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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 07 Jun 2009 11:16:44 -0600

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/07/t1244395037okh65ukjrnew8sh.htm/, Retrieved Mon, 13 May 2024 11:57:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42204, Retrieved Mon, 13 May 2024 11:57:52 +0000

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

-       [(Partial) Autocorrelation Function] [Thomas Van den Bo...] [2009-06-07 17:16:44] [50e97696ebad247f45d73cd9926afb25] [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=42204&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=42204&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42204&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	0.923737	8.9082	0
2	0.829499	7.9994	0
3	0.726309	7.0043	0
4	0.627072	6.0473	0
5	0.542941	5.2359	1e-06
6	0.460395	4.4399	1.2e-05
7	0.395064	3.8099	0.000125
8	0.307404	2.9645	0.001925
9	0.229811	2.2162	0.014558
10	0.163575	1.5775	0.059043
11	0.12487	1.2042	0.115784
12	0.121464	1.1714	0.122225
13	0.128445	1.2387	0.109291
14	0.154281	1.4878	0.070089
15	0.177153	1.7084	0.045449
16	0.196491	1.8949	0.030607
17	0.216179	2.0848	0.019916
18	0.247427	2.3861	0.009527
19	0.279812	2.6984	0.004137

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.923737 & 8.9082 & 0 \tabularnewline
2 & 0.829499 & 7.9994 & 0 \tabularnewline
3 & 0.726309 & 7.0043 & 0 \tabularnewline
4 & 0.627072 & 6.0473 & 0 \tabularnewline
5 & 0.542941 & 5.2359 & 1e-06 \tabularnewline
6 & 0.460395 & 4.4399 & 1.2e-05 \tabularnewline
7 & 0.395064 & 3.8099 & 0.000125 \tabularnewline
8 & 0.307404 & 2.9645 & 0.001925 \tabularnewline
9 & 0.229811 & 2.2162 & 0.014558 \tabularnewline
10 & 0.163575 & 1.5775 & 0.059043 \tabularnewline
11 & 0.12487 & 1.2042 & 0.115784 \tabularnewline
12 & 0.121464 & 1.1714 & 0.122225 \tabularnewline
13 & 0.128445 & 1.2387 & 0.109291 \tabularnewline
14 & 0.154281 & 1.4878 & 0.070089 \tabularnewline
15 & 0.177153 & 1.7084 & 0.045449 \tabularnewline
16 & 0.196491 & 1.8949 & 0.030607 \tabularnewline
17 & 0.216179 & 2.0848 & 0.019916 \tabularnewline
18 & 0.247427 & 2.3861 & 0.009527 \tabularnewline
19 & 0.279812 & 2.6984 & 0.004137 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42204&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]0.923737[/C][C]8.9082[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.829499[/C][C]7.9994[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.726309[/C][C]7.0043[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.627072[/C][C]6.0473[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.542941[/C][C]5.2359[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.460395[/C][C]4.4399[/C][C]1.2e-05[/C][/ROW]
[ROW][C]7[/C][C]0.395064[/C][C]3.8099[/C][C]0.000125[/C][/ROW]
[ROW][C]8[/C][C]0.307404[/C][C]2.9645[/C][C]0.001925[/C][/ROW]
[ROW][C]9[/C][C]0.229811[/C][C]2.2162[/C][C]0.014558[/C][/ROW]
[ROW][C]10[/C][C]0.163575[/C][C]1.5775[/C][C]0.059043[/C][/ROW]
[ROW][C]11[/C][C]0.12487[/C][C]1.2042[/C][C]0.115784[/C][/ROW]
[ROW][C]12[/C][C]0.121464[/C][C]1.1714[/C][C]0.122225[/C][/ROW]
[ROW][C]13[/C][C]0.128445[/C][C]1.2387[/C][C]0.109291[/C][/ROW]
[ROW][C]14[/C][C]0.154281[/C][C]1.4878[/C][C]0.070089[/C][/ROW]
[ROW][C]15[/C][C]0.177153[/C][C]1.7084[/C][C]0.045449[/C][/ROW]
[ROW][C]16[/C][C]0.196491[/C][C]1.8949[/C][C]0.030607[/C][/ROW]
[ROW][C]17[/C][C]0.216179[/C][C]2.0848[/C][C]0.019916[/C][/ROW]
[ROW][C]18[/C][C]0.247427[/C][C]2.3861[/C][C]0.009527[/C][/ROW]
[ROW][C]19[/C][C]0.279812[/C][C]2.6984[/C][C]0.004137[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42204&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42204&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	0.923737	8.9082	0
2	0.829499	7.9994	0
3	0.726309	7.0043	0
4	0.627072	6.0473	0
5	0.542941	5.2359	1e-06
6	0.460395	4.4399	1.2e-05
7	0.395064	3.8099	0.000125
8	0.307404	2.9645	0.001925
9	0.229811	2.2162	0.014558
10	0.163575	1.5775	0.059043
11	0.12487	1.2042	0.115784
12	0.121464	1.1714	0.122225
13	0.128445	1.2387	0.109291
14	0.154281	1.4878	0.070089
15	0.177153	1.7084	0.045449
16	0.196491	1.8949	0.030607
17	0.216179	2.0848	0.019916
18	0.247427	2.3861	0.009527
19	0.279812	2.6984	0.004137

