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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 06:04:50 -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/22/t11957362094nd3cm1ev4w0cy2.htm/, Retrieved Thu, 02 May 2024 18:02:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5966, Retrieved Thu, 02 May 2024 18:02:32 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

WS10 G29 Q2

Estimated Impact

168

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

-       [(Partial) Autocorrelation Function] [partial auto corr] [2007-11-22 13:04:50] [7a600ca82a81f1b71fd92dcbb183f5b4] [Current]

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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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5966&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5966&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5966&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	11.8743	0
1	0.93367	11.0867	0
2	0.849929	10.0923	0
3	0.759615	9.0199	0
4	0.669467	7.9495	0
5	0.587359	6.9745	0
6	0.52142	6.1915	0
7	0.458226	5.4411	0
8	0.40459	4.8042	2e-06
9	0.359546	4.2694	1.8e-05
10	0.335402	3.9827	5.4e-05
11	0.319373	3.7923	0.00011
12	0.308221	3.6599	0.000178
13	0.29535	3.5071	0.000304
14	0.275255	3.2685	0.000679
15	0.240417	2.8548	0.002478
16	0.203837	2.4204	0.008387
17	0.166378	1.9756	0.025074
18	0.137536	1.6332	0.052334
19	0.109912	1.3051	0.096986
20	0.078118	0.9276	0.1776

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 11.8743 & 0 \tabularnewline
1 & 0.93367 & 11.0867 & 0 \tabularnewline
2 & 0.849929 & 10.0923 & 0 \tabularnewline
3 & 0.759615 & 9.0199 & 0 \tabularnewline
4 & 0.669467 & 7.9495 & 0 \tabularnewline
5 & 0.587359 & 6.9745 & 0 \tabularnewline
6 & 0.52142 & 6.1915 & 0 \tabularnewline
7 & 0.458226 & 5.4411 & 0 \tabularnewline
8 & 0.40459 & 4.8042 & 2e-06 \tabularnewline
9 & 0.359546 & 4.2694 & 1.8e-05 \tabularnewline
10 & 0.335402 & 3.9827 & 5.4e-05 \tabularnewline
11 & 0.319373 & 3.7923 & 0.00011 \tabularnewline
12 & 0.308221 & 3.6599 & 0.000178 \tabularnewline
13 & 0.29535 & 3.5071 & 0.000304 \tabularnewline
14 & 0.275255 & 3.2685 & 0.000679 \tabularnewline
15 & 0.240417 & 2.8548 & 0.002478 \tabularnewline
16 & 0.203837 & 2.4204 & 0.008387 \tabularnewline
17 & 0.166378 & 1.9756 & 0.025074 \tabularnewline
18 & 0.137536 & 1.6332 & 0.052334 \tabularnewline
19 & 0.109912 & 1.3051 & 0.096986 \tabularnewline
20 & 0.078118 & 0.9276 & 0.1776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5966&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]11.8743[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.93367[/C][C]11.0867[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.849929[/C][C]10.0923[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.759615[/C][C]9.0199[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.669467[/C][C]7.9495[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.587359[/C][C]6.9745[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.52142[/C][C]6.1915[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.458226[/C][C]5.4411[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.40459[/C][C]4.8042[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.359546[/C][C]4.2694[/C][C]1.8e-05[/C][/ROW]
[ROW][C]10[/C][C]0.335402[/C][C]3.9827[/C][C]5.4e-05[/C][/ROW]
[ROW][C]11[/C][C]0.319373[/C][C]3.7923[/C][C]0.00011[/C][/ROW]
[ROW][C]12[/C][C]0.308221[/C][C]3.6599[/C][C]0.000178[/C][/ROW]
[ROW][C]13[/C][C]0.29535[/C][C]3.5071[/C][C]0.000304[/C][/ROW]
[ROW][C]14[/C][C]0.275255[/C][C]3.2685[/C][C]0.000679[/C][/ROW]
[ROW][C]15[/C][C]0.240417[/C][C]2.8548[/C][C]0.002478[/C][/ROW]
[ROW][C]16[/C][C]0.203837[/C][C]2.4204[/C][C]0.008387[/C][/ROW]
[ROW][C]17[/C][C]0.166378[/C][C]1.9756[/C][C]0.025074[/C][/ROW]
[ROW][C]18[/C][C]0.137536[/C][C]1.6332[/C][C]0.052334[/C][/ROW]
[ROW][C]19[/C][C]0.109912[/C][C]1.3051[/C][C]0.096986[/C][/ROW]
[ROW][C]20[/C][C]0.078118[/C][C]0.9276[/C][C]0.1776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5966&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5966&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	11.8743	0
1	0.93367	11.0867	0
2	0.849929	10.0923	0
3	0.759615	9.0199	0
4	0.669467	7.9495	0
5	0.587359	6.9745	0
6	0.52142	6.1915	0
7	0.458226	5.4411	0
8	0.40459	4.8042	2e-06
9	0.359546	4.2694	1.8e-05
10	0.335402	3.9827	5.4e-05
11	0.319373	3.7923	0.00011
12	0.308221	3.6599	0.000178
13	0.29535	3.5071	0.000304
14	0.275255	3.2685	0.000679
15	0.240417	2.8548	0.002478
16	0.203837	2.4204	0.008387
17	0.166378	1.9756	0.025074
18	0.137536	1.6332	0.052334
19	0.109912	1.3051	0.096986
20	0.078118	0.9276	0.1776

