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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 01 Dec 2012 09:26:54 -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/2012/Dec/01/t13543720381c9mkz7vqu2wgoj.htm/, Retrieved Sun, 28 Apr 2024 20:10:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195320, Retrieved Sun, 28 Apr 2024 20:10:59 +0000

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User-defined keywords

Estimated Impact

128

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

-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Soldiers] [2010-11-29 09:48:36] [b98453cac15ba1066b407e146608df68]
- R P     [(Partial) Autocorrelation Function] [Soldiers autocorr...] [2012-12-01 14:17:53] [22a7ed72f77de7f3efc5689ed05063a7]
- R P       [(Partial) Autocorrelation Function] [Soldiers] [2012-12-01 14:22:50] [22a7ed72f77de7f3efc5689ed05063a7]
-   P           [(Partial) Autocorrelation Function] [Soldiers] [2012-12-01 14:26:54] [8a8ce1ece063ce616102c2c7ff02990f] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195320&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195320&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.460995	-3.7734	0.000172
2	0.198885	1.6279	0.054116
3	-0.24417	-1.9986	0.024855
4	0.092574	0.7577	0.225629
5	0.007034	0.0576	0.477127
6	-0.01968	-0.1611	0.436253
7	-0.045384	-0.3715	0.355724
8	-0.006668	-0.0546	0.478317
9	0.177997	1.457	0.074898
10	-0.12617	-1.0327	0.152717
11	0.149583	1.2244	0.112546
12	-0.340062	-2.7835	0.003491
13	0.104203	0.8529	0.198365
14	-0.024683	-0.202	0.420248
15	0.039356	0.3221	0.374174
16	0.04121	0.3373	0.368464
17	-0.084819	-0.6943	0.244957
18	-0.034638	-0.2835	0.388826
19	0.159754	1.3076	0.097732

