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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 21 Dec 2008 04:01:16 -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/2008/Dec/21/t1229857498py8rb1p5v2mh6rx.htm/, Retrieved Sun, 19 May 2024 11:31:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35491, Retrieved Sun, 19 May 2024 11:31:09 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

204

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

-     [Standard Deviation-Mean Plot] [] [2008-12-21 10:26:45] [339926f84f7378398edd9a77d1fc8e74]
- RMPD    [(Partial) Autocorrelation Function] [] [2008-12-21 11:01:16] [76e580e81b2082744334eb1f6d9ccc3e] [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	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35491&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35491&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35491&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	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.971388	8.9558	0
2	0.935254	8.6226	0
3	0.90722	8.3642	0
4	0.876417	8.0802	0
5	0.842646	7.7688	0
6	0.79755	7.353	0
7	0.752193	6.9349	0
8	0.71039	6.5495	0
9	0.670498	6.1817	0
10	0.635482	5.8589	0
11	0.601139	5.5422	0
12	0.559524	5.1586	1e-06
13	0.516116	4.7584	4e-06
14	0.481368	4.438	1.4e-05
15	0.448873	4.1384	4.1e-05
16	0.41157	3.7945	0.000138
17	0.370911	3.4196	0.000483
18	0.328744	3.0309	0.001616
19	0.290017	2.6738	0.004496

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.971388 & 8.9558 & 0 \tabularnewline
2 & 0.935254 & 8.6226 & 0 \tabularnewline
3 & 0.90722 & 8.3642 & 0 \tabularnewline
4 & 0.876417 & 8.0802 & 0 \tabularnewline
5 & 0.842646 & 7.7688 & 0 \tabularnewline
6 & 0.79755 & 7.353 & 0 \tabularnewline
7 & 0.752193 & 6.9349 & 0 \tabularnewline
8 & 0.71039 & 6.5495 & 0 \tabularnewline
9 & 0.670498 & 6.1817 & 0 \tabularnewline
10 & 0.635482 & 5.8589 & 0 \tabularnewline
11 & 0.601139 & 5.5422 & 0 \tabularnewline
12 & 0.559524 & 5.1586 & 1e-06 \tabularnewline
13 & 0.516116 & 4.7584 & 4e-06 \tabularnewline
14 & 0.481368 & 4.438 & 1.4e-05 \tabularnewline
15 & 0.448873 & 4.1384 & 4.1e-05 \tabularnewline
16 & 0.41157 & 3.7945 & 0.000138 \tabularnewline
17 & 0.370911 & 3.4196 & 0.000483 \tabularnewline
18 & 0.328744 & 3.0309 & 0.001616 \tabularnewline
19 & 0.290017 & 2.6738 & 0.004496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35491&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]0.971388[/C][C]8.9558[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.935254[/C][C]8.6226[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.90722[/C][C]8.3642[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.876417[/C][C]8.0802[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.842646[/C][C]7.7688[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.79755[/C][C]7.353[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.752193[/C][C]6.9349[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.71039[/C][C]6.5495[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.670498[/C][C]6.1817[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.635482[/C][C]5.8589[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.601139[/C][C]5.5422[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.559524[/C][C]5.1586[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.516116[/C][C]4.7584[/C][C]4e-06[/C][/ROW]
[ROW][C]14[/C][C]0.481368[/C][C]4.438[/C][C]1.4e-05[/C][/ROW]
[ROW][C]15[/C][C]0.448873[/C][C]4.1384[/C][C]4.1e-05[/C][/ROW]
[ROW][C]16[/C][C]0.41157[/C][C]3.7945[/C][C]0.000138[/C][/ROW]
[ROW][C]17[/C][C]0.370911[/C][C]3.4196[/C][C]0.000483[/C][/ROW]
[ROW][C]18[/C][C]0.328744[/C][C]3.0309[/C][C]0.001616[/C][/ROW]
[ROW][C]19[/C][C]0.290017[/C][C]2.6738[/C][C]0.004496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35491&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35491&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	0.971388	8.9558	0
2	0.935254	8.6226	0
3	0.90722	8.3642	0
4	0.876417	8.0802	0
5	0.842646	7.7688	0
6	0.79755	7.353	0
7	0.752193	6.9349	0
8	0.71039	6.5495	0
9	0.670498	6.1817	0
10	0.635482	5.8589	0
11	0.601139	5.5422	0
12	0.559524	5.1586	1e-06
13	0.516116	4.7584	4e-06
14	0.481368	4.438	1.4e-05
15	0.448873	4.1384	4.1e-05
16	0.41157	3.7945	0.000138
17	0.370911	3.4196	0.000483
18	0.328744	3.0309	0.001616
19	0.290017	2.6738	0.004496

