Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 30 Dec 2007 07:21:21 -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/Dec/30/t119902321542bxw0yycsbrkkr.htm/, Retrieved Sat, 04 May 2024 06:55:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4930, Retrieved Sat, 04 May 2024 06:55:57 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

294

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

-       [(Partial) Autocorrelation Function] [PAPER-ACF] [2007-12-30 14:21:21] [6bdd947de0ee04552c8f0fc807f31807] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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 & 3 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=4930&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]3 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=4930&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4930&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	3 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	10.3441	0
1	-0.562216	-5.8156	1
2	0.09214	0.9531	0.171342
3	0.209543	2.1675	0.016206
4	-0.164183	-1.6983	0.953824
5	-0.023096	-0.2389	0.594183
6	0.202382	2.0935	0.019336
7	-0.304366	-3.1484	0.998936
8	0.146117	1.5114	0.066811
9	0.126556	1.3091	0.096652
10	-0.261269	-2.7026	0.995998
11	0.196761	2.0353	0.022146
12	-0.11267	-1.1655	0.87679
13	-0.109062	-1.1281	0.869109
14	0.079179	0.819	0.207294
15	0.053281	0.5511	0.291341
16	-0.222071	-2.2971	0.988221
17	0.177277	1.8338	0.034734
18	0.110857	1.1467	0.127029
19	-0.236472	-2.4461	0.991964
20	0.169973	1.7582	0.040785
21	0.004062	0.042	0.483283
22	-0.195657	-2.0239	0.977263
23	0.244857	2.5328	0.006383

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 10.3441 & 0 \tabularnewline
1 & -0.562216 & -5.8156 & 1 \tabularnewline
2 & 0.09214 & 0.9531 & 0.171342 \tabularnewline
3 & 0.209543 & 2.1675 & 0.016206 \tabularnewline
4 & -0.164183 & -1.6983 & 0.953824 \tabularnewline
5 & -0.023096 & -0.2389 & 0.594183 \tabularnewline
6 & 0.202382 & 2.0935 & 0.019336 \tabularnewline
7 & -0.304366 & -3.1484 & 0.998936 \tabularnewline
8 & 0.146117 & 1.5114 & 0.066811 \tabularnewline
9 & 0.126556 & 1.3091 & 0.096652 \tabularnewline
10 & -0.261269 & -2.7026 & 0.995998 \tabularnewline
11 & 0.196761 & 2.0353 & 0.022146 \tabularnewline
12 & -0.11267 & -1.1655 & 0.87679 \tabularnewline
13 & -0.109062 & -1.1281 & 0.869109 \tabularnewline
14 & 0.079179 & 0.819 & 0.207294 \tabularnewline
15 & 0.053281 & 0.5511 & 0.291341 \tabularnewline
16 & -0.222071 & -2.2971 & 0.988221 \tabularnewline
17 & 0.177277 & 1.8338 & 0.034734 \tabularnewline
18 & 0.110857 & 1.1467 & 0.127029 \tabularnewline
19 & -0.236472 & -2.4461 & 0.991964 \tabularnewline
