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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 07:33:21 -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/2007/Dec/06/t11969508436wrj3z3yvjvr26b.htm/, Retrieved Fri, 03 May 2024 14:23:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2629, Retrieved Fri, 03 May 2024 14:23:17 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

178

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

-       [(Partial) Autocorrelation Function] [WS4: Q2 Inflatie] [2007-12-06 14:33:21] [9b75aacdafaeee3fe66fbd4de075ccd6] [Current]

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1.1
1.3
1.2
1.6
1.7
1.5
0.9
1.5
1.4
1.6
1.7
1.4
1.8
1.7
1.4
1.2
1
1.7
2.4
2
2.1
2
1.8
2.7
2.3
1.9
2
2.3
2.8
2.4
2.3
2.7
2.7
2.9
3
2.2
2.3
2.8
2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2
2.1
1.7
1.8
1.8
1.8
1.3
1.3
1.3
1.2
1.4
2.2

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2629&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2629&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2629&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.6811	0
1	-0.123134	-0.9458	0.825949
2	-0.30719	-2.3596	0.989188
3	-0.004733	-0.0364	0.51444
4	-0.076632	-0.5886	0.720818
5	0.248614	1.9096	0.030523
6	0.02018	0.155	0.438674
7	-0.226721	-1.7415	0.956594
8	0.037354	0.2869	0.387589
9	-0.08879	-0.682	0.751049
10	0.289615	2.2246	0.014974
11	0.278389	2.1383	0.01832
12	-0.505015	-3.8791	0.999867
13	-0.114594	-0.8802	0.808842
14	0.217418	1.67	0.050106
15	0.019015	0.1461	0.442187
16	0.099669	0.7656	0.223491

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & -0.123134 & -0.9458 & 0.825949 \tabularnewline
2 & -0.30719 & -2.3596 & 0.989188 \tabularnewline
3 & -0.004733 & -0.0364 & 0.51444 \tabularnewline
4 & -0.076632 & -0.5886 & 0.720818 \tabularnewline
5 & 0.248614 & 1.9096 & 0.030523 \tabularnewline
6 & 0.02018 & 0.155 & 0.438674 \tabularnewline
7 & -0.226721 & -1.7415 & 0.956594 \tabularnewline
8 & 0.037354 & 0.2869 & 0.387589 \tabularnewline
9 & -0.08879 & -0.682 & 0.751049 \tabularnewline
10 & 0.289615 & 2.2246 & 0.014974 \tabularnewline
11 & 0.278389 & 2.1383 & 0.01832 \tabularnewline
12 & -0.505015 & -3.8791 & 0.999867 \tabularnewline
13 & -0.114594 & -0.8802 & 0.808842 \tabularnewline
14 & 0.217418 & 1.67 & 0.050106 \tabularnewline
15 & 0.019015 & 0.1461 & 0.442187 \tabularnewline
16 & 0.099669 & 0.7656 & 0.223491 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2629&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]0[/C][C]1[/C][C]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.123134[/C][C]-0.9458[/C][C]0.825949[/C][/ROW]
[ROW][C]2[/C][C]-0.30719[/C][C]-2.3596[/C][C]0.989188[/C][/ROW]
[ROW][C]3[/C][C]-0.004733[/C][C]-0.0364[/C][C]0.51444[/C][/ROW]
[ROW][C]4[/C][C]-0.076632[/C][C]-0.5886[/C][C]0.720818[/C][/ROW]
[ROW][C]5[/C][C]0.248614[/C][C]1.9096[/C][C]0.030523[/C][/ROW]
[ROW][C]6[/C][C]0.02018[/C][C]0.155[/C][C]0.438674[/C][/ROW]
[ROW][C]7[/C][C]-0.226721[/C][C]-1.7415[/C][C]0.956594[/C][/ROW]
[ROW][C]8[/C][C]0.037354[/C][C]0.2869[/C][C]0.387589[/C][/ROW]
[ROW][C]9[/C][C]-0.08879[/C][C]-0.682[/C][C]0.751049[/C][/ROW]
[ROW][C]10[/C][C]0.289615[/C][C]2.2246[/C][C]0.014974[/C][/ROW]
[ROW][C]11[/C][C]0.278389[/C][C]2.1383[/C][C]0.01832[/C][/ROW]
[ROW][C]12[/C][C]-0.505015[/C][C]-3.8791[/C][C]0.999867[/C][/ROW]
[ROW][C]13[/C][C]-0.114594[/C][C]-0.8802[/C][C]0.808842[/C][/ROW]
[ROW][C]14[/C][C]0.217418[/C][C]1.67[/C][C]0.050106[/C][/ROW]
[ROW][C]15[/C][C]0.019015[/C][C]0.1461[/C][C]0.442187[/C][/ROW]
[ROW][C]16[/C][C]0.099669[/C][C]0.7656[/C][C]0.223491[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2629&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2629&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
0	1	7.6811	0
1	-0.123134	-0.9458	0.825949
2	-0.30719	-2.3596	0.989188
3	-0.004733	-0.0364	0.51444
4	-0.076632	-0.5886	0.720818
5	0.248614	1.9096	0.030523
6	0.02018	0.155	0.438674
7	-0.226721	-1.7415	0.956594
8	0.037354	0.2869	0.387589
9	-0.08879	-0.682	0.751049
10	0.289615	2.2246	0.014974
11	0.278389	2.1383	0.01832
12	-0.505015	-3.8791	0.999867
13	-0.114594	-0.8802	0.808842
14	0.217418	1.67	0.050106
15	0.019015	0.1461	0.442187
16	0.099669	0.7656	0.223491

