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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 01 Dec 2007 04:59:51 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/01/t1196509843c9rik7y3848qrdy.htm/, Retrieved Sun, 19 May 2024 20:29:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2218, Retrieved Sun, 19 May 2024 20:29:02 +0000

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Estimated Impact

210

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-       [(Partial) Autocorrelation Function] [autocorrelation w...] [2007-12-01 11:59:51] [bd02e85be52eb1cb060a2c60779eb820] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2218&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2218&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2218&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	10.3923	0
1	0.765288	7.9531	0
2	0.357412	3.7143	0.000162
3	0.021529	0.2237	0.411691
4	-0.140091	-1.4559	0.925835
5	-0.161216	-1.6754	0.951626
6	-0.142438	-1.4803	0.929142
7	-0.13526	-1.4057	0.918652
8	-0.108896	-1.1317	0.869862
9	0.032939	0.3423	0.36639
10	0.312814	3.2509	0.000767
11	0.650649	6.7617	0
12	0.822888	8.5517	0
13	0.593751	6.1704	0
14	0.22243	2.3116	0.01135
15	-0.084526	-0.8784	0.809168
16	-0.232948	-2.4209	0.991425
17	-0.251687	-2.6156	0.99491
18	-0.232124	-2.4123	0.991231
19	-0.229944	-2.3896	0.990701

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 10.3923 & 0 \tabularnewline
1 & 0.765288 & 7.9531 & 0 \tabularnewline
2 & 0.357412 & 3.7143 & 0.000162 \tabularnewline
3 & 0.021529 & 0.2237 & 0.411691 \tabularnewline
4 & -0.140091 & -1.4559 & 0.925835 \tabularnewline
5 & -0.161216 & -1.6754 & 0.951626 \tabularnewline
6 & -0.142438 & -1.4803 & 0.929142 \tabularnewline
7 & -0.13526 & -1.4057 & 0.918652 \tabularnewline
8 & -0.108896 & -1.1317 & 0.869862 \tabularnewline
9 & 0.032939 & 0.3423 & 0.36639 \tabularnewline
10 & 0.312814 & 3.2509 & 0.000767 \tabularnewline
11 & 0.650649 & 6.7617 & 0 \tabularnewline
12 & 0.822888 & 8.5517 & 0 \tabularnewline
13 & 0.593751 & 6.1704 & 0 \tabularnewline
14 & 0.22243 & 2.3116 & 0.01135 \tabularnewline
15 & -0.084526 & -0.8784 & 0.809168 \tabularnewline
16 & -0.232948 & -2.4209 & 0.991425 \tabularnewline
17 & -0.251687 & -2.6156 & 0.99491 \tabularnewline
18 & -0.232124 & -2.4123 & 0.991231 \tabularnewline
19 & -0.229944 & -2.3896 & 0.990701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2218&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]10.3923[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.765288[/C][C]7.9531[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.357412[/C][C]3.7143[/C][C]0.000162[/C][/ROW]
[ROW][C]3[/C][C]0.021529[/C][C]0.2237[/C][C]0.411691[/C][/ROW]
[ROW][C]4[/C][C]-0.140091[/C][C]-1.4559[/C][C]0.925835[/C][/ROW]
[ROW][C]5[/C][C]-0.161216[/C][C]-1.6754[/C][C]0.951626[/C][/ROW]
[ROW][C]6[/C][C]-0.142438[/C][C]-1.4803[/C][C]0.929142[/C][/ROW]
[ROW][C]7[/C][C]-0.13526[/C][C]-1.4057[/C][C]0.918652[/C][/ROW]
[ROW][C]8[/C][C]-0.108896[/C][C]-1.1317[/C][C]0.869862[/C][/ROW]
[ROW][C]9[/C][C]0.032939[/C][C]0.3423[/C][C]0.36639[/C][/ROW]
[ROW][C]10[/C][C]0.312814[/C][C]3.2509[/C][C]0.000767[/C][/ROW]
[ROW][C]11[/C][C]0.650649[/C][C]6.7617[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.822888[/C][C]8.5517[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.593751[/C][C]6.1704[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.22243[/C][C]2.3116[/C][C]0.01135[/C][/ROW]
[ROW][C]15[/C][C]-0.084526[/C][C]-0.8784[/C][C]0.809168[/C][/ROW]
[ROW][C]16[/C][C]-0.232948[/C][C]-2.4209[/C][C]0.991425[/C][/ROW]
[ROW][C]17[/C][C]-0.251687[/C][C]-2.6156[/C][C]0.99491[/C][/ROW]
[ROW][C]18[/C][C]-0.232124[/C][C]-2.4123[/C][C]0.991231[/C][/ROW]
[ROW][C]19[/C][C]-0.229944[/C][C]-2.3896[/C][C]0.990701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2218&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2218&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	10.3923	0
1	0.765288	7.9531	0
2	0.357412	3.7143	0.000162
3	0.021529	0.2237	0.411691
4	-0.140091	-1.4559	0.925835
5	-0.161216	-1.6754	0.951626
6	-0.142438	-1.4803	0.929142
7	-0.13526	-1.4057	0.918652
8	-0.108896	-1.1317	0.869862
9	0.032939	0.3423	0.36639
10	0.312814	3.2509	0.000767
11	0.650649	6.7617	0
12	0.822888	8.5517	0
13	0.593751	6.1704	0
14	0.22243	2.3116	0.01135
15	-0.084526	-0.8784	0.809168
16	-0.232948	-2.4209	0.991425
17	-0.251687	-2.6156	0.99491
18	-0.232124	-2.4123	0.991231
19	-0.229944	-2.3896	0.990701

