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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 08 Mar 2016 11:15:49 +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/2016/Mar/08/t1457435829a1m8heaoyut3mfo.htm/, Retrieved Sun, 28 Apr 2024 21:22:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293671, Retrieved Sun, 28 Apr 2024 21:22:36 +0000

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Estimated Impact

112

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

-       [(Partial) Autocorrelation Function] [] [2016-03-08 11:15:49] [3fd8a2781b4a66a294f894c9e659cf7e] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293671&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293671&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293671&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.060272	0.463	0.32255
2	-0.006047	-0.0465	0.481554
3	0.007392	0.0568	0.477455
4	-0.093156	-0.7155	0.238548
5	-0.001637	-0.0126	0.495004
6	-0.208464	-1.6012	0.057332
7	-0.092906	-0.7136	0.239137
8	-0.033452	-0.257	0.399055
9	-0.122736	-0.9428	0.174827
10	-0.011485	-0.0882	0.465002
11	0.088171	0.6773	0.250447
12	0.272555	2.0935	0.020304
13	0.030048	0.2308	0.409134
14	0.072875	0.5598	0.288879
15	-0.074466	-0.572	0.284754
16	-0.158898	-1.2205	0.113563
17	0.023843	0.1831	0.427656

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.060272 & 0.463 & 0.32255 \tabularnewline
2 & -0.006047 & -0.0465 & 0.481554 \tabularnewline
3 & 0.007392 & 0.0568 & 0.477455 \tabularnewline
4 & -0.093156 & -0.7155 & 0.238548 \tabularnewline
5 & -0.001637 & -0.0126 & 0.495004 \tabularnewline
6 & -0.208464 & -1.6012 & 0.057332 \tabularnewline
7 & -0.092906 & -0.7136 & 0.239137 \tabularnewline
8 & -0.033452 & -0.257 & 0.399055 \tabularnewline
9 & -0.122736 & -0.9428 & 0.174827 \tabularnewline
10 & -0.011485 & -0.0882 & 0.465002 \tabularnewline
11 & 0.088171 & 0.6773 & 0.250447 \tabularnewline
12 & 0.272555 & 2.0935 & 0.020304 \tabularnewline
13 & 0.030048 & 0.2308 & 0.409134 \tabularnewline
14 & 0.072875 & 0.5598 & 0.288879 \tabularnewline
15 & -0.074466 & -0.572 & 0.284754 \tabularnewline
16 & -0.158898 & -1.2205 & 0.113563 \tabularnewline
17 & 0.023843 & 0.1831 & 0.427656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293671&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]0.060272[/C][C]0.463[/C][C]0.32255[/C][/ROW]
[ROW][C]2[/C][C]-0.006047[/C][C]-0.0465[/C][C]0.481554[/C][/ROW]
[ROW][C]3[/C][C]0.007392[/C][C]0.0568[/C][C]0.477455[/C][/ROW]
[ROW][C]4[/C][C]-0.093156[/C][C]-0.7155[/C][C]0.238548[/C][/ROW]
[ROW][C]5[/C][C]-0.001637[/C][C]-0.0126[/C][C]0.495004[/C][/ROW]
[ROW][C]6[/C][C]-0.208464[/C][C]-1.6012[/C][C]0.057332[/C][/ROW]
[ROW][C]7[/C][C]-0.092906[/C][C]-0.7136[/C][C]0.239137[/C][/ROW]
[ROW][C]8[/C][C]-0.033452[/C][C]-0.257[/C][C]0.399055[/C][/ROW]
[ROW][C]9[/C][C]-0.122736[/C][C]-0.9428[/C][C]0.174827[/C][/ROW]
[ROW][C]10[/C][C]-0.011485[/C][C]-0.0882[/C][C]0.465002[/C][/ROW]
[ROW][C]11[/C][C]0.088171[/C][C]0.6773[/C][C]0.250447[/C][/ROW]
[ROW][C]12[/C][C]0.272555[/C][C]2.0935[/C][C]0.020304[/C][/ROW]
[ROW][C]13[/C][C]0.030048[/C][C]0.2308[/C][C]0.409134[/C][/ROW]
[ROW][C]14[/C][C]0.072875[/C][C]0.5598[/C][C]0.288879[/C][/ROW]
[ROW][C]15[/C][C]-0.074466[/C][C]-0.572[/C][C]0.284754[/C][/ROW]
[ROW][C]16[/C][C]-0.158898[/C][C]-1.2205[/C][C]0.113563[/C][/ROW]
[ROW][C]17[/C][C]0.023843[/C][C]0.1831[/C][C]0.427656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293671&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293671&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	0.060272	0.463	0.32255
2	-0.006047	-0.0465	0.481554
3	0.007392	0.0568	0.477455
4	-0.093156	-0.7155	0.238548
5	-0.001637	-0.0126	0.495004
6	-0.208464	-1.6012	0.057332
7	-0.092906	-0.7136	0.239137
8	-0.033452	-0.257	0.399055
9	-0.122736	-0.9428	0.174827
10	-0.011485	-0.0882	0.465002
11	0.088171	0.6773	0.250447
12	0.272555	2.0935	0.020304
13	0.030048	0.2308	0.409134
14	0.072875	0.5598	0.288879
15	-0.074466	-0.572	0.284754
16	-0.158898	-1.2205	0.113563
17	0.023843	0.1831	0.427656

