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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Nov 2007 04:19:19 -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/Nov/28/t1196248206ofqgsa6q3ea60qt.htm/, Retrieved Thu, 02 May 2024 06:36:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7021, Retrieved Thu, 02 May 2024 06:36:23 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

193

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

-       [(Partial) Autocorrelation Function] [Inducing Stationa...] [2007-11-28 11:19:19] [157a0cf3c12a7482b4e6935b4c49d48f] [Current]

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Dataseries X:

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Histogram

Boxplots

1.43
1.43
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1.57
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1.65

Summary of compuational 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 compuational 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=7021&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]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=7021&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7021&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.4853	0
1	0.957206	8.1222	0
2	0.910896	7.7292	0
3	0.864117	7.3323	0
4	0.816636	6.9294	0
5	0.77195	6.5502	0
6	0.724452	6.1472	0
7	0.674141	5.7203	0
8	0.623128	5.2874	1e-06
9	0.569536	4.8327	4e-06
10	0.518975	4.4036	1.8e-05
11	0.468179	3.9726	8.3e-05
12	0.41807	3.5474	0.000344
13	0.369117	3.1321	0.001255
14	0.319696	2.7127	0.004171
15	0.26793	2.2735	0.012991
16	0.219429	1.8619	0.033348
17	0.170929	1.4504	0.075648

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.957206 & 8.1222 & 0 \tabularnewline
2 & 0.910896 & 7.7292 & 0 \tabularnewline
3 & 0.864117 & 7.3323 & 0 \tabularnewline
4 & 0.816636 & 6.9294 & 0 \tabularnewline
5 & 0.77195 & 6.5502 & 0 \tabularnewline
6 & 0.724452 & 6.1472 & 0 \tabularnewline
7 & 0.674141 & 5.7203 & 0 \tabularnewline
8 & 0.623128 & 5.2874 & 1e-06 \tabularnewline
9 & 0.569536 & 4.8327 & 4e-06 \tabularnewline
10 & 0.518975 & 4.4036 & 1.8e-05 \tabularnewline
11 & 0.468179 & 3.9726 & 8.3e-05 \tabularnewline
12 & 0.41807 & 3.5474 & 0.000344 \tabularnewline
13 & 0.369117 & 3.1321 & 0.001255 \tabularnewline
14 & 0.319696 & 2.7127 & 0.004171 \tabularnewline
15 & 0.26793 & 2.2735 & 0.012991 \tabularnewline
16 & 0.219429 & 1.8619 & 0.033348 \tabularnewline
17 & 0.170929 & 1.4504 & 0.075648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7021&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.957206[/C][C]8.1222[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.910896[/C][C]7.7292[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.864117[/C][C]7.3323[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.816636[/C][C]6.9294[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.77195[/C][C]6.5502[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.724452[/C][C]6.1472[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.674141[/C][C]5.7203[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.623128[/C][C]5.2874[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.569536[/C][C]4.8327[/C][C]4e-06[/C][/ROW]
[ROW][C]10[/C][C]0.518975[/C][C]4.4036[/C][C]1.8e-05[/C][/ROW]
[ROW][C]11[/C][C]0.468179[/C][C]3.9726[/C][C]8.3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.41807[/C][C]3.5474[/C][C]0.000344[/C][/ROW]
[ROW][C]13[/C][C]0.369117[/C][C]3.1321[/C][C]0.001255[/C][/ROW]
[ROW][C]14[/C][C]0.319696[/C][C]2.7127[/C][C]0.004171[/C][/ROW]
[ROW][C]15[/C][C]0.26793[/C][C]2.2735[/C][C]0.012991[/C][/ROW]
[ROW][C]16[/C][C]0.219429[/C][C]1.8619[/C][C]0.033348[/C][/ROW]
[ROW][C]17[/C][C]0.170929[/C][C]1.4504[/C][C]0.075648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7021&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7021&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	8.4853	0
1	0.957206	8.1222	0
2	0.910896	7.7292	0
3	0.864117	7.3323	0
4	0.816636	6.9294	0
5	0.77195	6.5502	0
6	0.724452	6.1472	0
7	0.674141	5.7203	0
8	0.623128	5.2874	1e-06
9	0.569536	4.8327	4e-06
10	0.518975	4.4036	1.8e-05
11	0.468179	3.9726	8.3e-05
12	0.41807	3.5474	0.000344
13	0.369117	3.1321	0.001255
14	0.319696	2.7127	0.004171
15	0.26793	2.2735	0.012991
16	0.219429	1.8619	0.033348
17	0.170929	1.4504	0.075648