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.765288	7.9531	0
1	-0.550894	-5.7251	1
2	0.065549	0.6812	0.2486
3	0.028248	0.2936	0.384828
4	-0.033752	-0.3508	0.636775
5	-0.104873	-1.0899	0.860902
6	-0.038213	-0.3971	0.653968
7	0.075298	0.7825	0.217812
8	0.304491	3.1644	0.00101
9	0.362279	3.7649	0.000136
10	0.477444	4.9617	1e-06
11	0.189966	1.9742	0.025457
12	-0.621431	-6.4581	1
13	0.336687	3.499	0.00034
14	-0.139334	-1.448	0.924743
15	-0.157222	-1.6339	0.947404
16	-0.060928	-0.6332	0.736025
17	-0.172181	-1.7894	0.96182
18	-0.146014	-1.5174	0.93396
19	-0.033982	-0.3532	0.63767

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.765288 & 7.9531 & 0 \tabularnewline
1 & -0.550894 & -5.7251 & 1 \tabularnewline
2 & 0.065549 & 0.6812 & 0.2486 \tabularnewline
3 & 0.028248 & 0.2936 & 0.384828 \tabularnewline
4 & -0.033752 & -0.3508 & 0.636775 \tabularnewline
5 & -0.104873 & -1.0899 & 0.860902 \tabularnewline
6 & -0.038213 & -0.3971 & 0.653968 \tabularnewline
7 & 0.075298 & 0.7825 & 0.217812 \tabularnewline
8 & 0.304491 & 3.1644 & 0.00101 \tabularnewline
9 & 0.362279 & 3.7649 & 0.000136 \tabularnewline
10 & 0.477444 & 4.9617 & 1e-06 \tabularnewline
11 & 0.189966 & 1.9742 & 0.025457 \tabularnewline
12 & -0.621431 & -6.4581 & 1 \tabularnewline
13 & 0.336687 & 3.499 & 0.00034 \tabularnewline
14 & -0.139334 & -1.448 & 0.924743 \tabularnewline
15 & -0.157222 & -1.6339 & 0.947404 \tabularnewline
16 & -0.060928 & -0.6332 & 0.736025 \tabularnewline
17 & -0.172181 & -1.7894 & 0.96182 \tabularnewline
18 & -0.146014 & -1.5174 & 0.93396 \tabularnewline
19 & -0.033982 & -0.3532 & 0.63767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2218&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]0.765288[/C][C]7.9531[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.550894[/C][C]-5.7251[/C][C]1[/C][/ROW]
[ROW][C]2[/C][C]0.065549[/C][C]0.6812[/C][C]0.2486[/C][/ROW]
[ROW][C]3[/C][C]0.028248[/C][C]0.2936[/C][C]0.384828[/C][/ROW]
[ROW][C]4[/C][C]-0.033752[/C][C]-0.3508[/C][C]0.636775[/C][/ROW]
[ROW][C]5[/C][C]-0.104873[/C][C]-1.0899[/C][C]0.860902[/C][/ROW]
[ROW][C]6[/C][C]-0.038213[/C][C]-0.3971[/C][C]0.653968[/C][/ROW]
[ROW][C]7[/C][C]0.075298[/C][C]0.7825[/C][C]0.217812[/C][/ROW]
[ROW][C]8[/C][C]0.304491[/C][C]3.1644[/C][C]0.00101[/C][/ROW]
[ROW][C]9[/C][C]0.362279[/C][C]3.7649[/C][C]0.000136[/C][/ROW]
[ROW][C]10[/C][C]0.477444[/C][C]4.9617[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.189966[/C][C]1.9742[/C][C]0.025457[/C][/ROW]
[ROW][C]12[/C][C]-0.621431[/C][C]-6.4581[/C][C]1[/C][/ROW]
[ROW][C]13[/C][C]0.336687[/C][C]3.499[/C][C]0.00034[/C][/ROW]
[ROW][C]14[/C][C]-0.139334[/C][C]-1.448[/C][C]0.924743[/C][/ROW]
[ROW][C]15[/C][C]-0.157222[/C][C]-1.6339[/C][C]0.947404[/C][/ROW]
[ROW][C]16[/C][C]-0.060928[/C][C]-0.6332[/C][C]0.736025[/C][/ROW]
[ROW][C]17[/C][C]-0.172181[/C][C]-1.7894[/C][C]0.96182[/C][/ROW]
[ROW][C]18[/C][C]-0.146014[/C][C]-1.5174[/C][C]0.93396[/C][/ROW]
[ROW][C]19[/C][C]-0.033982[/C][C]-0.3532[/C][C]0.63767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2218&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2218&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	0.765288	7.9531	0
1	-0.550894	-5.7251	1
2	0.065549	0.6812	0.2486
3	0.028248	0.2936	0.384828
4	-0.033752	-0.3508	0.636775
5	-0.104873	-1.0899	0.860902
6	-0.038213	-0.3971	0.653968
7	0.075298	0.7825	0.217812
8	0.304491	3.1644	0.00101
9	0.362279	3.7649	0.000136
10	0.477444	4.9617	1e-06
11	0.189966	1.9742	0.025457
12	-0.621431	-6.4581	1
13	0.336687	3.499	0.00034
14	-0.139334	-1.448	0.924743
15	-0.157222	-1.6339	0.947404
16	-0.060928	-0.6332	0.736025
17	-0.172181	-1.7894	0.96182
18	-0.146014	-1.5174	0.93396
19	-0.033982	-0.3532	0.63767

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')

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