Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 17 Oct 2014 22:56:45 +0100

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/2014/Oct/17/t1413583055r97afestyvz45j9.htm/, Retrieved Fri, 10 May 2024 04:28:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243391, Retrieved Fri, 10 May 2024 04:28:59 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

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] [] [2014-10-17 21:56:45] [bdd4dd5e616b71837cf1c04213e8fe07] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243391&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243391&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243391&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	1 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.147113	1.2396	0.109603
2	0.009446	0.0796	0.468391
3	0.139486	1.1753	0.121895
4	-0.072679	-0.6124	0.271113
5	-0.143454	-1.2088	0.115381
6	-0.096651	-0.8144	0.20907
7	-0.011457	-0.0965	0.461681
8	-0.047297	-0.3985	0.345717
9	-0.090532	-0.7628	0.224044
10	0.045004	0.3792	0.352833
11	-0.069386	-0.5847	0.280317
12	0.023233	0.1958	0.422676
13	-0.028809	-0.2428	0.404449
14	-0.168913	-1.4233	0.079516
15	-0.085566	-0.721	0.23664
16	-0.206324	-1.7385	0.043228
17	-0.012236	-0.1031	0.459085
18	-0.13014	-1.0966	0.138265

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.147113 & 1.2396 & 0.109603 \tabularnewline
2 & 0.009446 & 0.0796 & 0.468391 \tabularnewline
3 & 0.139486 & 1.1753 & 0.121895 \tabularnewline
4 & -0.072679 & -0.6124 & 0.271113 \tabularnewline
5 & -0.143454 & -1.2088 & 0.115381 \tabularnewline
6 & -0.096651 & -0.8144 & 0.20907 \tabularnewline
7 & -0.011457 & -0.0965 & 0.461681 \tabularnewline
8 & -0.047297 & -0.3985 & 0.345717 \tabularnewline
9 & -0.090532 & -0.7628 & 0.224044 \tabularnewline
10 & 0.045004 & 0.3792 & 0.352833 \tabularnewline
11 & -0.069386 & -0.5847 & 0.280317 \tabularnewline
12 & 0.023233 & 0.1958 & 0.422676 \tabularnewline
13 & -0.028809 & -0.2428 & 0.404449 \tabularnewline
14 & -0.168913 & -1.4233 & 0.079516 \tabularnewline
15 & -0.085566 & -0.721 & 0.23664 \tabularnewline
16 & -0.206324 & -1.7385 & 0.043228 \tabularnewline
17 & -0.012236 & -0.1031 & 0.459085 \tabularnewline
18 & -0.13014 & -1.0966 & 0.138265 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243391&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]0.147113[/C][C]1.2396[/C][C]0.109603[/C][/ROW]
[ROW][C]2[/C][C]0.009446[/C][C]0.0796[/C][C]0.468391[/C][/ROW]
[ROW][C]3[/C][C]0.139486[/C][C]1.1753[/C][C]0.121895[/C][/ROW]
[ROW][C]4[/C][C]-0.072679[/C][C]-0.6124[/C][C]0.271113[/C][/ROW]
[ROW][C]5[/C][C]-0.143454[/C][C]-1.2088[/C][C]0.115381[/C][/ROW]
[ROW][C]6[/C][C]-0.096651[/C][C]-0.8144[/C][C]0.20907[/C][/ROW]
[ROW][C]7[/C][C]-0.011457[/C][C]-0.0965[/C][C]0.461681[/C][/ROW]
[ROW][C]8[/C][C]-0.047297[/C][C]-0.3985[/C][C]0.345717[/C][/ROW]
[ROW][C]9[/C][C]-0.090532[/C][C]-0.7628[/C][C]0.224044[/C][/ROW]
[ROW][C]10[/C][C]0.045004[/C][C]0.3792[/C][C]0.352833[/C][/ROW]
[ROW][C]11[/C][C]-0.069386[/C][C]-0.5847[/C][C]0.280317[/C][/ROW]
[ROW][C]12[/C][C]0.023233[/C][C]0.1958[/C][C]0.422676[/C][/ROW]
[ROW][C]13[/C][C]-0.028809[/C][C]-0.2428[/C][C]0.404449[/C][/ROW]
[ROW][C]14[/C][C]-0.168913[/C][C]-1.4233[/C][C]0.079516[/C][/ROW]
[ROW][C]15[/C][C]-0.085566[/C][C]-0.721[/C][C]0.23664[/C][/ROW]
[ROW][C]16[/C][C]-0.206324[/C][C]-1.7385[/C][C]0.043228[/C][/ROW]
[ROW][C]17[/C][C]-0.012236[/C][C]-0.1031[/C][C]0.459085[/C][/ROW]
[ROW][C]18[/C][C]-0.13014[/C][C]-1.0966[/C][C]0.138265[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243391&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243391&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	0.147113	1.2396	0.109603
2	0.009446	0.0796	0.468391
3	0.139486	1.1753	0.121895
4	-0.072679	-0.6124	0.271113
5	-0.143454	-1.2088	0.115381
6	-0.096651	-0.8144	0.20907
7	-0.011457	-0.0965	0.461681
8	-0.047297	-0.3985	0.345717
9	-0.090532	-0.7628	0.224044
10	0.045004	0.3792	0.352833
11	-0.069386	-0.5847	0.280317
12	0.023233	0.1958	0.422676
13	-0.028809	-0.2428	0.404449
14	-0.168913	-1.4233	0.079516
15	-0.085566	-0.721	0.23664
16	-0.206324	-1.7385	0.043228
17	-0.012236	-0.1031	0.459085
18	-0.13014	-1.0966	0.138265