20 & 0.169973 & 1.7582 & 0.040785 \tabularnewline
21 & 0.004062 & 0.042 & 0.483283 \tabularnewline
22 & -0.195657 & -2.0239 & 0.977263 \tabularnewline
23 & 0.244857 & 2.5328 & 0.006383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4930&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]10.3441[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.562216[/C][C]-5.8156[/C][C]1[/C][/ROW]
[ROW][C]2[/C][C]0.09214[/C][C]0.9531[/C][C]0.171342[/C][/ROW]
[ROW][C]3[/C][C]0.209543[/C][C]2.1675[/C][C]0.016206[/C][/ROW]
[ROW][C]4[/C][C]-0.164183[/C][C]-1.6983[/C][C]0.953824[/C][/ROW]
[ROW][C]5[/C][C]-0.023096[/C][C]-0.2389[/C][C]0.594183[/C][/ROW]
[ROW][C]6[/C][C]0.202382[/C][C]2.0935[/C][C]0.019336[/C][/ROW]
[ROW][C]7[/C][C]-0.304366[/C][C]-3.1484[/C][C]0.998936[/C][/ROW]
[ROW][C]8[/C][C]0.146117[/C][C]1.5114[/C][C]0.066811[/C][/ROW]
[ROW][C]9[/C][C]0.126556[/C][C]1.3091[/C][C]0.096652[/C][/ROW]
[ROW][C]10[/C][C]-0.261269[/C][C]-2.7026[/C][C]0.995998[/C][/ROW]
[ROW][C]11[/C][C]0.196761[/C][C]2.0353[/C][C]0.022146[/C][/ROW]
[ROW][C]12[/C][C]-0.11267[/C][C]-1.1655[/C][C]0.87679[/C][/ROW]
[ROW][C]13[/C][C]-0.109062[/C][C]-1.1281[/C][C]0.869109[/C][/ROW]
[ROW][C]14[/C][C]0.079179[/C][C]0.819[/C][C]0.207294[/C][/ROW]
[ROW][C]15[/C][C]0.053281[/C][C]0.5511[/C][C]0.291341[/C][/ROW]
[ROW][C]16[/C][C]-0.222071[/C][C]-2.2971[/C][C]0.988221[/C][/ROW]
[ROW][C]17[/C][C]0.177277[/C][C]1.8338[/C][C]0.034734[/C][/ROW]
[ROW][C]18[/C][C]0.110857[/C][C]1.1467[/C][C]0.127029[/C][/ROW]
[ROW][C]19[/C][C]-0.236472[/C][C]-2.4461[/C][C]0.991964[/C][/ROW]
[ROW][C]20[/C][C]0.169973[/C][C]1.7582[/C][C]0.040785[/C][/ROW]
[ROW][C]21[/C][C]0.004062[/C][C]0.042[/C][C]0.483283[/C][/ROW]
[ROW][C]22[/C][C]-0.195657[/C][C]-2.0239[/C][C]0.977263[/C][/ROW]
[ROW][C]23[/C][C]0.244857[/C][C]2.5328[/C][C]0.006383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4930&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4930&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	10.3441	0
1	-0.562216	-5.8156	1
2	0.09214	0.9531	0.171342
3	0.209543	2.1675	0.016206
4	-0.164183	-1.6983	0.953824
5	-0.023096	-0.2389	0.594183
6	0.202382	2.0935	0.019336
7	-0.304366	-3.1484	0.998936
8	0.146117	1.5114	0.066811
9	0.126556	1.3091	0.096652
10	-0.261269	-2.7026	0.995998
11	0.196761	2.0353	0.022146
12	-0.11267	-1.1655	0.87679
13	-0.109062	-1.1281	0.869109
14	0.079179	0.819	0.207294
15	0.053281	0.5511	0.291341
16	-0.222071	-2.2971	0.988221
17	0.177277	1.8338	0.034734
18	0.110857	1.1467	0.127029
19	-0.236472	-2.4461	0.991964
20	0.169973	1.7582	0.040785
21	0.004062	0.042	0.483283
22	-0.195657	-2.0239	0.977263
23	0.244857	2.5328	0.006383