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.460995 & -3.7734 & 0.000172 \tabularnewline
2 & 0.198885 & 1.6279 & 0.054116 \tabularnewline
3 & -0.24417 & -1.9986 & 0.024855 \tabularnewline
4 & 0.092574 & 0.7577 & 0.225629 \tabularnewline
5 & 0.007034 & 0.0576 & 0.477127 \tabularnewline
6 & -0.01968 & -0.1611 & 0.436253 \tabularnewline
7 & -0.045384 & -0.3715 & 0.355724 \tabularnewline
8 & -0.006668 & -0.0546 & 0.478317 \tabularnewline
9 & 0.177997 & 1.457 & 0.074898 \tabularnewline
10 & -0.12617 & -1.0327 & 0.152717 \tabularnewline
11 & 0.149583 & 1.2244 & 0.112546 \tabularnewline
12 & -0.340062 & -2.7835 & 0.003491 \tabularnewline
13 & 0.104203 & 0.8529 & 0.198365 \tabularnewline
14 & -0.024683 & -0.202 & 0.420248 \tabularnewline
15 & 0.039356 & 0.3221 & 0.374174 \tabularnewline
16 & 0.04121 & 0.3373 & 0.368464 \tabularnewline
17 & -0.084819 & -0.6943 & 0.244957 \tabularnewline
18 & -0.034638 & -0.2835 & 0.388826 \tabularnewline
19 & 0.159754 & 1.3076 & 0.097732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195320&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]-0.460995[/C][C]-3.7734[/C][C]0.000172[/C][/ROW]
[ROW][C]2[/C][C]0.198885[/C][C]1.6279[/C][C]0.054116[/C][/ROW]
[ROW][C]3[/C][C]-0.24417[/C][C]-1.9986[/C][C]0.024855[/C][/ROW]
[ROW][C]4[/C][C]0.092574[/C][C]0.7577[/C][C]0.225629[/C][/ROW]
[ROW][C]5[/C][C]0.007034[/C][C]0.0576[/C][C]0.477127[/C][/ROW]
[ROW][C]6[/C][C]-0.01968[/C][C]-0.1611[/C][C]0.436253[/C][/ROW]
[ROW][C]7[/C][C]-0.045384[/C][C]-0.3715[/C][C]0.355724[/C][/ROW]
[ROW][C]8[/C][C]-0.006668[/C][C]-0.0546[/C][C]0.478317[/C][/ROW]
[ROW][C]9[/C][C]0.177997[/C][C]1.457[/C][C]0.074898[/C][/ROW]
[ROW][C]10[/C][C]-0.12617[/C][C]-1.0327[/C][C]0.152717[/C][/ROW]
[ROW][C]11[/C][C]0.149583[/C][C]1.2244[/C][C]0.112546[/C][/ROW]
[ROW][C]12[/C][C]-0.340062[/C][C]-2.7835[/C][C]0.003491[/C][/ROW]
[ROW][C]13[/C][C]0.104203[/C][C]0.8529[/C][C]0.198365[/C][/ROW]
[ROW][C]14[/C][C]-0.024683[/C][C]-0.202[/C][C]0.420248[/C][/ROW]
[ROW][C]15[/C][C]0.039356[/C][C]0.3221[/C][C]0.374174[/C][/ROW]
[ROW][C]16[/C][C]0.04121[/C][C]0.3373[/C][C]0.368464[/C][/ROW]
[ROW][C]17[/C][C]-0.084819[/C][C]-0.6943[/C][C]0.244957[/C][/ROW]
[ROW][C]18[/C][C]-0.034638[/C][C]-0.2835[/C][C]0.388826[/C][/ROW]
[ROW][C]19[/C][C]0.159754[/C][C]1.3076[/C][C]0.097732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195320&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	-0.460995	-3.7734	0.000172
2	0.198885	1.6279	0.054116
3	-0.24417	-1.9986	0.024855
4	0.092574	0.7577	0.225629
5	0.007034	0.0576	0.477127
6	-0.01968	-0.1611	0.436253
7	-0.045384	-0.3715	0.355724
8	-0.006668	-0.0546	0.478317
9	0.177997	1.457	0.074898
10	-0.12617	-1.0327	0.152717
11	0.149583	1.2244	0.112546
12	-0.340062	-2.7835	0.003491
13	0.104203	0.8529	0.198365
14	-0.024683	-0.202	0.420248
15	0.039356	0.3221	0.374174
16	0.04121	0.3373	0.368464
17	-0.084819	-0.6943	0.244957
18	-0.034638	-0.2835	0.388826
19	0.159754	1.3076	0.097732

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.460995	-3.7734	0.000172
2	-0.017311	-0.1417	0.443873
3	-0.201815	-1.6519	0.051615
4	-0.123888	-1.0141	0.1571
5	0.022904	0.1875	0.425925
6	-0.047145	-0.3859	0.350398
7	-0.107554	-0.8804	0.190903
8	-0.067112	-0.5493	0.292301
9	0.188837	1.5457	0.063445
10	0.005968	0.0488	0.480593
11	0.113749	0.9311	0.177578
12	-0.218323	-1.7871	0.039226
13	-0.236513	-1.9359	0.028548
14	-0.0626	-0.5124	0.305027
15	-0.090041	-0.737	0.231842
16	0.022493	0.1841	0.427241
17	-0.054839	-0.4489	0.327485
18	-0.214252	-1.7537	0.042025
19	0.082751	0.6773	0.25026