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.147113	1.2396	0.109603
2	-0.012466	-0.105	0.458321
3	0.14303	1.2052	0.116066
4	-0.119419	-1.0062	0.158859
5	-0.116395	-0.9808	0.165021
6	-0.085581	-0.7211	0.236603
7	0.04171	0.3515	0.363143
8	-0.023597	-0.1988	0.421483
9	-0.080584	-0.679	0.249669
10	0.035493	0.2991	0.38288
11	-0.100973	-0.8508	0.198867
12	0.072623	0.6119	0.271268
13	-0.086405	-0.7281	0.234485
14	-0.158097	-1.3321	0.093536
15	-0.080818	-0.681	0.249049
16	-0.205588	-1.7323	0.04378
17	0.083427	0.703	0.242186
18	-0.205155	-1.7287	0.044108

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.147113 & 1.2396 & 0.109603 \tabularnewline
2 & -0.012466 & -0.105 & 0.458321 \tabularnewline
3 & 0.14303 & 1.2052 & 0.116066 \tabularnewline
4 & -0.119419 & -1.0062 & 0.158859 \tabularnewline
5 & -0.116395 & -0.9808 & 0.165021 \tabularnewline
6 & -0.085581 & -0.7211 & 0.236603 \tabularnewline
7 & 0.04171 & 0.3515 & 0.363143 \tabularnewline
8 & -0.023597 & -0.1988 & 0.421483 \tabularnewline
9 & -0.080584 & -0.679 & 0.249669 \tabularnewline
10 & 0.035493 & 0.2991 & 0.38288 \tabularnewline
11 & -0.100973 & -0.8508 & 0.198867 \tabularnewline
12 & 0.072623 & 0.6119 & 0.271268 \tabularnewline
13 & -0.086405 & -0.7281 & 0.234485 \tabularnewline
14 & -0.158097 & -1.3321 & 0.093536 \tabularnewline
15 & -0.080818 & -0.681 & 0.249049 \tabularnewline
16 & -0.205588 & -1.7323 & 0.04378 \tabularnewline
17 & 0.083427 & 0.703 & 0.242186 \tabularnewline
18 & -0.205155 & -1.7287 & 0.044108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243391&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]0.147113[/C][C]1.2396[/C][C]0.109603[/C][/ROW]
[ROW][C]2[/C][C]-0.012466[/C][C]-0.105[/C][C]0.458321[/C][/ROW]
[ROW][C]3[/C][C]0.14303[/C][C]1.2052[/C][C]0.116066[/C][/ROW]
[ROW][C]4[/C][C]-0.119419[/C][C]-1.0062[/C][C]0.158859[/C][/ROW]
[ROW][C]5[/C][C]-0.116395[/C][C]-0.9808[/C][C]0.165021[/C][/ROW]
[ROW][C]6[/C][C]-0.085581[/C][C]-0.7211[/C][C]0.236603[/C][/ROW]
[ROW][C]7[/C][C]0.04171[/C][C]0.3515[/C][C]0.363143[/C][/ROW]
[ROW][C]8[/C][C]-0.023597[/C][C]-0.1988[/C][C]0.421483[/C][/ROW]
[ROW][C]9[/C][C]-0.080584[/C][C]-0.679[/C][C]0.249669[/C][/ROW]
[ROW][C]10[/C][C]0.035493[/C][C]0.2991[/C][C]0.38288[/C][/ROW]
[ROW][C]11[/C][C]-0.100973[/C][C]-0.8508[/C][C]0.198867[/C][/ROW]
[ROW][C]12[/C][C]0.072623[/C][C]0.6119[/C][C]0.271268[/C][/ROW]
[ROW][C]13[/C][C]-0.086405[/C][C]-0.7281[/C][C]0.234485[/C][/ROW]
[ROW][C]14[/C][C]-0.158097[/C][C]-1.3321[/C][C]0.093536[/C][/ROW]
[ROW][C]15[/C][C]-0.080818[/C][C]-0.681[/C][C]0.249049[/C][/ROW]
[ROW][C]16[/C][C]-0.205588[/C][C]-1.7323[/C][C]0.04378[/C][/ROW]
[ROW][C]17[/C][C]0.083427[/C][C]0.703[/C][C]0.242186[/C][/ROW]
[ROW][C]18[/C][C]-0.205155[/C][C]-1.7287[/C][C]0.044108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243391&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243391&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	0.147113	1.2396	0.109603
2	-0.012466	-0.105	0.458321
3	0.14303	1.2052	0.116066
4	-0.119419	-1.0062	0.158859
5	-0.116395	-0.9808	0.165021
6	-0.085581	-0.7211	0.236603
7	0.04171	0.3515	0.363143
8	-0.023597	-0.1988	0.421483
9	-0.080584	-0.679	0.249669
10	0.035493	0.2991	0.38288
11	-0.100973	-0.8508	0.198867
12	0.072623	0.6119	0.271268
13	-0.086405	-0.7281	0.234485
14	-0.158097	-1.3321	0.093536
15	-0.080818	-0.681	0.249049
16	-0.205588	-1.7323	0.04378
17	0.083427	0.703	0.242186
18	-0.205155	-1.7287	0.044108

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)
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