0.069953	-1.5501	0.060886
14	-0.033588	-0.7443	0.228536
15	-0.029111	-0.6451	0.259597
16	0.0141	0.3124	0.377419
17	0.028711	0.6362	0.262476
18	0.03282	0.7272	0.233715
19	0.018256	0.4045	0.343
20	-0.032309	-0.7159	0.237189
21	-0.008992	-0.1993	0.421072
22	-0.0241	-0.534	0.296788
23	-0.01442	-0.3195	0.374733
24	-0.003157	-0.0699	0.472132
25	0.045942	1.018	0.154587
26	0.010902	0.2416	0.404603

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 <- 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