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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 11 Dec 2008 03:51:35 -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/11/t1228992877k5nf3vg4bpqeq46.htm/, Retrieved Sat, 25 May 2024 00:05:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32164, Retrieved Sat, 25 May 2024 00:05:07 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

234

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

F     [(Partial) Autocorrelation Function] [step acf] [2008-12-09 15:39:34] [74be16979710d4c4e7c6647856088456]
-   P   [(Partial) Autocorrelation Function] [step 3 acf] [2008-12-09 18:41:47] [74be16979710d4c4e7c6647856088456]
-   P       [(Partial) Autocorrelation Function] [step 2 met d=0] [2008-12-11 10:51:35] [d41d8cd98f00b204e9800998ecf8427e] [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=32164&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=32164&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32164&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	0.344141	2.9403	0.002194
2	0.277083	2.3674	0.010283
3	0.365695	3.1245	0.001278
4	0.119429	1.0204	0.155454
5	0.085625	0.7316	0.233384
6	0.177584	1.5173	0.066757
7	0.052507	0.4486	0.327517
8	0.168232	1.4374	0.077442
9	-0.02201	-0.1881	0.425677
10	-0.041174	-0.3518	0.363004
11	-0.012311	-0.1052	0.45826
12	-0.233362	-1.9938	0.024952
13	-0.130291	-1.1132	0.134636
14	-0.156897	-1.3405	0.092116
15	-0.185458	-1.5846	0.058695
16	-0.099968	-0.8541	0.197915
17	-0.0567	-0.4844	0.31476
18	-0.183202	-1.5653	0.060922
19	-0.014983	-0.128	0.449246

