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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 20 Nov 2013 13:34:44 -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/2013/Nov/20/t1384972497uzem6xgwp2wih95.htm/, Retrieved Wed, 01 May 2024 13:20:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226706, Retrieved Wed, 01 May 2024 13:20:58 +0000

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Original text written by user:

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User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2013-11-20 18:34:44] [f6b0814d1ccce07ea30140b42d9cb647] [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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226706&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226706&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226706&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.156521	-0.7507	0.230237
2	-0.163043	-0.7819	0.221117
3	-0.169564	-0.8132	0.21222
4	-0.176086	-0.8445	0.20355
5	-0.182607	-0.8758	0.195109
6	0.677536	3.2493	0.001768
7	-0.095652	-0.4587	0.325366
8	-0.102174	-0.49	0.314385
9	-0.108695	-0.5213	0.303576
10	-0.115217	-0.5526	0.292948
11	-0.121738	-0.5838	0.282507
12	0.355072	1.7029	0.051036
13	-0.034783	-0.1668	0.434487
14	-0.041305	-0.1981	0.422357
15	-0.047826	-0.2294	0.410306
16	-0.054348	-0.2606	0.398344
17	-0.060869	-0.2919	0.386483
18	0.032607	0.1564	0.438549
19	0.026086	0.1251	0.450764
20	0.019564	0.0938	0.463029
21	0.013043	0.0626	0.475332
22	0.006521	0.0313	0.48766
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 & -0.156521 & -0.7507 & 0.230237 \tabularnewline
2 & -0.163043 & -0.7819 & 0.221117 \tabularnewline
3 & -0.169564 & -0.8132 & 0.21222 \tabularnewline
4 & -0.176086 & -0.8445 & 0.20355 \tabularnewline
5 & -0.182607 & -0.8758 & 0.195109 \tabularnewline
6 & 0.677536 & 3.2493 & 0.001768 \tabularnewline
7 & -0.095652 & -0.4587 & 0.325366 \tabularnewline
8 & -0.102174 & -0.49 & 0.314385 \tabularnewline
9 & -0.108695 & -0.5213 & 0.303576 \tabularnewline
10 & -0.115217 & -0.5526 & 0.292948 \tabularnewline
11 & -0.121738 & -0.5838 & 0.282507 \tabularnewline
12 & 0.355072 & 1.7029 & 0.051036 \tabularnewline
13 & -0.034783 & -0.1668 & 0.434487 \tabularnewline
14 & -0.041305 & -0.1981 & 0.422357 \tabularnewline
15 & -0.047826 & -0.2294 & 0.410306 \tabularnewline
16 & -0.054348 & -0.2606 & 0.398344 \tabularnewline
17 & -0.060869 & -0.2919 & 0.386483 \tabularnewline
18 & 0.032607 & 0.1564 & 0.438549 \tabularnewline
19 & 0.026086 & 0.1251 & 0.450764 \tabularnewline
20 & 0.019564 & 0.0938 & 0.463029 \tabularnewline
21 & 0.013043 & 0.0626 & 0.475332 \tabularnewline
22 & 0.006521 & 0.0313 & 0.48766 \tabularnewline
23 & NA & NA & NA \tabularnewline
24 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226706&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]-0.156521[/C][C]-0.7507[/C][C]0.230237[/C][/ROW]
[ROW][C]2[/C][C]-0.163043[/C][C]-0.7819[/C][C]0.221117[/C][/ROW]
[ROW][C]3[/C][C]-0.169564[/C][C]-0.8132[/C][C]0.21222[/C][/ROW]
[ROW][C]4[/C][C]-0.176086[/C][C]-0.8445[/C][C]0.20355[/C][/ROW]
[ROW][C]5[/C][C]-0.182607[/C][C]-0.8758[/C][C]0.195109[/C][/ROW]
