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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 12:12:49 -0700

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/2009/Nov/26/t1259262798vll0jncnmeid9rw.htm/, Retrieved Sun, 28 Apr 2024 23:57:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60300, Retrieved Sun, 28 Apr 2024 23:57:14 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

110

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [Industri�le produ...] [2009-11-26 19:12:49] [fcf610eda12f49b9bf9c81ec9669e97a] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60300&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60300&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.100558	0.7724	0.22148
2	0.355411	2.73	0.004169
3	-0.088951	-0.6832	0.248562
4	0.105314	0.8089	0.210902
5	0.088095	0.6767	0.250629
6	-0.032214	-0.2474	0.402713
7	-0.107095	-0.8226	0.207021
8	-0.145083	-1.1144	0.134812
9	-0.089086	-0.6843	0.248237
10	-0.086585	-0.6651	0.254299
11	0.002466	0.0189	0.492477
12	-0.18805	-1.4444	0.076953
13	0.035226	0.2706	0.393832
14	-0.062259	-0.4782	0.31713
15	0.035989	0.2764	0.391591
16	0.069862	0.5366	0.296774
17	-0.018056	-0.1387	0.445084

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.100558 & 0.7724 & 0.22148 \tabularnewline
2 & 0.355411 & 2.73 & 0.004169 \tabularnewline
3 & -0.088951 & -0.6832 & 0.248562 \tabularnewline
4 & 0.105314 & 0.8089 & 0.210902 \tabularnewline
5 & 0.088095 & 0.6767 & 0.250629 \tabularnewline
6 & -0.032214 & -0.2474 & 0.402713 \tabularnewline
7 & -0.107095 & -0.8226 & 0.207021 \tabularnewline
8 & -0.145083 & -1.1144 & 0.134812 \tabularnewline
9 & -0.089086 & -0.6843 & 0.248237 \tabularnewline
10 & -0.086585 & -0.6651 & 0.254299 \tabularnewline
11 & 0.002466 & 0.0189 & 0.492477 \tabularnewline
12 & -0.18805 & -1.4444 & 0.076953 \tabularnewline
13 & 0.035226 & 0.2706 & 0.393832 \tabularnewline
14 & -0.062259 & -0.4782 & 0.31713 \tabularnewline
15 & 0.035989 & 0.2764 & 0.391591 \tabularnewline
16 & 0.069862 & 0.5366 & 0.296774 \tabularnewline
17 & -0.018056 & -0.1387 & 0.445084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60300&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]0.100558[/C][C]0.7724[/C][C]0.22148[/C][/ROW]
[ROW][C]2[/C][C]0.355411[/C][C]2.73[/C][C]0.004169[/C][/ROW]
[ROW][C]3[/C][C]-0.088951[/C][C]-0.6832[/C][C]0.248562[/C][/ROW]
[ROW][C]4[/C][C]0.105314[/C][C]0.8089[/C][C]0.210902[/C][/ROW]
[ROW][C]5[/C][C]0.088095[/C][C]0.6767[/C][C]0.250629[/C][/ROW]
[ROW][C]6[/C][C]-0.032214[/C][C]-0.2474[/C][C]0.402713[/C][/ROW]
[ROW][C]7[/C][C]-0.107095[/C][C]-0.8226[/C][C]0.207021[/C][/ROW]
[ROW][C]8[/C][C]-0.145083[/C][C]-1.1144[/C][C]0.134812[/C][/ROW]
[ROW][C]9[/C][C]-0.089086[/C][C]-0.6843[/C][C]0.248237[/C][/ROW]
[ROW][C]10[/C][C]-0.086585[/C][C]-0.6651[/C][C]0.254299[/C][/ROW]
[ROW][C]11[/C][C]0.002466[/C][C]0.0189[/C][C]0.492477[/C][/ROW]
[ROW][C]12[/C][C]-0.18805[/C][C]-1.4444[/C][C]0.076953[/C][/ROW]
[ROW][C]13[/C][C]0.035226[/C][C]0.2706[/C][C]0.393832[/C][/ROW]
[ROW][C]14[/C][C]-0.062259[/C][C]-0.4782[/C][C]0.31713[/C][/ROW]
[ROW][C]15[/C][C]0.035989[/C][C]0.2764[/C][C]0.391591[/C][/ROW]
[ROW][C]16[/C][C]0.069862[/C][C]0.5366[/C][C]0.296774[/C][/ROW]
[ROW][C]17[/C][C]-0.018056[/C][C]-0.1387[/C][C]0.445084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60300&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	0.100558	0.7724	0.22148
2	0.355411	2.73	0.004169
3	-0.088951	-0.6832	0.248562
4	0.105314	0.8089	0.210902
5	0.088095	0.6767	0.250629
6	-0.032214	-0.2474	0.402713
7	-0.107095	-0.8226	0.207021
8	-0.145083	-1.1144	0.134812
9	-0.089086	-0.6843	0.248237
10	-0.086585	-0.6651	0.254299
11	0.002466	0.0189	0.492477
12	-0.18805	-1.4444	0.076953
13	0.035226	0.2706	0.393832
14	-0.062259	-0.4782	0.31713
15	0.035989	0.2764	0.391591
16	0.069862	0.5366	0.296774
17	-0.018056	-0.1387	0.445084

