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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 11:20:03 -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/Nov/25/t1196014266zk1ngo0vgu2c7nz.htm/, Retrieved Sat, 04 May 2024 10:15:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6519, Retrieved Sat, 04 May 2024 10:15:42 +0000

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Estimated Impact

179

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

-       [(Partial) Autocorrelation Function] [lll] [2007-11-25 18:20:03] [fa77851485501f69e030fcd6dbd2de67] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6519&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]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=6519&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6519&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.3066	0
1	0.900201	7.4776	0
2	0.760816	6.3198	0
3	0.649063	5.3915	0
4	0.569172	4.7279	6e-06
5	0.477607	3.9673	8.8e-05
6	0.388623	3.2281	0.000954
7	0.331239	2.7515	0.003786
8	0.276704	2.2985	0.012285
9	0.215442	1.7896	0.038954
10	0.118548	0.9847	0.164097
11	0.002202	0.0183	0.492729
12	-0.105286	-0.8746	0.807578
13	-0.137181	-1.1395	0.870784
14	-0.154449	-1.2829	0.898099
15	-0.188967	-1.5697	0.939467
16	-0.2145	-1.7818	0.960407
17	-0.182373	-1.5149	0.932818
18	-0.152512	-1.2669	0.895268

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.3066 & 0 \tabularnewline
1 & 0.900201 & 7.4776 & 0 \tabularnewline
2 & 0.760816 & 6.3198 & 0 \tabularnewline
3 & 0.649063 & 5.3915 & 0 \tabularnewline
4 & 0.569172 & 4.7279 & 6e-06 \tabularnewline
5 & 0.477607 & 3.9673 & 8.8e-05 \tabularnewline
6 & 0.388623 & 3.2281 & 0.000954 \tabularnewline
7 & 0.331239 & 2.7515 & 0.003786 \tabularnewline
8 & 0.276704 & 2.2985 & 0.012285 \tabularnewline
9 & 0.215442 & 1.7896 & 0.038954 \tabularnewline
10 & 0.118548 & 0.9847 & 0.164097 \tabularnewline
11 & 0.002202 & 0.0183 & 0.492729 \tabularnewline
12 & -0.105286 & -0.8746 & 0.807578 \tabularnewline
13 & -0.137181 & -1.1395 & 0.870784 \tabularnewline
14 & -0.154449 & -1.2829 & 0.898099 \tabularnewline
15 & -0.188967 & -1.5697 & 0.939467 \tabularnewline
16 & -0.2145 & -1.7818 & 0.960407 \tabularnewline
17 & -0.182373 & -1.5149 & 0.932818 \tabularnewline
18 & -0.152512 & -1.2669 & 0.895268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6519&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]8.3066[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.900201[/C][C]7.4776[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.760816[/C][C]6.3198[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.649063[/C][C]5.3915[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.569172[/C][C]4.7279[/C][C]6e-06[/C][/ROW]
[ROW][C]5[/C][C]0.477607[/C][C]3.9673[/C][C]8.8e-05[/C][/ROW]
[ROW][C]6[/C][C]0.388623[/C][C]3.2281[/C][C]0.000954[/C][/ROW]
[ROW][C]7[/C][C]0.331239[/C][C]2.7515[/C][C]0.003786[/C][/ROW]
[ROW][C]8[/C][C]0.276704[/C][C]2.2985[/C][C]0.012285[/C][/ROW]
[ROW][C]9[/C][C]0.215442[/C][C]1.7896[/C][C]0.038954[/C][/ROW]
[ROW][C]10[/C][C]0.118548[/C][C]0.9847[/C][C]0.164097[/C][/ROW]
[ROW][C]11[/C][C]0.002202[/C][C]0.0183[/C][C]0.492729[/C][/ROW]
[ROW][C]12[/C][C]-0.105286[/C][C]-0.8746[/C][C]0.807578[/C][/ROW]
[ROW][C]13[/C][C]-0.137181[/C][C]-1.1395[/C][C]0.870784[/C][/ROW]
[ROW][C]14[/C][C]-0.154449[/C][C]-1.2829[/C][C]0.898099[/C][/ROW]
[ROW][C]15[/C][C]-0.188967[/C][C]-1.5697[/C][C]0.939467[/C][/ROW]
[ROW][C]16[/C][C]-0.2145[/C][C]-1.7818[/C][C]0.960407[/C][/ROW]
[ROW][C]17[/C][C]-0.182373[/C][C]-1.5149[/C][C]0.932818[/C][/ROW]
[ROW][C]18[/C][C]-0.152512[/C][C]-1.2669[/C][C]0.895268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6519&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6519&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	8.3066	0
1	0.900201	7.4776	0
2	0.760816	6.3198	0
3	0.649063	5.3915	0
4	0.569172	4.7279	6e-06
5	0.477607	3.9673	8.8e-05
6	0.388623	3.2281	0.000954
7	0.331239	2.7515	0.003786
8	0.276704	2.2985	0.012285
9	0.215442	1.7896	0.038954
10	0.118548	0.9847	0.164097
11	0.002202	0.0183	0.492729
12	-0.105286	-0.8746	0.807578
13	-0.137181	-1.1395	0.870784
14	-0.154449	-1.2829	0.898099
15	-0.188967	-1.5697	0.939467
16	-0.2145	-1.7818	0.960407
17	-0.182373	-1.5149	0.932818
18	-0.152512	-1.2669	0.895268