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.460995 & -3.7734 & 0.000172 \tabularnewline
2 & -0.017311 & -0.1417 & 0.443873 \tabularnewline
3 & -0.201815 & -1.6519 & 0.051615 \tabularnewline
4 & -0.123888 & -1.0141 & 0.1571 \tabularnewline
5 & 0.022904 & 0.1875 & 0.425925 \tabularnewline
6 & -0.047145 & -0.3859 & 0.350398 \tabularnewline
7 & -0.107554 & -0.8804 & 0.190903 \tabularnewline
8 & -0.067112 & -0.5493 & 0.292301 \tabularnewline
9 & 0.188837 & 1.5457 & 0.063445 \tabularnewline
10 & 0.005968 & 0.0488 & 0.480593 \tabularnewline
11 & 0.113749 & 0.9311 & 0.177578 \tabularnewline
12 & -0.218323 & -1.7871 & 0.039226 \tabularnewline
13 & -0.236513 & -1.9359 & 0.028548 \tabularnewline
14 & -0.0626 & -0.5124 & 0.305027 \tabularnewline
15 & -0.090041 & -0.737 & 0.231842 \tabularnewline
16 & 0.022493 & 0.1841 & 0.427241 \tabularnewline
17 & -0.054839 & -0.4489 & 0.327485 \tabularnewline
18 & -0.214252 & -1.7537 & 0.042025 \tabularnewline
19 & 0.082751 & 0.6773 & 0.25026 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195320&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]-0.460995[/C][C]-3.7734[/C][C]0.000172[/C][/ROW]
[ROW][C]2[/C][C]-0.017311[/C][C]-0.1417[/C][C]0.443873[/C][/ROW]
[ROW][C]3[/C][C]-0.201815[/C][C]-1.6519[/C][C]0.051615[/C][/ROW]
[ROW][C]4[/C][C]-0.123888[/C][C]-1.0141[/C][C]0.1571[/C][/ROW]
[ROW][C]5[/C][C]0.022904[/C][C]0.1875[/C][C]0.425925[/C][/ROW]
[ROW][C]6[/C][C]-0.047145[/C][C]-0.3859[/C][C]0.350398[/C][/ROW]
[ROW][C]7[/C][C]-0.107554[/C][C]-0.8804[/C][C]0.190903[/C][/ROW]
[ROW][C]8[/C][C]-0.067112[/C][C]-0.5493[/C][C]0.292301[/C][/ROW]
[ROW][C]9[/C][C]0.188837[/C][C]1.5457[/C][C]0.063445[/C][/ROW]
[ROW][C]10[/C][C]0.005968[/C][C]0.0488[/C][C]0.480593[/C][/ROW]
[ROW][C]11[/C][C]0.113749[/C][C]0.9311[/C][C]0.177578[/C][/ROW]
[ROW][C]12[/C][C]-0.218323[/C][C]-1.7871[/C][C]0.039226[/C][/ROW]
[ROW][C]13[/C][C]-0.236513[/C][C]-1.9359[/C][C]0.028548[/C][/ROW]
[ROW][C]14[/C][C]-0.0626[/C][C]-0.5124[/C][C]0.305027[/C][/ROW]
[ROW][C]15[/C][C]-0.090041[/C][C]-0.737[/C][C]0.231842[/C][/ROW]
[ROW][C]16[/C][C]0.022493[/C][C]0.1841[/C][C]0.427241[/C][/ROW]
[ROW][C]17[/C][C]-0.054839[/C][C]-0.4489[/C][C]0.327485[/C][/ROW]
[ROW][C]18[/C][C]-0.214252[/C][C]-1.7537[/C][C]0.042025[/C][/ROW]
[ROW][C]19[/C][C]0.082751[/C][C]0.6773[/C][C]0.25026[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195320&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195320&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	-0.460995	-3.7734	0.000172
2	-0.017311	-0.1417	0.443873
3	-0.201815	-1.6519	0.051615
4	-0.123888	-1.0141	0.1571
5	0.022904	0.1875	0.425925
6	-0.047145	-0.3859	0.350398
7	-0.107554	-0.8804	0.190903
8	-0.067112	-0.5493	0.292301
9	0.188837	1.5457	0.063445
10	0.005968	0.0488	0.480593
11	0.113749	0.9311	0.177578
12	-0.218323	-1.7871	0.039226
13	-0.236513	-1.9359	0.028548
14	-0.0626	-0.5124	0.305027
15	-0.090041	-0.737	0.231842
16	0.022493	0.1841	0.427241
17	-0.054839	-0.4489	0.327485
18	-0.214252	-1.7537	0.042025
19	0.082751	0.6773	0.25026

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code