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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

Thu, 13 Aug 2009 03:24:32 -0600

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/Aug/13/t12501555333fklgbl7fls17rz.htm/, Retrieved Mon, 29 Apr 2024 11:40:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42589, Retrieved Mon, 29 Apr 2024 11:40:49 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

208

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

-       [(Partial) Autocorrelation Function] [Hotelkamers autoc...] [2009-08-13 09:24:32] [21449d9c1cc0a758249d2b9b9c4686bc] [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=42589&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=42589&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42589&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	0.971988	11.1673	0
2	0.941231	10.8139	0
3	0.910309	10.4587	0
4	0.879423	10.1038	0
5	0.851598	9.7841	0
6	0.818985	9.4094	0
7	0.786507	9.0363	0
8	0.763775	8.7751	0
9	0.745909	8.5698	0
10	0.734473	8.4385	0
11	0.722733	8.3036	0
12	0.708017	8.1345	0
13	0.684494	7.8642	0
14	0.658742	7.5684	0
15	0.63298	7.2724	0
16	0.605016	6.9511	0
17	0.577196	6.6315	0
18	0.545646	6.269	0
19	0.514715	5.9136	0
20	0.490422	5.6345	0
21	0.470771	5.4087	0
22	0.453823	5.214	0
23	0.436978	5.0205	1e-06
24	0.418636	4.8098	2e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.971988 & 11.1673 & 0 \tabularnewline
2 & 0.941231 & 10.8139 & 0 \tabularnewline
3 & 0.910309 & 10.4587 & 0 \tabularnewline
4 & 0.879423 & 10.1038 & 0 \tabularnewline
5 & 0.851598 & 9.7841 & 0 \tabularnewline
6 & 0.818985 & 9.4094 & 0 \tabularnewline
7 & 0.786507 & 9.0363 & 0 \tabularnewline
8 & 0.763775 & 8.7751 & 0 \tabularnewline
9 & 0.745909 & 8.5698 & 0 \tabularnewline
10 & 0.734473 & 8.4385 & 0 \tabularnewline
11 & 0.722733 & 8.3036 & 0 \tabularnewline
12 & 0.708017 & 8.1345 & 0 \tabularnewline
13 & 0.684494 & 7.8642 & 0 \tabularnewline
14 & 0.658742 & 7.5684 & 0 \tabularnewline
15 & 0.63298 & 7.2724 & 0 \tabularnewline
16 & 0.605016 & 6.9511 & 0 \tabularnewline
17 & 0.577196 & 6.6315 & 0 \tabularnewline
18 & 0.545646 & 6.269 & 0 \tabularnewline
19 & 0.514715 & 5.9136 & 0 \tabularnewline
20 & 0.490422 & 5.6345 & 0 \tabularnewline
21 & 0.470771 & 5.4087 & 0 \tabularnewline
22 & 0.453823 & 5.214 & 0 \tabularnewline
23 & 0.436978 & 5.0205 & 1e-06 \tabularnewline
24 & 0.418636 & 4.8098 & 