[ROW][C]6[/C][C]0.677536[/C][C]3.2493[/C][C]0.001768[/C][/ROW]
[ROW][C]7[/C][C]-0.095652[/C][C]-0.4587[/C][C]0.325366[/C][/ROW]
[ROW][C]8[/C][C]-0.102174[/C][C]-0.49[/C][C]0.314385[/C][/ROW]
[ROW][C]9[/C][C]-0.108695[/C][C]-0.5213[/C][C]0.303576[/C][/ROW]
[ROW][C]10[/C][C]-0.115217[/C][C]-0.5526[/C][C]0.292948[/C][/ROW]
[ROW][C]11[/C][C]-0.121738[/C][C]-0.5838[/C][C]0.282507[/C][/ROW]
[ROW][C]12[/C][C]0.355072[/C][C]1.7029[/C][C]0.051036[/C][/ROW]
[ROW][C]13[/C][C]-0.034783[/C][C]-0.1668[/C][C]0.434487[/C][/ROW]
[ROW][C]14[/C][C]-0.041305[/C][C]-0.1981[/C][C]0.422357[/C][/ROW]
[ROW][C]15[/C][C]-0.047826[/C][C]-0.2294[/C][C]0.410306[/C][/ROW]
[ROW][C]16[/C][C]-0.054348[/C][C]-0.2606[/C][C]0.398344[/C][/ROW]
[ROW][C]17[/C][C]-0.060869[/C][C]-0.2919[/C][C]0.386483[/C][/ROW]
[ROW][C]18[/C][C]0.032607[/C][C]0.1564[/C][C]0.438549[/C][/ROW]
[ROW][C]19[/C][C]0.026086[/C][C]0.1251[/C][C]0.450764[/C][/ROW]
[ROW][C]20[/C][C]0.019564[/C][C]0.0938[/C][C]0.463029[/C][/ROW]
[ROW][C]21[/C][C]0.013043[/C][C]0.0626[/C][C]0.475332[/C][/ROW]
[ROW][C]22[/C][C]0.006521[/C][C]0.0313[/C][C]0.48766[/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=226706&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226706&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	-0.156521	-0.7507	0.230237
2	-0.163043	-0.7819	0.221117
3	-0.169564	-0.8132	0.21222
4	-0.176086	-0.8445	0.20355
5	-0.182607	-0.8758	0.195109
6	0.677536	3.2493	0.001768
7	-0.095652	-0.4587	0.325366
8	-0.102174	-0.49	0.314385
9	-0.108695	-0.5213	0.303576
10	-0.115217	-0.5526	0.292948
11	-0.121738	-0.5838	0.282507
12	0.355072	1.7029	0.051036
13	-0.034783	-0.1668	0.434487
14	-0.041305	-0.1981	0.422357
15	-0.047826	-0.2294	0.410306
16	-0.054348	-0.2606	0.398344
17	-0.060869	-0.2919	0.386483
18	0.032607	0.1564	0.438549
19	0.026086	0.1251	0.450764
20	0.019564	0.0938	0.463029
21	0.013043	0.0626	0.475332
22	0.006521	0.0313	0.48766
23	NA	NA	NA
24	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.156522	-0.7507	0.230237
2	-0.192253	-0.922	0.183047
3	-0.244914	-1.1746	0.126093
4	-0.331613	-1.5904	0.062703
5	-0.504161	-2.4179	0.011968
6	0.451137	2.1636	0.020565
7	-0.084525	-0.4054	0.344477
8	-0.068584	-0.3289	0.372597
9	-0.041813	-0.2005	0.421414
10	-0.000461	-0.0022	0.499127
11	0.059541	0.2855	0.388891
12	-0.22676	-1.0875	0.14404
13	-0.037031	-0.1776	0.430299
14	-0.029804	-0.1429	0.443793
15	-0.024906	-0.1194	0.45298
16	-0.024906	-0.1194	0.452979
17	-0.033402	-0.1602	0.437065
18	-0.292292	-1.4018	0.087166
19	-0.078325	-0.3756	0.355315
20	-0.084488	-0.4052	0.344541
21	-0.092494	-0.4436	0.330744
22	-0.102123	-0.4898	0.31447
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 & -0.156522 & -0.7507 & 0.230237 \tabularnewline
2 & -0.192253 & -0.922 & 0.183047 \tabularnewline
3 & -0.244914 & -1.1746 & 0.126093 \tabularnewline
4 & -0.331613 & -1.5904 & 0.062703 \tabularnewline
5 & -0.504161 & -2.4179 & 0.011968 \tabularnewline
6 & 0.451137 & 2.1636 & 0.020565 \tabularnewline
7 & -0.084525 & -0.4054 & 0.344477 \tabularnewline
8 & -0.068584 & -0.3289 & 0.372597 \tabularnewline
9 & -0.041813 & -0.2005 & 0.421414 \tabularnewline
