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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2011 06:17:12 -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/23/t1324639107iin5b9p5gb9g8za.htm/, Retrieved Mon, 29 Apr 2024 22:55:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160285, Retrieved Mon, 29 Apr 2024 22:55:05 +0000

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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)

-     [Variance Reduction Matrix] [] [2011-12-06 08:04:41] [80bca13c5f9401fbb753952fd2952f4a]
- R  D  [Variance Reduction Matrix] [Paper VRM] [2011-12-23 10:59:49] [805a2cd4f7b6665cd8870eed4006f53c]
- RMPD      [(Partial) Autocorrelation Function] [Paper autocorr] [2011-12-23 11:17:12] [c18e83883fa784c15a15b4fbc0636edd] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160285&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160285&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160285&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.235903	1.812	0.037538
2	0.293518	2.2546	0.013944
3	0.327947	2.519	0.007249
4	0.210666	1.6182	0.055482
5	0.100125	0.7691	0.222457
6	0.205258	1.5766	0.060116
7	0.08158	0.6266	0.266661
8	0.169727	1.3037	0.0987
9	0.075936	0.5833	0.280965
10	-0.089753	-0.6894	0.246635
11	0.182757	1.4038	0.082813
12	-0.228052	-1.7517	0.042511
13	-0.161684	-1.2419	0.10959
14	-0.010423	-0.0801	0.46823
15	-0.054255	-0.4167	0.339191
16	-0.152355	-1.1703	0.1233
17	-0.042068	-0.3231	0.373871
18	-0.150739	-1.1579	0.125795

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.235903 & 1.812 & 0.037538 \tabularnewline
2 & 0.293518 & 2.2546 & 0.013944 \tabularnewline
3 & 0.327947 & 2.519 & 0.007249 \tabularnewline
4 & 0.210666 & 1.6182 & 0.055482 \tabularnewline
5 & 0.100125 & 0.7691 & 0.222457 \tabularnewline
6 & 0.205258 & 1.5766 & 0.060116 \tabularnewline
7 & 0.08158 & 0.6266 & 0.266661 \tabularnewline
8 & 0.169727 & 1.3037 & 0.0987 \tabularnewline
9 & 0.075936 & 0.5833 & 0.280965 \tabularnewline
10 & -0.089753 & -0.6894 & 0.246635 \tabularnewline
11 & 0.182757 & 1.4038 & 0.082813 \tabularnewline
12 & -0.228052 & -1.7517 & 0.042511 \tabularnewline
13 & -0.161684 & -1.2419 & 0.10959 \tabularnewline
14 & -0.010423 & -0.0801 & 0.46823 \tabularnewline
15 & -0.054255 & -0.4167 & 0.339191 \tabularnewline
16 & -0.152355 & -1.1703 & 0.1233 \tabularnewline
17 & -0.042068 & -0.3231 & 0.373871 \tabularnewline
18 & -0.150739 & -1.1579 & 0.125795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160285&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]0.235903[/C][C]1.812[/C][C]0.037538[/C][/ROW]
[ROW][C]2[/C][C]0.293518[/C][C]2.2546[/C][C]0.013944[/C][/ROW]
[ROW][C]3[/C][C]0.327947[/C][C]2.519[/C][C]0.007249[/C][/ROW]
[ROW][C]4[/C][C]0.210666[/C][C]1.6182[/C][C]0.055482[/C][/ROW]
[ROW][C]5[/C][C]0.100125[/C][C]0.7691[/C][C]0.222457[/C][/ROW]
[ROW][C]6[/C][C]0.205258[/C][C]1.5766[/C][C]0.060116[/C][/ROW]
[ROW][C]7[/C][C]0.08158[/C][C]0.6266[/C][C]0.266661[/C][/ROW]
[ROW][C]8[/C][C]0.169727[/C][C]1.3037[/C][C]0.0987[/C][/ROW]
[ROW][C]9[/C][C]0.075936[/C][C]0.5833[/C][C]0.280965[/C][/ROW]
[ROW][C]10[/C][C]-0.089753[/C][C]-0.6894[/C][C]0.246635[/C][/ROW]
[ROW][C]11[/C][C]0.182757[/C][C]1.4038[/C][C]0.082813[/C][/ROW]
[ROW][C]12[/C][C]-0.228052[/C][C]-1.7517[/C][C]0.042511[/C][/ROW]
[ROW][C]13[/C][C]-0.161684[/C][C]-1.2419[/C][C]0.10959[/C][/ROW]
[ROW][C]14[/C][C]-0.010423[/C][C]-0.0801[/C][C]0.46823[/C][/ROW]
[ROW][C]15[/C][C]-0.054255[/C][C]-0.4167[/C][C]0.339191[/C][/ROW]
[ROW][C]16[/C][C]-0.152355[/C][C]-1.1703[/C][C]0.1233[/C][/ROW]
[ROW][C]17[/C][C]-0.042068[/C][C]-0.3231[/C][C]0.373871[/C][/ROW]
[ROW][C]18[/C][C]-0.150739[/C][C]-1.1579[/C][C]0.125795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160285&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160285&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	0.235903	1.812	0.037538
2	0.293518	2.2546	0.013944
3	0.327947	2.519	0.007249
4	0.210666	1.6182	0.055482
5	0.100125	0.7691	0.222457
6	0.205258	1.5766	0.060116
7	0.08158	0.6266	0.266661
8	0.169727	1.3037	0.0987
9	0.075936	0.5833	0.280965
10	-0.089753	-0.6894	0.246635
11	0.182757	1.4038	0.082813
12	-0.228052	-1.7517	0.042511
13	-0.161684	-1.2419	0.10959
14	-0.010423	-0.0801	0.46823
15	-0.054255	-0.4167	0.339191
16	-0.152355	-1.1703	0.1233
17	-0.042068	-0.3231	0.373871
18	-0.150739	-1.1579	0.125795