2e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42589&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]0.971988[/C][C]11.1673[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.941231[/C][C]10.8139[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.910309[/C][C]10.4587[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.879423[/C][C]10.1038[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.851598[/C][C]9.7841[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.818985[/C][C]9.4094[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.786507[/C][C]9.0363[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.763775[/C][C]8.7751[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.745909[/C][C]8.5698[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.734473[/C][C]8.4385[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.722733[/C][C]8.3036[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.708017[/C][C]8.1345[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.684494[/C][C]7.8642[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.658742[/C][C]7.5684[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.63298[/C][C]7.2724[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.605016[/C][C]6.9511[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.577196[/C][C]6.6315[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.545646[/C][C]6.269[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.514715[/C][C]5.9136[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.490422[/C][C]5.6345[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.470771[/C][C]5.4087[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.453823[/C][C]5.214[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.436978[/C][C]5.0205[/C][C]1e-06[/C][/ROW]
[ROW][C]24[/C][C]0.418636[/C][C]4.8098[/C][C]2e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42589&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42589&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	0.971988	11.1673	0
2	0.941231	10.8139	0
3	0.910309	10.4587	0
4	0.879423	10.1038	0
5	0.851598	9.7841	0
6	0.818985	9.4094	0
7	0.786507	9.0363	0
8	0.763775	8.7751	0
9	0.745909	8.5698	0
10	0.734473	8.4385	0
11	0.722733	8.3036	0
12	0.708017	8.1345	0
13	0.684494	7.8642	0
14	0.658742	7.5684	0
15	0.63298	7.2724	0
16	0.605016	6.9511	0
17	0.577196	6.6315	0
18	0.545646	6.269	0
19	0.514715	5.9136	0
20	0.490422	5.6345	0
21	0.470771	5.4087	0
22	0.453823	5.214	0
23	0.436978	5.0205	1e-06
24	0.418636	4.8098	2e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.971988	11.1673	0
2	-0.063904	-0.7342	0.232064
3	-0.016463	-0.1891	0.425135
4	-0.01537	-0.1766	0.430049
5	0.039163	0.45	0.326742
6	-0.107608	-1.2363	0.109266
7	-0.006624	-0.0761	0.469726
8	0.160877	1.8483	0.033396
9	0.062785	0.7213	0.235988
10	0.088785	1.0201	0.154783
11	-0.016001	-0.1838	0.427213
12	-0.04624	-0.5313	0.298066
13	-0.198296	-2.2782	0.012159
14	-0.050264	-0.5775	0.282295
15	-0.001479	-0.017	0.493233
16	-0.029282	-0.3364	0.368543
17	0.030035	0.3451	0.365292
18	-0.04061	-0.4666	0.320788
19	0.002571	0.0295	0.488242
20	0.034995	0.4021	0.344143
21	0.029448	0.3383	0.367824
22	-0.016205	-0.1862	0.426293
23	-0.0201	-0.2309	0.408865
24	-0.021346	-0.2452	0.403323