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.971388	8.9558	0
2	-0.147865	-1.3633	0.088202
3	0.145443	1.3409	0.09176
4	-0.110771	-1.0213	0.155016
5	-0.02409	-0.2221	0.412383
6	-0.243516	-2.2451	0.013679
7	0.037259	0.3435	0.366032
8	-0.040151	-0.3702	0.356086
9	0.052142	0.4807	0.315975
10	0.064981	0.5991	0.27535
11	0.020852	0.1922	0.424005
12	-0.162452	-1.4977	0.068953
13	-0.040294	-0.3715	0.355597
14	0.07771	0.7164	0.237839
15	-0.043719	-0.4031	0.343954
16	-0.070197	-0.6472	0.259628
17	-0.027029	-0.2492	0.401906
18	-0.063836	-0.5885	0.278865
19	-0.010557	-0.0973	0.461345

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.971388 & 8.9558 & 0 \tabularnewline
2 & -0.147865 & -1.3633 & 0.088202 \tabularnewline
3 & 0.145443 & 1.3409 & 0.09176 \tabularnewline
4 & -0.110771 & -1.0213 & 0.155016 \tabularnewline
5 & -0.02409 & -0.2221 & 0.412383 \tabularnewline
6 & -0.243516 & -2.2451 & 0.013679 \tabularnewline
7 & 0.037259 & 0.3435 & 0.366032 \tabularnewline
8 & -0.040151 & -0.3702 & 0.356086 \tabularnewline
9 & 0.052142 & 0.4807 & 0.315975 \tabularnewline
10 & 0.064981 & 0.5991 & 0.27535 \tabularnewline
11 & 0.020852 & 0.1922 & 0.424005 \tabularnewline
12 & -0.162452 & -1.4977 & 0.068953 \tabularnewline
13 & -0.040294 & -0.3715 & 0.355597 \tabularnewline
14 & 0.07771 & 0.7164 & 0.237839 \tabularnewline
15 & -0.043719 & -0.4031 & 0.343954 \tabularnewline
16 & -0.070197 & -0.6472 & 0.259628 \tabularnewline
17 & -0.027029 & -0.2492 & 0.401906 \tabularnewline
18 & -0.063836 & -0.5885 & 0.278865 \tabularnewline
19 & -0.010557 & -0.0973 & 0.461345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35491&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]0.971388[/C][C]8.9558[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.147865[/C][C]-1.3633[/C][C]0.088202[/C][/ROW]
[ROW][C]3[/C][C]0.145443[/C][C]1.3409[/C][C]0.09176[/C][/ROW]
[ROW][C]4[/C][C]-0.110771[/C][C]-1.0213[/C][C]0.155016[/C][/ROW]
[ROW][C]5[/C][C]-0.02409[/C][C]-0.2221[/C][C]0.412383[/C][/ROW]
[ROW][C]6[/C][C]-0.243516[/C][C]-2.2451[/C][C]0.013679[/C][/ROW]
[ROW][C]7[/C][C]0.037259[/C][C]0.3435[/C][C]0.366032[/C][/ROW]
[ROW][C]8[/C][C]-0.040151[/C][C]-0.3702[/C][C]0.356086[/C][/ROW]
[ROW][C]9[/C][C]0.052142[/C][C]0.4807[/C][C]0.315975[/C][/ROW]
[ROW][C]10[/C][C]0.064981[/C][C]0.5991[/C][C]0.27535[/C][/ROW]
[ROW][C]11[/C][C]0.020852[/C][C]0.1922[/C][C]0.424005[/C][/ROW]
[ROW][C]12[/C][C]-0.162452[/C][C]-1.4977[/C][C]0.068953[/C][/ROW]
[ROW][C]13[/C][C]-0.040294[/C][C]-0.3715[/C][C]0.355597[/C][/ROW]
[ROW][C]14[/C][C]0.07771[/C][C]0.7164[/C][C]0.237839[/C][/ROW]
[ROW][C]15[/C][C]-0.043719[/C][C]-0.4031[/C][C]0.343954[/C][/ROW]
[ROW][C]16[/C][C]-0.070197[/C][C]-0.6472[/C][C]0.259628[/C][/ROW]
[ROW][C]17[/C][C]-0.027029[/C][C]-0.2492[/C][C]0.401906[/C][/ROW]
[ROW][C]18[/C][C]-0.063836[/C][C]-0.5885[/C][C]0.278865[/C][/ROW]
[ROW][C]19[/C][C]-0.010557[/C][C]-0.0973[/C][C]0.461345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35491&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35491&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	0.971388	8.9558	0
2	-0.147865	-1.3633	0.088202
3	0.145443	1.3409	0.09176
4	-0.110771	-1.0213	0.155016
5	-0.02409	-0.2221	0.412383
6	-0.243516	-2.2451	0.013679
7	0.037259	0.3435	0.366032
8	-0.040151	-0.3702	0.356086
9	0.052142	0.4807	0.315975
10	0.064981	0.5991	0.27535
11	0.020852	0.1922	0.424005
12	-0.162452	-1.4977	0.068953
13	-0.040294	-0.3715	0.355597
14	0.07771	0.7164	0.237839
15	-0.043719	-0.4031	0.343954
16	-0.070197	-0.6472	0.259628
17	-0.027029	-0.2492	0.401906
18	-0.063836	-0.5885	0.278865
19	-0.010557	-0.0973	0.461345

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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