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.235903	1.812	0.037538
2	0.251885	1.9348	0.028909
3	0.245045	1.8822	0.03237
4	0.064939	0.4988	0.309887
5	-0.084238	-0.647	0.260056
6	0.078543	0.6033	0.274312
7	-0.026133	-0.2007	0.420799
8	0.112781	0.8663	0.194921
9	-0.032408	-0.2489	0.402139
10	-0.225589	-1.7328	0.044179
11	0.192678	1.48	0.072098
12	-0.345294	-2.6523	0.005127
13	-0.089813	-0.6899	0.24649
14	0.092015	0.7068	0.241242
15	0.067038	0.5149	0.304264
16	0.014146	0.1087	0.456921
17	-0.118999	-0.914	0.182206
18	-0.026601	-0.2043	0.419401

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.235903 & 1.812 & 0.037538 \tabularnewline
2 & 0.251885 & 1.9348 & 0.028909 \tabularnewline
3 & 0.245045 & 1.8822 & 0.03237 \tabularnewline
4 & 0.064939 & 0.4988 & 0.309887 \tabularnewline
5 & -0.084238 & -0.647 & 0.260056 \tabularnewline
6 & 0.078543 & 0.6033 & 0.274312 \tabularnewline
7 & -0.026133 & -0.2007 & 0.420799 \tabularnewline
8 & 0.112781 & 0.8663 & 0.194921 \tabularnewline
9 & -0.032408 & -0.2489 & 0.402139 \tabularnewline
10 & -0.225589 & -1.7328 & 0.044179 \tabularnewline
11 & 0.192678 & 1.48 & 0.072098 \tabularnewline
12 & -0.345294 & -2.6523 & 0.005127 \tabularnewline
13 & -0.089813 & -0.6899 & 0.24649 \tabularnewline
14 & 0.092015 & 0.7068 & 0.241242 \tabularnewline
15 & 0.067038 & 0.5149 & 0.304264 \tabularnewline
16 & 0.014146 & 0.1087 & 0.456921 \tabularnewline
17 & -0.118999 & -0.914 & 0.182206 \tabularnewline
18 & -0.026601 & -0.2043 & 0.419401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160285&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]0.235903[/C][C]1.812[/C][C]0.037538[/C][/ROW]
[ROW][C]2[/C][C]0.251885[/C][C]1.9348[/C][C]0.028909[/C][/ROW]
[ROW][C]3[/C][C]0.245045[/C][C]1.8822[/C][C]0.03237[/C][/ROW]
[ROW][C]4[/C][C]0.064939[/C][C]0.4988[/C][C]0.309887[/C][/ROW]
[ROW][C]5[/C][C]-0.084238[/C][C]-0.647[/C][C]0.260056[/C][/ROW]
[ROW][C]6[/C][C]0.078543[/C][C]0.6033[/C][C]0.274312[/C][/ROW]
[ROW][C]7[/C][C]-0.026133[/C][C]-0.2007[/C][C]0.420799[/C][/ROW]
[ROW][C]8[/C][C]0.112781[/C][C]0.8663[/C][C]0.194921[/C][/ROW]
[ROW][C]9[/C][C]-0.032408[/C][C]-0.2489[/C][C]0.402139[/C][/ROW]
[ROW][C]10[/C][C]-0.225589[/C][C]-1.7328[/C][C]0.044179[/C][/ROW]
[ROW][C]11[/C][C]0.192678[/C][C]1.48[/C][C]0.072098[/C][/ROW]
[ROW][C]12[/C][C]-0.345294[/C][C]-2.6523[/C][C]0.005127[/C][/ROW]
[ROW][C]13[/C][C]-0.089813[/C][C]-0.6899[/C][C]0.24649[/C][/ROW]
[ROW][C]14[/C][C]0.092015[/C][C]0.7068[/C][C]0.241242[/C][/ROW]
[ROW][C]15[/C][C]0.067038[/C][C]0.5149[/C][C]0.304264[/C][/ROW]
[ROW][C]16[/C][C]0.014146[/C][C]0.1087[/C][C]0.456921[/C][/ROW]
[ROW][C]17[/C][C]-0.118999[/C][C]-0.914[/C][C]0.182206[/C][/ROW]
[ROW][C]18[/C][C]-0.026601[/C][C]-0.2043[/C][C]0.419401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160285&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160285&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	0.235903	1.812	0.037538
2	0.251885	1.9348	0.028909
3	0.245045	1.8822	0.03237
4	0.064939	0.4988	0.309887
5	-0.084238	-0.647	0.260056
6	0.078543	0.6033	0.274312
7	-0.026133	-0.2007	0.420799
8	0.112781	0.8663	0.194921
9	-0.032408	-0.2489	0.402139
10	-0.225589	-1.7328	0.044179
11	0.192678	1.48	0.072098
12	-0.345294	-2.6523	0.005127
13	-0.089813	-0.6899	0.24649
14	0.092015	0.7068	0.241242
15	0.067038	0.5149	0.304264
16	0.014146	0.1087	0.456921
17	-0.118999	-0.914	0.182206
18	-0.026601	-0.2043	0.419401

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code