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.100558	0.7724	0.22148
2	0.348826	2.6794	0.004772
3	-0.169421	-1.3013	0.099099
4	0.006528	0.0501	0.480089
5	0.197184	1.5146	0.067606
6	-0.146769	-1.1274	0.132078
7	-0.208569	-1.602	0.057243
8	-0.005655	-0.0434	0.482751
9	0.00177	0.0136	0.4946
10	-0.095949	-0.737	0.232022
11	0.079711	0.6123	0.271355
12	-0.140867	-1.082	0.141824
13	0.04427	0.34	0.367514
14	0.083956	0.6449	0.260754
15	-0.107256	-0.8239	0.206671
16	0.092109	0.7075	0.241019
17	0.024682	0.1896	0.425144

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.100558 & 0.7724 & 0.22148 \tabularnewline
2 & 0.348826 & 2.6794 & 0.004772 \tabularnewline
3 & -0.169421 & -1.3013 & 0.099099 \tabularnewline
4 & 0.006528 & 0.0501 & 0.480089 \tabularnewline
5 & 0.197184 & 1.5146 & 0.067606 \tabularnewline
6 & -0.146769 & -1.1274 & 0.132078 \tabularnewline
7 & -0.208569 & -1.602 & 0.057243 \tabularnewline
8 & -0.005655 & -0.0434 & 0.482751 \tabularnewline
9 & 0.00177 & 0.0136 & 0.4946 \tabularnewline
10 & -0.095949 & -0.737 & 0.232022 \tabularnewline
11 & 0.079711 & 0.6123 & 0.271355 \tabularnewline
12 & -0.140867 & -1.082 & 0.141824 \tabularnewline
13 & 0.04427 & 0.34 & 0.367514 \tabularnewline
14 & 0.083956 & 0.6449 & 0.260754 \tabularnewline
15 & -0.107256 & -0.8239 & 0.206671 \tabularnewline
16 & 0.092109 & 0.7075 & 0.241019 \tabularnewline
17 & 0.024682 & 0.1896 & 0.425144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60300&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]0.100558[/C][C]0.7724[/C][C]0.22148[/C][/ROW]
[ROW][C]2[/C][C]0.348826[/C][C]2.6794[/C][C]0.004772[/C][/ROW]
[ROW][C]3[/C][C]-0.169421[/C][C]-1.3013[/C][C]0.099099[/C][/ROW]
[ROW][C]4[/C][C]0.006528[/C][C]0.0501[/C][C]0.480089[/C][/ROW]
[ROW][C]5[/C][C]0.197184[/C][C]1.5146[/C][C]0.067606[/C][/ROW]
[ROW][C]6[/C][C]-0.146769[/C][C]-1.1274[/C][C]0.132078[/C][/ROW]
[ROW][C]7[/C][C]-0.208569[/C][C]-1.602[/C][C]0.057243[/C][/ROW]
[ROW][C]8[/C][C]-0.005655[/C][C]-0.0434[/C][C]0.482751[/C][/ROW]
[ROW][C]9[/C][C]0.00177[/C][C]0.0136[/C][C]0.4946[/C][/ROW]
[ROW][C]10[/C][C]-0.095949[/C][C]-0.737[/C][C]0.232022[/C][/ROW]
[ROW][C]11[/C][C]0.079711[/C][C]0.6123[/C][C]0.271355[/C][/ROW]
[ROW][C]12[/C][C]-0.140867[/C][C]-1.082[/C][C]0.141824[/C][/ROW]
[ROW][C]13[/C][C]0.04427[/C][C]0.34[/C][C]0.367514[/C][/ROW]
[ROW][C]14[/C][C]0.083956[/C][C]0.6449[/C][C]0.260754[/C][/ROW]
[ROW][C]15[/C][C]-0.107256[/C][C]-0.8239[/C][C]0.206671[/C][/ROW]
[ROW][C]16[/C][C]0.092109[/C][C]0.7075[/C][C]0.241019[/C][/ROW]
[ROW][C]17[/C][C]0.024682[/C][C]0.1896[/C][C]0.425144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60300&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60300&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	0.100558	0.7724	0.22148
2	0.348826	2.6794	0.004772
3	-0.169421	-1.3013	0.099099
4	0.006528	0.0501	0.480089
5	0.197184	1.5146	0.067606
6	-0.146769	-1.1274	0.132078
7	-0.208569	-1.602	0.057243
8	-0.005655	-0.0434	0.482751
9	0.00177	0.0136	0.4946
10	-0.095949	-0.737	0.232022
11	0.079711	0.6123	0.271355
12	-0.140867	-1.082	0.141824
13	0.04427	0.34	0.367514
14	0.083956	0.6449	0.260754
15	-0.107256	-0.8239	0.206671
16	0.092109	0.7075	0.241019
17	0.024682	0.1896	0.425144

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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