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.123134	-0.9458	0.825949
1	-0.327315	-2.5142	0.99266
2	-0.108314	-0.832	0.795611
3	-0.226575	-1.7404	0.956495
4	0.187377	1.4393	0.077679
5	0.001165	0.0089	0.496445
6	-0.09281	-0.7129	0.760638
7	-0.004588	-0.0352	0.513995
8	-0.172178	-1.3225	0.904452
9	0.268661	2.0636	0.021731
10	0.324948	2.496	0.007688
11	-0.257475	-1.9777	0.97368
12	-0.1157	-0.8887	0.811115
13	0.066407	0.5101	0.305948
14	-0.067104	-0.5154	0.695914
15	-0.013836	-0.1063	0.542138
16	-0.149127	-1.1455	0.87168

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.123134 & -0.9458 & 0.825949 \tabularnewline
1 & -0.327315 & -2.5142 & 0.99266 \tabularnewline
2 & -0.108314 & -0.832 & 0.795611 \tabularnewline
3 & -0.226575 & -1.7404 & 0.956495 \tabularnewline
4 & 0.187377 & 1.4393 & 0.077679 \tabularnewline
5 & 0.001165 & 0.0089 & 0.496445 \tabularnewline
6 & -0.09281 & -0.7129 & 0.760638 \tabularnewline
7 & -0.004588 & -0.0352 & 0.513995 \tabularnewline
8 & -0.172178 & -1.3225 & 0.904452 \tabularnewline
9 & 0.268661 & 2.0636 & 0.021731 \tabularnewline
10 & 0.324948 & 2.496 & 0.007688 \tabularnewline
11 & -0.257475 & -1.9777 & 0.97368 \tabularnewline
12 & -0.1157 & -0.8887 & 0.811115 \tabularnewline
13 & 0.066407 & 0.5101 & 0.305948 \tabularnewline
14 & -0.067104 & -0.5154 & 0.695914 \tabularnewline
15 & -0.013836 & -0.1063 & 0.542138 \tabularnewline
16 & -0.149127 & -1.1455 & 0.87168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2629&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]0[/C][C]-0.123134[/C][C]-0.9458[/C][C]0.825949[/C][/ROW]
[ROW][C]1[/C][C]-0.327315[/C][C]-2.5142[/C][C]0.99266[/C][/ROW]
[ROW][C]2[/C][C]-0.108314[/C][C]-0.832[/C][C]0.795611[/C][/ROW]
[ROW][C]3[/C][C]-0.226575[/C][C]-1.7404[/C][C]0.956495[/C][/ROW]
[ROW][C]4[/C][C]0.187377[/C][C]1.4393[/C][C]0.077679[/C][/ROW]
[ROW][C]5[/C][C]0.001165[/C][C]0.0089[/C][C]0.496445[/C][/ROW]
[ROW][C]6[/C][C]-0.09281[/C][C]-0.7129[/C][C]0.760638[/C][/ROW]
[ROW][C]7[/C][C]-0.004588[/C][C]-0.0352[/C][C]0.513995[/C][/ROW]
[ROW][C]8[/C][C]-0.172178[/C][C]-1.3225[/C][C]0.904452[/C][/ROW]
[ROW][C]9[/C][C]0.268661[/C][C]2.0636[/C][C]0.021731[/C][/ROW]
[ROW][C]10[/C][C]0.324948[/C][C]2.496[/C][C]0.007688[/C][/ROW]
[ROW][C]11[/C][C]-0.257475[/C][C]-1.9777[/C][C]0.97368[/C][/ROW]
[ROW][C]12[/C][C]-0.1157[/C][C]-0.8887[/C][C]0.811115[/C][/ROW]
[ROW][C]13[/C][C]0.066407[/C][C]0.5101[/C][C]0.305948[/C][/ROW]
[ROW][C]14[/C][C]-0.067104[/C][C]-0.5154[/C][C]0.695914[/C][/ROW]
[ROW][C]15[/C][C]-0.013836[/C][C]-0.1063[/C][C]0.542138[/C][/ROW]
[ROW][C]16[/C][C]-0.149127[/C][C]-1.1455[/C][C]0.87168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2629&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2629&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
0	-0.123134	-0.9458	0.825949
1	-0.327315	-2.5142	0.99266
2	-0.108314	-0.832	0.795611
3	-0.226575	-1.7404	0.956495
4	0.187377	1.4393	0.077679
5	0.001165	0.0089	0.496445
6	-0.09281	-0.7129	0.760638
7	-0.004588	-0.0352	0.513995
8	-0.172178	-1.3225	0.904452
9	0.268661	2.0636	0.021731
10	0.324948	2.496	0.007688
11	-0.257475	-1.9777	0.97368
12	-0.1157	-0.8887	0.811115
13	0.066407	0.5101	0.305948
14	-0.067104	-0.5154	0.695914
15	-0.013836	-0.1063	0.542138
16	-0.149127	-1.1455	0.87168

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code