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.562216	-5.8156	1
1	-0.327449	-3.3872	0.999506
2	0.154298	1.5961	0.056711
3	0.147513	1.5259	0.064995
4	-0.075269	-0.7786	0.781029
5	0.099339	1.0276	0.153236
6	-0.169506	-1.7534	0.9588
7	-0.150444	-1.5562	0.938694
8	0.154184	1.5949	0.056843
9	0.022036	0.2279	0.410064
10	0.030038	0.3107	0.378309
11	-0.180815	-1.8704	0.967917
12	-0.270054	-2.7935	0.99691
13	-0.2745	-2.8395	0.997295
14	0.090569	0.9368	0.175473
15	0.085391	0.8833	0.189529
16	-0.057516	-0.595	0.723435
17	0.258949	2.6786	0.00428
18	0.01706	0.1765	0.430128
19	-0.192493	-1.9912	0.975494
20	-0.042629	-0.441	0.669932
21	-0.121532	-1.2571	0.894279
22	0.049147	0.5084	0.306117
23	-0.057747	-0.5973	0.72423

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.562216 & -5.8156 & 1 \tabularnewline
1 & -0.327449 & -3.3872 & 0.999506 \tabularnewline
2 & 0.154298 & 1.5961 & 0.056711 \tabularnewline
3 & 0.147513 & 1.5259 & 0.064995 \tabularnewline
4 & -0.075269 & -0.7786 & 0.781029 \tabularnewline
5 & 0.099339 & 1.0276 & 0.153236 \tabularnewline
6 & -0.169506 & -1.7534 & 0.9588 \tabularnewline
7 & -0.150444 & -1.5562 & 0.938694 \tabularnewline
8 & 0.154184 & 1.5949 & 0.056843 \tabularnewline
9 & 0.022036 & 0.2279 & 0.410064 \tabularnewline
10 & 0.030038 & 0.3107 & 0.378309 \tabularnewline
11 & -0.180815 & -1.8704 & 0.967917 \tabularnewline
12 & -0.270054 & -2.7935 & 0.99691 \tabularnewline
13 & -0.2745 & -2.8395 & 0.997295 \tabularnewline
14 & 0.090569 & 0.9368 & 0.175473 \tabularnewline
15 & 0.085391 & 0.8833 & 0.189529 \tabularnewline
16 & -0.057516 & -0.595 & 0.723435 \tabularnewline
17 & 0.258949 & 2.6786 & 0.00428 \tabularnewline
18 & 0.01706 & 0.1765 & 0.430128 \tabularnewline
19 & -0.192493 & -1.9912 & 0.975494 \tabularnewline
20 & -0.042629 & -0.441 & 0.669932 \tabularnewline
21 & -0.121532 & -1.2571 & 0.894279 \tabularnewline
22 & 0.049147 & 0.5084 & 0.306117 \tabularnewline
23 & -0.057747 & -0.5973 & 0.72423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4930&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]-0.562216[/C][C]-5.8156[/C][C]1[/C][/ROW]
[ROW][C]1[/C][C]-0.327449[/C][C]-3.3872[/C][C]0.999506[/C][/ROW]
[ROW][C]2[/C][C]0.154298[/C][C]1.5961[/C][C]0.056711[/C][/ROW]
[ROW][C]3[/C][C]0.147513[/C][C]1.5259[/C][C]0.064995[/C][/ROW]
[ROW][C]4[/C][C]-0.075269[/C][C]-0.7786[/C][C]0.781029[/C][/ROW]
[ROW][C]5[/C][C]0.099339[/C][C]1.0276[/C][C]0.153236[/C][/ROW]
[ROW][C]6[/C][C]-0.169506[/C][C]-1.7534[/C][C]0.9588[/C][/ROW]
[ROW][C]7[/C][C]-0.150444[/C][C]-1.5562[/C][C]0.938694[/C][/ROW]
[ROW][C]8[/C][C]0.154184[/C][C]1.5949[/C][C]0.056843[/C][/ROW]
[ROW][C]9[/C][C]0.022036[/C][C]0.2279[/C][C]0.410064[/C][/ROW]
[ROW][C]10[/C][C]0.030038[/C][C]0.3107[/C][C]0.378309[/C][/ROW]
[ROW][C]11[/C][C]-0.180815[/C][C]-1.8704[/C][C]0.967917[/C][/ROW]
[ROW][C]12[/C][C]-0.270054[/C][C]-2.7935[/C][C]0.99691[/C][/ROW]
[ROW][C]13[/C][C]-0.2745[/C][C]-2.8395[/C][C]0.997295[/C][/ROW]
[ROW][C]14[/C][C]0.090569[/C][C]0.9368[/C][C]0.175473[/C][/ROW]
[ROW][C]15[/C][C]0.085391[/C][C]0.8833[/C][C]0.189529[/C][/ROW]
[ROW][C]16[/C][C]-0.057516[/C][C]-0.595[/C][C]0.723435[/C][/ROW]
[ROW][C]17[/C][C]0.258949[/C][C]2.6786[/C][C]0.00428[/C][/ROW]
[ROW][C]18[/C][C]0.01706[/C][C]0.1765[/C][C]0.430128[/C][/ROW]
[ROW][C]19[/C][C]-0.192493[/C][C]-1.9912[/C][C]0.975494[/C][/ROW]
[ROW][C]20[/C][C]-0.042629[/C][C]-0.441[/C][C]0.669932[/C][/ROW]
[ROW][C]21[/C][C]-0.121532[/C][C]-1.2571[/C][C]0.894279[/C][/ROW]
[ROW][C]22[/C][C]0.049147[/C][C]0.5084[/C][C]0.306117[/C][/ROW]
[ROW][C]23[/C][C]-0.057747[/C][C]-0.5973[/C][C]0.72423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4930&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4930&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	-0.562216	-5.8156	1
1	-0.327449	-3.3872	0.999506
2	0.154298	1.5961	0.056711
3	0.147513	1.5259	0.064995
4	-0.075269	-0.7786	0.781029
5	0.099339	1.0276	0.153236
6	-0.169506	-1.7534	0.9588
7	-0.150444	-1.5562	0.938694
8	0.154184	1.5949	0.056843
9	0.022036	0.2279	0.410064
10	0.030038	0.3107	0.378309
11	-0.180815	-1.8704	0.967917
12	-0.270054	-2.7935	0.99691
13	-0.2745	-2.8395	0.997295
14	0.090569	0.9368	0.175473
15	0.085391	0.8833	0.189529
16	-0.057516	-0.595	0.723435
17	0.258949	2.6786	0.00428
18	0.01706	0.1765	0.430128
19	-0.192493	-1.9912	0.975494
20	-0.042629	-0.441	0.669932
21	-0.121532	-1.2571	0.894279
22	0.049147	0.5084	0.306117
23	-0.057747	-0.5973	0.72423

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code