10 & -0.000461 & -0.0022 & 0.499127 \tabularnewline
11 & 0.059541 & 0.2855 & 0.388891 \tabularnewline
12 & -0.22676 & -1.0875 & 0.14404 \tabularnewline
13 & -0.037031 & -0.1776 & 0.430299 \tabularnewline
14 & -0.029804 & -0.1429 & 0.443793 \tabularnewline
15 & -0.024906 & -0.1194 & 0.45298 \tabularnewline
16 & -0.024906 & -0.1194 & 0.452979 \tabularnewline
17 & -0.033402 & -0.1602 & 0.437065 \tabularnewline
18 & -0.292292 & -1.4018 & 0.087166 \tabularnewline
19 & -0.078325 & -0.3756 & 0.355315 \tabularnewline
20 & -0.084488 & -0.4052 & 0.344541 \tabularnewline
21 & -0.092494 & -0.4436 & 0.330744 \tabularnewline
22 & -0.102123 & -0.4898 & 0.31447 \tabularnewline
23 & NA & NA & NA \tabularnewline
24 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226706&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]-0.156522[/C][C]-0.7507[/C][C]0.230237[/C][/ROW]
[ROW][C]2[/C][C]-0.192253[/C][C]-0.922[/C][C]0.183047[/C][/ROW]
[ROW][C]3[/C][C]-0.244914[/C][C]-1.1746[/C][C]0.126093[/C][/ROW]
[ROW][C]4[/C][C]-0.331613[/C][C]-1.5904[/C][C]0.062703[/C][/ROW]
[ROW][C]5[/C][C]-0.504161[/C][C]-2.4179[/C][C]0.011968[/C][/ROW]
[ROW][C]6[/C][C]0.451137[/C][C]2.1636[/C][C]0.020565[/C][/ROW]
[ROW][C]7[/C][C]-0.084525[/C][C]-0.4054[/C][C]0.344477[/C][/ROW]
[ROW][C]8[/C][C]-0.068584[/C][C]-0.3289[/C][C]0.372597[/C][/ROW]
[ROW][C]9[/C][C]-0.041813[/C][C]-0.2005[/C][C]0.421414[/C][/ROW]
[ROW][C]10[/C][C]-0.000461[/C][C]-0.0022[/C][C]0.499127[/C][/ROW]
[ROW][C]11[/C][C]0.059541[/C][C]0.2855[/C][C]0.388891[/C][/ROW]
[ROW][C]12[/C][C]-0.22676[/C][C]-1.0875[/C][C]0.14404[/C][/ROW]
[ROW][C]13[/C][C]-0.037031[/C][C]-0.1776[/C][C]0.430299[/C][/ROW]
[ROW][C]14[/C][C]-0.029804[/C][C]-0.1429[/C][C]0.443793[/C][/ROW]
[ROW][C]15[/C][C]-0.024906[/C][C]-0.1194[/C][C]0.45298[/C][/ROW]
[ROW][C]16[/C][C]-0.024906[/C][C]-0.1194[/C][C]0.452979[/C][/ROW]
[ROW][C]17[/C][C]-0.033402[/C][C]-0.1602[/C][C]0.437065[/C][/ROW]
[ROW][C]18[/C][C]-0.292292[/C][C]-1.4018[/C][C]0.087166[/C][/ROW]
[ROW][C]19[/C][C]-0.078325[/C][C]-0.3756[/C][C]0.355315[/C][/ROW]
[ROW][C]20[/C][C]-0.084488[/C][C]-0.4052[/C][C]0.344541[/C][/ROW]
[ROW][C]21[/C][C]-0.092494[/C][C]-0.4436[/C][C]0.330744[/C][/ROW]
[ROW][C]22[/C][C]-0.102123[/C][C]-0.4898[/C][C]0.31447[/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=226706&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226706&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	-0.156522	-0.7507	0.230237
2	-0.192253	-0.922	0.183047
3	-0.244914	-1.1746	0.126093
4	-0.331613	-1.5904	0.062703
5	-0.504161	-2.4179	0.011968
6	0.451137	2.1636	0.020565
7	-0.084525	-0.4054	0.344477
8	-0.068584	-0.3289	0.372597
9	-0.041813	-0.2005	0.421414
10	-0.000461	-0.0022	0.499127
11	0.059541	0.2855	0.388891
12	-0.22676	-1.0875	0.14404
13	-0.037031	-0.1776	0.430299
14	-0.029804	-0.1429	0.443793
15	-0.024906	-0.1194	0.45298
16	-0.024906	-0.1194	0.452979
17	-0.033402	-0.1602	0.437065
18	-0.292292	-1.4018	0.087166
19	-0.078325	-0.3756	0.355315
20	-0.084488	-0.4052	0.344541
21	-0.092494	-0.4436	0.330744
22	-0.102123	-0.4898	0.31447
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 <- 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