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.957206	8.1222	0
1	-0.063839	-0.5417	0.705149
2	-0.028204	-0.2393	0.59423
3	-0.033162	-0.2814	0.610389
4	0.0081	0.0687	0.472697
5	-0.061597	-0.5227	0.698595
6	-0.0589	-0.4998	0.690625
7	-0.036397	-0.3088	0.620832
8	-0.060199	-0.5108	0.694476
9	0.00296	0.0251	0.490017
10	-0.03985	-0.3381	0.631877
11	-0.024188	-0.2052	0.581019
12	-0.023229	-0.1971	0.577851
13	-0.03768	-0.3197	0.62495
14	-0.066598	-0.5651	0.71312
15	0.000184	0.0016	0.49938
16	-0.041572	-0.3528	0.637348
17	-0.004675	-0.0397	0.515768

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.957206 & 8.1222 & 0 \tabularnewline
1 & -0.063839 & -0.5417 & 0.705149 \tabularnewline
2 & -0.028204 & -0.2393 & 0.59423 \tabularnewline
3 & -0.033162 & -0.2814 & 0.610389 \tabularnewline
4 & 0.0081 & 0.0687 & 0.472697 \tabularnewline
5 & -0.061597 & -0.5227 & 0.698595 \tabularnewline
6 & -0.0589 & -0.4998 & 0.690625 \tabularnewline
7 & -0.036397 & -0.3088 & 0.620832 \tabularnewline
8 & -0.060199 & -0.5108 & 0.694476 \tabularnewline
9 & 0.00296 & 0.0251 & 0.490017 \tabularnewline
10 & -0.03985 & -0.3381 & 0.631877 \tabularnewline
11 & -0.024188 & -0.2052 & 0.581019 \tabularnewline
12 & -0.023229 & -0.1971 & 0.577851 \tabularnewline
13 & -0.03768 & -0.3197 & 0.62495 \tabularnewline
14 & -0.066598 & -0.5651 & 0.71312 \tabularnewline
15 & 0.000184 & 0.0016 & 0.49938 \tabularnewline
16 & -0.041572 & -0.3528 & 0.637348 \tabularnewline
17 & -0.004675 & -0.0397 & 0.515768 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7021&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]0.957206[/C][C]8.1222[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.063839[/C][C]-0.5417[/C][C]0.705149[/C][/ROW]
[ROW][C]2[/C][C]-0.028204[/C][C]-0.2393[/C][C]0.59423[/C][/ROW]
[ROW][C]3[/C][C]-0.033162[/C][C]-0.2814[/C][C]0.610389[/C][/ROW]
[ROW][C]4[/C][C]0.0081[/C][C]0.0687[/C][C]0.472697[/C][/ROW]
[ROW][C]5[/C][C]-0.061597[/C][C]-0.5227[/C][C]0.698595[/C][/ROW]
[ROW][C]6[/C][C]-0.0589[/C][C]-0.4998[/C][C]0.690625[/C][/ROW]
[ROW][C]7[/C][C]-0.036397[/C][C]-0.3088[/C][C]0.620832[/C][/ROW]
[ROW][C]8[/C][C]-0.060199[/C][C]-0.5108[/C][C]0.694476[/C][/ROW]
[ROW][C]9[/C][C]0.00296[/C][C]0.0251[/C][C]0.490017[/C][/ROW]
[ROW][C]10[/C][C]-0.03985[/C][C]-0.3381[/C][C]0.631877[/C][/ROW]
[ROW][C]11[/C][C]-0.024188[/C][C]-0.2052[/C][C]0.581019[/C][/ROW]
[ROW][C]12[/C][C]-0.023229[/C][C]-0.1971[/C][C]0.577851[/C][/ROW]
[ROW][C]13[/C][C]-0.03768[/C][C]-0.3197[/C][C]0.62495[/C][/ROW]
[ROW][C]14[/C][C]-0.066598[/C][C]-0.5651[/C][C]0.71312[/C][/ROW]
[ROW][C]15[/C][C]0.000184[/C][C]0.0016[/C][C]0.49938[/C][/ROW]
[ROW][C]16[/C][C]-0.041572[/C][C]-0.3528[/C][C]0.637348[/C][/ROW]
[ROW][C]17[/C][C]-0.004675[/C][C]-0.0397[/C][C]0.515768[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7021&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7021&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	0.957206	8.1222	0
1	-0.063839	-0.5417	0.705149
2	-0.028204	-0.2393	0.59423
3	-0.033162	-0.2814	0.610389
4	0.0081	0.0687	0.472697
5	-0.061597	-0.5227	0.698595
6	-0.0589	-0.4998	0.690625
7	-0.036397	-0.3088	0.620832
8	-0.060199	-0.5108	0.694476
9	0.00296	0.0251	0.490017
10	-0.03985	-0.3381	0.631877
11	-0.024188	-0.2052	0.581019
12	-0.023229	-0.1971	0.577851
13	-0.03768	-0.3197	0.62495
14	-0.066598	-0.5651	0.71312
15	0.000184	0.0016	0.49938
16	-0.041572	-0.3528	0.637348
17	-0.004675	-0.0397	0.515768

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 = 3 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 3 ;

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code