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.344141 & 2.9403 & 0.002194 \tabularnewline
2 & 0.277083 & 2.3674 & 0.010283 \tabularnewline
3 & 0.365695 & 3.1245 & 0.001278 \tabularnewline
4 & 0.119429 & 1.0204 & 0.155454 \tabularnewline
5 & 0.085625 & 0.7316 & 0.233384 \tabularnewline
6 & 0.177584 & 1.5173 & 0.066757 \tabularnewline
7 & 0.052507 & 0.4486 & 0.327517 \tabularnewline
8 & 0.168232 & 1.4374 & 0.077442 \tabularnewline
9 & -0.02201 & -0.1881 & 0.425677 \tabularnewline
10 & -0.041174 & -0.3518 & 0.363004 \tabularnewline
11 & -0.012311 & -0.1052 & 0.45826 \tabularnewline
12 & -0.233362 & -1.9938 & 0.024952 \tabularnewline
13 & -0.130291 & -1.1132 & 0.134636 \tabularnewline
14 & -0.156897 & -1.3405 & 0.092116 \tabularnewline
15 & -0.185458 & -1.5846 & 0.058695 \tabularnewline
16 & -0.099968 & -0.8541 & 0.197915 \tabularnewline
17 & -0.0567 & -0.4844 & 0.31476 \tabularnewline
18 & -0.183202 & -1.5653 & 0.060922 \tabularnewline
19 & -0.014983 & -0.128 & 0.449246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32164&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]0.344141[/C][C]2.9403[/C][C]0.002194[/C][/ROW]
[ROW][C]2[/C][C]0.277083[/C][C]2.3674[/C][C]0.010283[/C][/ROW]
[ROW][C]3[/C][C]0.365695[/C][C]3.1245[/C][C]0.001278[/C][/ROW]
[ROW][C]4[/C][C]0.119429[/C][C]1.0204[/C][C]0.155454[/C][/ROW]
[ROW][C]5[/C][C]0.085625[/C][C]0.7316[/C][C]0.233384[/C][/ROW]
[ROW][C]6[/C][C]0.177584[/C][C]1.5173[/C][C]0.066757[/C][/ROW]
[ROW][C]7[/C][C]0.052507[/C][C]0.4486[/C][C]0.327517[/C][/ROW]
[ROW][C]8[/C][C]0.168232[/C][C]1.4374[/C][C]0.077442[/C][/ROW]
[ROW][C]9[/C][C]-0.02201[/C][C]-0.1881[/C][C]0.425677[/C][/ROW]
[ROW][C]10[/C][C]-0.041174[/C][C]-0.3518[/C][C]0.363004[/C][/ROW]
[ROW][C]11[/C][C]-0.012311[/C][C]-0.1052[/C][C]0.45826[/C][/ROW]
[ROW][C]12[/C][C]-0.233362[/C][C]-1.9938[/C][C]0.024952[/C][/ROW]
[ROW][C]13[/C][C]-0.130291[/C][C]-1.1132[/C][C]0.134636[/C][/ROW]
[ROW][C]14[/C][C]-0.156897[/C][C]-1.3405[/C][C]0.092116[/C][/ROW]
[ROW][C]15[/C][C]-0.185458[/C][C]-1.5846[/C][C]0.058695[/C][/ROW]
[ROW][C]16[/C][C]-0.099968[/C][C]-0.8541[/C][C]0.197915[/C][/ROW]
[ROW][C]17[/C][C]-0.0567[/C][C]-0.4844[/C][C]0.31476[/C][/ROW]
[ROW][C]18[/C][C]-0.183202[/C][C]-1.5653[/C][C]0.060922[/C][/ROW]
[ROW][C]19[/C][C]-0.014983[/C][C]-0.128[/C][C]0.449246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32164&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32164&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	0.344141	2.9403	0.002194
2	0.277083	2.3674	0.010283
3	0.365695	3.1245	0.001278
4	0.119429	1.0204	0.155454
5	0.085625	0.7316	0.233384
6	0.177584	1.5173	0.066757
7	0.052507	0.4486	0.327517
8	0.168232	1.4374	0.077442
9	-0.02201	-0.1881	0.425677
10	-0.041174	-0.3518	0.363004
11	-0.012311	-0.1052	0.45826
12	-0.233362	-1.9938	0.024952
13	-0.130291	-1.1132	0.134636
14	-0.156897	-1.3405	0.092116
15	-0.185458	-1.5846	0.058695
16	-0.099968	-0.8541	0.197915
17	-0.0567	-0.4844	0.31476
18	-0.183202	-1.5653	0.060922
19	-0.014983	-0.128	0.449246

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.344141	2.9403	0.002194
2	0.179964	1.5376	0.064234
3	0.264434	2.2593	0.013424
4	-0.109105	-0.9322	0.177155
5	-0.040031	-0.342	0.366658
6	0.093744	0.8009	0.21288
7	-0.015277	-0.1305	0.448253
8	0.156005	1.3329	0.093354
9	-0.222023	-1.897	0.030894
10	-0.036709	-0.3136	0.377343
11	-0.050741	-0.4335	0.332952
12	-0.20092	-1.7167	0.045141
13	0.04955	0.4234	0.336639
14	-0.151698	-1.2961	0.09951
15	0.076424	0.653	0.257914
16	-0.037319	-0.3189	0.375374
17	0.104917	0.8964	0.18649
18	-0.12312	-1.0519	0.148148
19	0.091498	0.7818	0.218442