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.060272	0.463	0.32255
2	-0.009715	-0.0746	0.470382
3	0.008377	0.0643	0.474456
4	-0.094532	-0.7261	0.23532
5	0.010108	0.0776	0.46919
6	-0.213439	-1.6395	0.05322
7	-0.068032	-0.5226	0.301618
8	-0.044063	-0.3385	0.368112
9	-0.124677	-0.9577	0.17107
10	-0.044874	-0.3447	0.365778
11	0.075318	0.5785	0.282555
12	0.233454	1.7932	0.039034
13	-0.043003	-0.3303	0.371167
14	0.076592	0.5883	0.279283
15	-0.137123	-1.0533	0.148258
16	-0.156414	-1.2014	0.117192
17	0.036432	0.2798	0.390289

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.060272 & 0.463 & 0.32255 \tabularnewline
2 & -0.009715 & -0.0746 & 0.470382 \tabularnewline
3 & 0.008377 & 0.0643 & 0.474456 \tabularnewline
4 & -0.094532 & -0.7261 & 0.23532 \tabularnewline
5 & 0.010108 & 0.0776 & 0.46919 \tabularnewline
6 & -0.213439 & -1.6395 & 0.05322 \tabularnewline
7 & -0.068032 & -0.5226 & 0.301618 \tabularnewline
8 & -0.044063 & -0.3385 & 0.368112 \tabularnewline
9 & -0.124677 & -0.9577 & 0.17107 \tabularnewline
10 & -0.044874 & -0.3447 & 0.365778 \tabularnewline
11 & 0.075318 & 0.5785 & 0.282555 \tabularnewline
12 & 0.233454 & 1.7932 & 0.039034 \tabularnewline
13 & -0.043003 & -0.3303 & 0.371167 \tabularnewline
14 & 0.076592 & 0.5883 & 0.279283 \tabularnewline
15 & -0.137123 & -1.0533 & 0.148258 \tabularnewline
16 & -0.156414 & -1.2014 & 0.117192 \tabularnewline
17 & 0.036432 & 0.2798 & 0.390289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293671&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]0.060272[/C][C]0.463[/C][C]0.32255[/C][/ROW]
[ROW][C]2[/C][C]-0.009715[/C][C]-0.0746[/C][C]0.470382[/C][/ROW]
[ROW][C]3[/C][C]0.008377[/C][C]0.0643[/C][C]0.474456[/C][/ROW]
[ROW][C]4[/C][C]-0.094532[/C][C]-0.7261[/C][C]0.23532[/C][/ROW]
[ROW][C]5[/C][C]0.010108[/C][C]0.0776[/C][C]0.46919[/C][/ROW]
[ROW][C]6[/C][C]-0.213439[/C][C]-1.6395[/C][C]0.05322[/C][/ROW]
[ROW][C]7[/C][C]-0.068032[/C][C]-0.5226[/C][C]0.301618[/C][/ROW]
[ROW][C]8[/C][C]-0.044063[/C][C]-0.3385[/C][C]0.368112[/C][/ROW]
[ROW][C]9[/C][C]-0.124677[/C][C]-0.9577[/C][C]0.17107[/C][/ROW]
[ROW][C]10[/C][C]-0.044874[/C][C]-0.3447[/C][C]0.365778[/C][/ROW]
[ROW][C]11[/C][C]0.075318[/C][C]0.5785[/C][C]0.282555[/C][/ROW]
[ROW][C]12[/C][C]0.233454[/C][C]1.7932[/C][C]0.039034[/C][/ROW]
[ROW][C]13[/C][C]-0.043003[/C][C]-0.3303[/C][C]0.371167[/C][/ROW]
[ROW][C]14[/C][C]0.076592[/C][C]0.5883[/C][C]0.279283[/C][/ROW]
[ROW][C]15[/C][C]-0.137123[/C][C]-1.0533[/C][C]0.148258[/C][/ROW]
[ROW][C]16[/C][C]-0.156414[/C][C]-1.2014[/C][C]0.117192[/C][/ROW]
[ROW][C]17[/C][C]0.036432[/C][C]0.2798[/C][C]0.390289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293671&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293671&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	0.060272	0.463	0.32255
2	-0.009715	-0.0746	0.470382
3	0.008377	0.0643	0.474456
4	-0.094532	-0.7261	0.23532
5	0.010108	0.0776	0.46919
6	-0.213439	-1.6395	0.05322
7	-0.068032	-0.5226	0.301618
8	-0.044063	-0.3385	0.368112
9	-0.124677	-0.9577	0.17107
10	-0.044874	-0.3447	0.365778
11	0.075318	0.5785	0.282555
12	0.233454	1.7932	0.039034
13	-0.043003	-0.3303	0.371167
14	0.076592	0.5883	0.279283
15	-0.137123	-1.0533	0.148258
16	-0.156414	-1.2014	0.117192
17	0.036432	0.2798	0.390289

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

Parameters (R input):

par1 = Default ; 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)
x <- na.omit(x)
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')

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