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.900201	7.4776	0
1	-0.261267	-2.1702	0.983283
2	0.115622	0.9604	0.170096
3	0.041259	0.3427	0.366423
4	-0.15717	-1.3056	0.901979
5	0.030139	0.2504	0.401529
6	0.093656	0.778	0.219624
7	-0.124388	-1.0332	0.847452
8	-0.01384	-0.115	0.545595
9	-0.227241	-1.8876	0.968358
10	-0.159701	-1.3266	0.905488
11	-0.03417	-0.2838	0.611309
12	0.294527	2.4465	0.008488
13	-0.165697	-1.3764	0.913423
14	-0.050091	-0.4161	0.660682
15	0.081413	0.6763	0.250566
16	0.186409	1.5484	0.063047
17	-0.170296	-1.4146	0.919156
18	-0.079203	-0.6579	0.743607

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.900201 & 7.4776 & 0 \tabularnewline
1 & -0.261267 & -2.1702 & 0.983283 \tabularnewline
2 & 0.115622 & 0.9604 & 0.170096 \tabularnewline
3 & 0.041259 & 0.3427 & 0.366423 \tabularnewline
4 & -0.15717 & -1.3056 & 0.901979 \tabularnewline
5 & 0.030139 & 0.2504 & 0.401529 \tabularnewline
6 & 0.093656 & 0.778 & 0.219624 \tabularnewline
7 & -0.124388 & -1.0332 & 0.847452 \tabularnewline
8 & -0.01384 & -0.115 & 0.545595 \tabularnewline
9 & -0.227241 & -1.8876 & 0.968358 \tabularnewline
10 & -0.159701 & -1.3266 & 0.905488 \tabularnewline
11 & -0.03417 & -0.2838 & 0.611309 \tabularnewline
12 & 0.294527 & 2.4465 & 0.008488 \tabularnewline
13 & -0.165697 & -1.3764 & 0.913423 \tabularnewline
14 & -0.050091 & -0.4161 & 0.660682 \tabularnewline
15 & 0.081413 & 0.6763 & 0.250566 \tabularnewline
16 & 0.186409 & 1.5484 & 0.063047 \tabularnewline
17 & -0.170296 & -1.4146 & 0.919156 \tabularnewline
18 & -0.079203 & -0.6579 & 0.743607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6519&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]0.900201[/C][C]7.4776[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.261267[/C][C]-2.1702[/C][C]0.983283[/C][/ROW]
[ROW][C]2[/C][C]0.115622[/C][C]0.9604[/C][C]0.170096[/C][/ROW]
[ROW][C]3[/C][C]0.041259[/C][C]0.3427[/C][C]0.366423[/C][/ROW]
[ROW][C]4[/C][C]-0.15717[/C][C]-1.3056[/C][C]0.901979[/C][/ROW]
[ROW][C]5[/C][C]0.030139[/C][C]0.2504[/C][C]0.401529[/C][/ROW]
[ROW][C]6[/C][C]0.093656[/C][C]0.778[/C][C]0.219624[/C][/ROW]
[ROW][C]7[/C][C]-0.124388[/C][C]-1.0332[/C][C]0.847452[/C][/ROW]
[ROW][C]8[/C][C]-0.01384[/C][C]-0.115[/C][C]0.545595[/C][/ROW]
[ROW][C]9[/C][C]-0.227241[/C][C]-1.8876[/C][C]0.968358[/C][/ROW]
[ROW][C]10[/C][C]-0.159701[/C][C]-1.3266[/C][C]0.905488[/C][/ROW]
[ROW][C]11[/C][C]-0.03417[/C][C]-0.2838[/C][C]0.611309[/C][/ROW]
[ROW][C]12[/C][C]0.294527[/C][C]2.4465[/C][C]0.008488[/C][/ROW]
[ROW][C]13[/C][C]-0.165697[/C][C]-1.3764[/C][C]0.913423[/C][/ROW]
[ROW][C]14[/C][C]-0.050091[/C][C]-0.4161[/C][C]0.660682[/C][/ROW]
[ROW][C]15[/C][C]0.081413[/C][C]0.6763[/C][C]0.250566[/C][/ROW]
[ROW][C]16[/C][C]0.186409[/C][C]1.5484[/C][C]0.063047[/C][/ROW]
[ROW][C]17[/C][C]-0.170296[/C][C]-1.4146[/C][C]0.919156[/C][/ROW]
[ROW][C]18[/C][C]-0.079203[/C][C]-0.6579[/C][C]0.743607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6519&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6519&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	0.900201	7.4776	0
1	-0.261267	-2.1702	0.983283
2	0.115622	0.9604	0.170096
3	0.041259	0.3427	0.366423
4	-0.15717	-1.3056	0.901979
5	0.030139	0.2504	0.401529
6	0.093656	0.778	0.219624
7	-0.124388	-1.0332	0.847452
8	-0.01384	-0.115	0.545595
9	-0.227241	-1.8876	0.968358
10	-0.159701	-1.3266	0.905488
11	-0.03417	-0.2838	0.611309
12	0.294527	2.4465	0.008488
13	-0.165697	-1.3764	0.913423
14	-0.050091	-0.4161	0.660682
15	0.081413	0.6763	0.250566
16	0.186409	1.5484	0.063047
17	-0.170296	-1.4146	0.919156
18	-0.079203	-0.6579	0.743607

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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