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.93367	11.0867	0
1	-0.170055	-2.0193	0.977324
2	-0.081176	-0.9639	0.831629
3	-0.03985	-0.4732	0.681596
4	0.010958	0.1301	0.44833
5	0.063507	0.7541	0.226022
6	-0.055787	-0.6624	0.745611
7	0.021285	0.2528	0.400415
8	0.014354	0.1704	0.43245
9	0.124477	1.4781	0.070808
10	0.009213	0.1094	0.456523
11	-0.001833	-0.0218	0.508667
12	-0.026871	-0.3191	0.624927
13	-0.052459	-0.6229	0.732826
14	-0.091008	-1.0807	0.859154
15	-0.004096	-0.0486	0.519361
16	-0.008559	-0.1016	0.540404
17	0.051091	0.6067	0.272521
18	-0.022544	-0.2677	0.605339
19	-0.072409	-0.8598	0.804324
20	-0.052443	-0.6227	0.732766

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.93367 & 11.0867 & 0 \tabularnewline
1 & -0.170055 & -2.0193 & 0.977324 \tabularnewline
2 & -0.081176 & -0.9639 & 0.831629 \tabularnewline
3 & -0.03985 & -0.4732 & 0.681596 \tabularnewline
4 & 0.010958 & 0.1301 & 0.44833 \tabularnewline
5 & 0.063507 & 0.7541 & 0.226022 \tabularnewline
6 & -0.055787 & -0.6624 & 0.745611 \tabularnewline
7 & 0.021285 & 0.2528 & 0.400415 \tabularnewline
8 & 0.014354 & 0.1704 & 0.43245 \tabularnewline
9 & 0.124477 & 1.4781 & 0.070808 \tabularnewline
10 & 0.009213 & 0.1094 & 0.456523 \tabularnewline
11 & -0.001833 & -0.0218 & 0.508667 \tabularnewline
12 & -0.026871 & -0.3191 & 0.624927 \tabularnewline
13 & -0.052459 & -0.6229 & 0.732826 \tabularnewline
14 & -0.091008 & -1.0807 & 0.859154 \tabularnewline
15 & -0.004096 & -0.0486 & 0.519361 \tabularnewline
16 & -0.008559 & -0.1016 & 0.540404 \tabularnewline
17 & 0.051091 & 0.6067 & 0.272521 \tabularnewline
18 & -0.022544 & -0.2677 & 0.605339 \tabularnewline
19 & -0.072409 & -0.8598 & 0.804324 \tabularnewline
20 & -0.052443 & -0.6227 & 0.732766 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5966&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]0.93367[/C][C]11.0867[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.170055[/C][C]-2.0193[/C][C]0.977324[/C][/ROW]
[ROW][C]2[/C][C]-0.081176[/C][C]-0.9639[/C][C]0.831629[/C][/ROW]
[ROW][C]3[/C][C]-0.03985[/C][C]-0.4732[/C][C]0.681596[/C][/ROW]
[ROW][C]4[/C][C]0.010958[/C][C]0.1301[/C][C]0.44833[/C][/ROW]
[ROW][C]5[/C][C]0.063507[/C][C]0.7541[/C][C]0.226022[/C][/ROW]
[ROW][C]6[/C][C]-0.055787[/C][C]-0.6624[/C][C]0.745611[/C][/ROW]
[ROW][C]7[/C][C]0.021285[/C][C]0.2528[/C][C]0.400415[/C][/ROW]
[ROW][C]8[/C][C]0.014354[/C][C]0.1704[/C][C]0.43245[/C][/ROW]
[ROW][C]9[/C][C]0.124477[/C][C]1.4781[/C][C]0.070808[/C][/ROW]
[ROW][C]10[/C][C]0.009213[/C][C]0.1094[/C][C]0.456523[/C][/ROW]
[ROW][C]11[/C][C]-0.001833[/C][C]-0.0218[/C][C]0.508667[/C][/ROW]
[ROW][C]12[/C][C]-0.026871[/C][C]-0.3191[/C][C]0.624927[/C][/ROW]
[ROW][C]13[/C][C]-0.052459[/C][C]-0.6229[/C][C]0.732826[/C][/ROW]
[ROW][C]14[/C][C]-0.091008[/C][C]-1.0807[/C][C]0.859154[/C][/ROW]
[ROW][C]15[/C][C]-0.004096[/C][C]-0.0486[/C][C]0.519361[/C][/ROW]
[ROW][C]16[/C][C]-0.008559[/C][C]-0.1016[/C][C]0.540404[/C][/ROW]
[ROW][C]17[/C][C]0.051091[/C][C]0.6067[/C][C]0.272521[/C][/ROW]
[ROW][C]18[/C][C]-0.022544[/C][C]-0.2677[/C][C]0.605339[/C][/ROW]
[ROW][C]19[/C][C]-0.072409[/C][C]-0.8598[/C][C]0.804324[/C][/ROW]
[ROW][C]20[/C][C]-0.052443[/C][C]-0.6227[/C][C]0.732766[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5966&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5966&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	0.93367	11.0867	0
1	-0.170055	-2.0193	0.977324
2	-0.081176	-0.9639	0.831629
3	-0.03985	-0.4732	0.681596
4	0.010958	0.1301	0.44833
5	0.063507	0.7541	0.226022
6	-0.055787	-0.6624	0.745611
7	0.021285	0.2528	0.400415
8	0.014354	0.1704	0.43245
9	0.124477	1.4781	0.070808
10	0.009213	0.1094	0.456523
11	-0.001833	-0.0218	0.508667
12	-0.026871	-0.3191	0.624927
13	-0.052459	-0.6229	0.732826
14	-0.091008	-1.0807	0.859154
15	-0.004096	-0.0486	0.519361
16	-0.008559	-0.1016	0.540404
17	0.051091	0.6067	0.272521
18	-0.022544	-0.2677	0.605339
19	-0.072409	-0.8598	0.804324
20	-0.052443	-0.6227	0.732766

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 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code