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.344141 & 2.9403 & 0.002194 \tabularnewline
2 & 0.179964 & 1.5376 & 0.064234 \tabularnewline
3 & 0.264434 & 2.2593 & 0.013424 \tabularnewline
4 & -0.109105 & -0.9322 & 0.177155 \tabularnewline
5 & -0.040031 & -0.342 & 0.366658 \tabularnewline
6 & 0.093744 & 0.8009 & 0.21288 \tabularnewline
7 & -0.015277 & -0.1305 & 0.448253 \tabularnewline
8 & 0.156005 & 1.3329 & 0.093354 \tabularnewline
9 & -0.222023 & -1.897 & 0.030894 \tabularnewline
10 & -0.036709 & -0.3136 & 0.377343 \tabularnewline
11 & -0.050741 & -0.4335 & 0.332952 \tabularnewline
12 & -0.20092 & -1.7167 & 0.045141 \tabularnewline
13 & 0.04955 & 0.4234 & 0.336639 \tabularnewline
14 & -0.151698 & -1.2961 & 0.09951 \tabularnewline
15 & 0.076424 & 0.653 & 0.257914 \tabularnewline
16 & -0.037319 & -0.3189 & 0.375374 \tabularnewline
17 & 0.104917 & 0.8964 & 0.18649 \tabularnewline
18 & -0.12312 & -1.0519 & 0.148148 \tabularnewline
19 & 0.091498 & 0.7818 & 0.218442 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32164&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]0.344141[/C][C]2.9403[/C][C]0.002194[/C][/ROW]
[ROW][C]2[/C][C]0.179964[/C][C]1.5376[/C][C]0.064234[/C][/ROW]
[ROW][C]3[/C][C]0.264434[/C][C]2.2593[/C][C]0.013424[/C][/ROW]
[ROW][C]4[/C][C]-0.109105[/C][C]-0.9322[/C][C]0.177155[/C][/ROW]
[ROW][C]5[/C][C]-0.040031[/C][C]-0.342[/C][C]0.366658[/C][/ROW]
[ROW][C]6[/C][C]0.093744[/C][C]0.8009[/C][C]0.21288[/C][/ROW]
[ROW][C]7[/C][C]-0.015277[/C][C]-0.1305[/C][C]0.448253[/C][/ROW]
[ROW][C]8[/C][C]0.156005[/C][C]1.3329[/C][C]0.093354[/C][/ROW]
[ROW][C]9[/C][C]-0.222023[/C][C]-1.897[/C][C]0.030894[/C][/ROW]
[ROW][C]10[/C][C]-0.036709[/C][C]-0.3136[/C][C]0.377343[/C][/ROW]
[ROW][C]11[/C][C]-0.050741[/C][C]-0.4335[/C][C]0.332952[/C][/ROW]
[ROW][C]12[/C][C]-0.20092[/C][C]-1.7167[/C][C]0.045141[/C][/ROW]
[ROW][C]13[/C][C]0.04955[/C][C]0.4234[/C][C]0.336639[/C][/ROW]
[ROW][C]14[/C][C]-0.151698[/C][C]-1.2961[/C][C]0.09951[/C][/ROW]
[ROW][C]15[/C][C]0.076424[/C][C]0.653[/C][C]0.257914[/C][/ROW]
[ROW][C]16[/C][C]-0.037319[/C][C]-0.3189[/C][C]0.375374[/C][/ROW]
[ROW][C]17[/C][C]0.104917[/C][C]0.8964[/C][C]0.18649[/C][/ROW]
[ROW][C]18[/C][C]-0.12312[/C][C]-1.0519[/C][C]0.148148[/C][/ROW]
[ROW][C]19[/C][C]0.091498[/C][C]0.7818[/C][C]0.218442[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32164&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32164&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	0.344141	2.9403	0.002194
2	0.179964	1.5376	0.064234
3	0.264434	2.2593	0.013424
4	-0.109105	-0.9322	0.177155
5	-0.040031	-0.342	0.366658
6	0.093744	0.8009	0.21288
7	-0.015277	-0.1305	0.448253
8	0.156005	1.3329	0.093354
9	-0.222023	-1.897	0.030894
10	-0.036709	-0.3136	0.377343
11	-0.050741	-0.4335	0.332952
12	-0.20092	-1.7167	0.045141
13	0.04955	0.4234	0.336639
14	-0.151698	-1.2961	0.09951
15	0.076424	0.653	0.257914
16	-0.037319	-0.3189	0.375374
17	0.104917	0.8964	0.18649
18	-0.12312	-1.0519	0.148148
19	0.091498	0.7818	0.218442

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.1 ; 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 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code