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.971988 & 11.1673 & 0 \tabularnewline
2 & -0.063904 & -0.7342 & 0.232064 \tabularnewline
3 & -0.016463 & -0.1891 & 0.425135 \tabularnewline
4 & -0.01537 & -0.1766 & 0.430049 \tabularnewline
5 & 0.039163 & 0.45 & 0.326742 \tabularnewline
6 & -0.107608 & -1.2363 & 0.109266 \tabularnewline
7 & -0.006624 & -0.0761 & 0.469726 \tabularnewline
8 & 0.160877 & 1.8483 & 0.033396 \tabularnewline
9 & 0.062785 & 0.7213 & 0.235988 \tabularnewline
10 & 0.088785 & 1.0201 & 0.154783 \tabularnewline
11 & -0.016001 & -0.1838 & 0.427213 \tabularnewline
12 & -0.04624 & -0.5313 & 0.298066 \tabularnewline
13 & -0.198296 & -2.2782 & 0.012159 \tabularnewline
14 & -0.050264 & -0.5775 & 0.282295 \tabularnewline
15 & -0.001479 & -0.017 & 0.493233 \tabularnewline
16 & -0.029282 & -0.3364 & 0.368543 \tabularnewline
17 & 0.030035 & 0.3451 & 0.365292 \tabularnewline
18 & -0.04061 & -0.4666 & 0.320788 \tabularnewline
19 & 0.002571 & 0.0295 & 0.488242 \tabularnewline
20 & 0.034995 & 0.4021 & 0.344143 \tabularnewline
21 & 0.029448 & 0.3383 & 0.367824 \tabularnewline
22 & -0.016205 & -0.1862 & 0.426293 \tabularnewline
23 & -0.0201 & -0.2309 & 0.408865 \tabularnewline
24 & -0.021346 & -0.2452 & 0.403323 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42589&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]0.971988[/C][C]11.1673[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.063904[/C][C]-0.7342[/C][C]0.232064[/C][/ROW]
[ROW][C]3[/C][C]-0.016463[/C][C]-0.1891[/C][C]0.425135[/C][/ROW]
[ROW][C]4[/C][C]-0.01537[/C][C]-0.1766[/C][C]0.430049[/C][/ROW]
[ROW][C]5[/C][C]0.039163[/C][C]0.45[/C][C]0.326742[/C][/ROW]
[ROW][C]6[/C][C]-0.107608[/C][C]-1.2363[/C][C]0.109266[/C][/ROW]
[ROW][C]7[/C][C]-0.006624[/C][C]-0.0761[/C][C]0.469726[/C][/ROW]
[ROW][C]8[/C][C]0.160877[/C][C]1.8483[/C][C]0.033396[/C][/ROW]
[ROW][C]9[/C][C]0.062785[/C][C]0.7213[/C][C]0.235988[/C][/ROW]
[ROW][C]10[/C][C]0.088785[/C][C]1.0201[/C][C]0.154783[/C][/ROW]
[ROW][C]11[/C][C]-0.016001[/C][C]-0.1838[/C][C]0.427213[/C][/ROW]
[ROW][C]12[/C][C]-0.04624[/C][C]-0.5313[/C][C]0.298066[/C][/ROW]
[ROW][C]13[/C][C]-0.198296[/C][C]-2.2782[/C][C]0.012159[/C][/ROW]
[ROW][C]14[/C][C]-0.050264[/C][C]-0.5775[/C][C]0.282295[/C][/ROW]
[ROW][C]15[/C][C]-0.001479[/C][C]-0.017[/C][C]0.493233[/C][/ROW]
[ROW][C]16[/C][C]-0.029282[/C][C]-0.3364[/C][C]0.368543[/C][/ROW]
[ROW][C]17[/C][C]0.030035[/C][C]0.3451[/C][C]0.365292[/C][/ROW]
[ROW][C]18[/C][C]-0.04061[/C][C]-0.4666[/C][C]0.320788[/C][/ROW]
[ROW][C]19[/C][C]0.002571[/C][C]0.0295[/C][C]0.488242[/C][/ROW]
[ROW][C]20[/C][C]0.034995[/C][C]0.4021[/C][C]0.344143[/C][/ROW]
[ROW][C]21[/C][C]0.029448[/C][C]0.3383[/C][C]0.367824[/C][/ROW]
[ROW][C]22[/C][C]-0.016205[/C][C]-0.1862[/C][C]0.426293[/C][/ROW]
[ROW][C]23[/C][C]-0.0201[/C][C]-0.2309[/C][C]0.408865[/C][/ROW]
[ROW][C]24[/C][C]-0.021346[/C][C]-0.2452[/C][C]0.403323[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42589&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42589&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	0.971988	11.1673	0
2	-0.063904	-0.7342	0.232064
3	-0.016463	-0.1891	0.425135
4	-0.01537	-0.1766	0.430049
5	0.039163	0.45	0.326742
6	-0.107608	-1.2363	0.109266
7	-0.006624	-0.0761	0.469726
8	0.160877	1.8483	0.033396
9	0.062785	0.7213	0.235988
10	0.088785	1.0201	0.154783
11	-0.016001	-0.1838	0.427213
12	-0.04624	-0.5313	0.298066
13	-0.198296	-2.2782	0.012159
14	-0.050264	-0.5775	0.282295
15	-0.001479	-0.017	0.493233
16	-0.029282	-0.3364	0.368543
17	0.030035	0.3451	0.365292
18	-0.04061	-0.4666	0.320788
19	0.002571	0.0295	0.488242
20	0.034995	0.4021	0.344143
21	0.029448	0.3383	0.367824
22	-0.016205	-0.1862	0.426293
23	-0.0201	-0.2309	0.408865
24	-0.021346	-0.2452	0.403323

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 24 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code