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.923737	8.9082	0
2	-0.162168	-1.5639	0.060619
3	-0.10073	-0.9714	0.166933
4	-0.020636	-0.199	0.421346
5	0.041574	0.4009	0.344696
6	-0.068511	-0.6607	0.255221
7	0.054827	0.5287	0.299127
8	-0.228237	-2.201	0.015104
9	0.043609	0.4205	0.337528
10	0.01824	0.1759	0.430378
11	0.135469	1.3064	0.097316
12	0.133211	1.2846	0.101054
13	0.019835	0.1913	0.424359
14	0.0662	0.6384	0.262387
15	0.026192	0.2526	0.400572
16	-0.013545	-0.1306	0.448179
17	0.039709	0.3829	0.351319
18	0.103061	0.9939	0.16143
19	-0.033443	-0.3225	0.373894

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.923737 & 8.9082 & 0 \tabularnewline
2 & -0.162168 & -1.5639 & 0.060619 \tabularnewline
3 & -0.10073 & -0.9714 & 0.166933 \tabularnewline
4 & -0.020636 & -0.199 & 0.421346 \tabularnewline
5 & 0.041574 & 0.4009 & 0.344696 \tabularnewline
6 & -0.068511 & -0.6607 & 0.255221 \tabularnewline
7 & 0.054827 & 0.5287 & 0.299127 \tabularnewline
8 & -0.228237 & -2.201 & 0.015104 \tabularnewline
9 & 0.043609 & 0.4205 & 0.337528 \tabularnewline
10 & 0.01824 & 0.1759 & 0.430378 \tabularnewline
11 & 0.135469 & 1.3064 & 0.097316 \tabularnewline
12 & 0.133211 & 1.2846 & 0.101054 \tabularnewline
13 & 0.019835 & 0.1913 & 0.424359 \tabularnewline
14 & 0.0662 & 0.6384 & 0.262387 \tabularnewline
15 & 0.026192 & 0.2526 & 0.400572 \tabularnewline
16 & -0.013545 & -0.1306 & 0.448179 \tabularnewline
17 & 0.039709 & 0.3829 & 0.351319 \tabularnewline
18 & 0.103061 & 0.9939 & 0.16143 \tabularnewline
19 & -0.033443 & -0.3225 & 0.373894 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42204&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]0.923737[/C][C]8.9082[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.162168[/C][C]-1.5639[/C][C]0.060619[/C][/ROW]
[ROW][C]3[/C][C]-0.10073[/C][C]-0.9714[/C][C]0.166933[/C][/ROW]
[ROW][C]4[/C][C]-0.020636[/C][C]-0.199[/C][C]0.421346[/C][/ROW]
[ROW][C]5[/C][C]0.041574[/C][C]0.4009[/C][C]0.344696[/C][/ROW]
[ROW][C]6[/C][C]-0.068511[/C][C]-0.6607[/C][C]0.255221[/C][/ROW]
[ROW][C]7[/C][C]0.054827[/C][C]0.5287[/C][C]0.299127[/C][/ROW]
[ROW][C]8[/C][C]-0.228237[/C][C]-2.201[/C][C]0.015104[/C][/ROW]
[ROW][C]9[/C][C]0.043609[/C][C]0.4205[/C][C]0.337528[/C][/ROW]
[ROW][C]10[/C][C]0.01824[/C][C]0.1759[/C][C]0.430378[/C][/ROW]
[ROW][C]11[/C][C]0.135469[/C][C]1.3064[/C][C]0.097316[/C][/ROW]
[ROW][C]12[/C][C]0.133211[/C][C]1.2846[/C][C]0.101054[/C][/ROW]
[ROW][C]13[/C][C]0.019835[/C][C]0.1913[/C][C]0.424359[/C][/ROW]
[ROW][C]14[/C][C]0.0662[/C][C]0.6384[/C][C]0.262387[/C][/ROW]
[ROW][C]15[/C][C]0.026192[/C][C]0.2526[/C][C]0.400572[/C][/ROW]
[ROW][C]16[/C][C]-0.013545[/C][C]-0.1306[/C][C]0.448179[/C][/ROW]
[ROW][C]17[/C][C]0.039709[/C][C]0.3829[/C][C]0.351319[/C][/ROW]
[ROW][C]18[/C][C]0.103061[/C][C]0.9939[/C][C]0.16143[/C][/ROW]
[ROW][C]19[/C][C]-0.033443[/C][C]-0.3225[/C][C]0.373894[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42204&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42204&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	0.923737	8.9082	0
2	-0.162168	-1.5639	0.060619
3	-0.10073	-0.9714	0.166933
4	-0.020636	-0.199	0.421346
5	0.041574	0.4009	0.344696
6	-0.068511	-0.6607	0.255221
7	0.054827	0.5287	0.299127
8	-0.228237	-2.201	0.015104
9	0.043609	0.4205	0.337528
10	0.01824	0.1759	0.430378
11	0.135469	1.3064	0.097316
12	0.133211	1.2846	0.101054
13	0.019835	0.1913	0.424359
14	0.0662	0.6384	0.262387
15	0.026192	0.2526	0.400572
16	-0.013545	-0.1306	0.448179
17	0.039709	0.3829	0.351319
18	0.103061	0.9939	0.16143
19	-0.033443	-0.3225	0.373894

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 = 0 ; 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 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')

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