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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 17 Dec 2007 11:48:08 -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/17/t1197916347xds2l595ou22h0b.htm/, Retrieved Sat, 04 May 2024 03:25:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4403, Retrieved Sat, 04 May 2024 03:25:26 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

LPG

Estimated Impact

192

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

-       [(Partial) Autocorrelation Function] [Paper XV AcorF] [2007-12-17 18:48:08] [fd802f308f037a9692de8c23f8b60e49] [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=4403&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=4403&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4403&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	14.2127	0
1	0.057136	0.8121	0.208859
2	-0.051112	-0.7264	0.765795
3	-0.038007	-0.5402	0.705166
4	-0.058479	-0.8311	0.796562
5	0.141099	2.0054	0.023128
6	-0.041338	-0.5875	0.721245
7	-0.119512	-1.6986	0.954531
8	-0.064647	-0.9188	0.820355
9	0.025562	0.3633	0.358381
10	0.19708	2.801	0.002794
11	-0.056515	-0.8032	0.788609
12	0.061979	0.8809	0.189713
13	0.035704	0.5075	0.306196
14	-0.088661	-1.2601	0.895459
15	-0.037561	-0.5338	0.70298
16	-0.01874	-0.2663	0.604876
17	0.056459	0.8024	0.211622
18	-0.046098	-0.6552	0.74345
19	-0.143226	-2.0356	0.978453
20	0.01953	0.2776	0.390812
21	0.069731	0.9911	0.161419
22	0.004514	0.0642	0.474456

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 14.2127 & 0 \tabularnewline
1 & 0.057136 & 0.8121 & 0.208859 \tabularnewline
2 & -0.051112 & -0.7264 & 0.765795 \tabularnewline
3 & -0.038007 & -0.5402 & 0.705166 \tabularnewline
4 & -0.058479 & -0.8311 & 0.796562 \tabularnewline
5 & 0.141099 & 2.0054 & 0.023128 \tabularnewline
6 & -0.041338 & -0.5875 & 0.721245 \tabularnewline
7 & -0.119512 & -1.6986 & 0.954531 \tabularnewline
8 & -0.064647 & -0.9188 & 0.820355 \tabularnewline
9 & 0.025562 & 0.3633 & 0.358381 \tabularnewline
10 & 0.19708 & 2.801 & 0.002794 \tabularnewline
11 & -0.056515 & -0.8032 & 0.788609 \tabularnewline
12 & 0.061979 & 0.8809 & 0.189713 \tabularnewline
13 & 0.035704 & 0.5075 & 0.306196 \tabularnewline
14 & -0.088661 & -1.2601 & 0.895459 \tabularnewline
15 & -0.037561 & -0.5338 & 0.70298 \tabularnewline
16 & -0.01874 & -0.2663 & 0.604876 \tabularnewline
17 & 0.056459 & 0.8024 & 0.211622 \tabularnewline
18 & -0.046098 & -0.6552 & 0.74345 \tabularnewline
19 & -0.143226 & -2.0356 & 0.978453 \tabularnewline
20 & 0.01953 & 0.2776 & 0.390812 \tabularnewline
21 & 0.069731 & 0.9911 & 0.161419 \tabularnewline
22 & 0.004514 & 0.0642 & 0.474456 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4403&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]14.2127[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.057136[/C][C]0.8121[/C][C]0.208859[/C][/ROW]
[ROW][C]2[/C][C]-0.051112[/C][C]-0.7264[/C][C]0.765795[/C][/ROW]
[ROW][C]3[/C][C]-0.038007[/C][C]-0.5402[/C][C]0.705166[/C][/ROW]
[ROW][C]4[/C][C]-0.058479[/C][C]-0.8311[/C][C]0.796562[/C][/ROW]
[ROW][C]5[/C][C]0.141099[/C][C]2.0054[/C][C]0.023128[/C][/ROW]
[ROW][C]6[/C][C]-0.041338[/C][C]-0.5875[/C][C]0.721245[/C][/ROW]
[ROW][C]7[/C][C]-0.119512[/C][C]-1.6986[/C][C]0.954531[/C][/ROW]
[ROW][C]8[/C][C]-0.064647[/C][C]-0.9188[/C][C]0.820355[/C][/ROW]
[ROW][C]9[/C][C]0.025562[/C][C]0.3633[/C][C]0.358381[/C][/ROW]
[ROW][C]10[/C][C]0.19708[/C][C]2.801[/C][C]0.002794[/C][/ROW]
[ROW][C]11[/C][C]-0.056515[/C][C]-0.8032[/C][C]0.788609[/C][/ROW]
[ROW][C]12[/C][C]0.061979[/C][C]0.8809[/C][C]0.189713[/C][/ROW]
[ROW][C]13[/C][C]0.035704[/C][C]0.5075[/C][C]0.306196[/C][/ROW]
[ROW][C]14[/C][C]-0.088661[/C][C]-1.2601[/C][C]0.895459[/C][/ROW]
[ROW][C]15[/C][C]-0.037561[/C][C]-0.5338[/C][C]0.70298[/C][/ROW]
[ROW][C]16[/C][C]-0.01874[/C][C]-0.2663[/C][C]0.604876[/C][/ROW]
[ROW][C]17[/C][C]0.056459[/C][C]0.8024[/C][C]0.211622[/C][/ROW]
[ROW][C]18[/C][C]-0.046098[/C][C]-0.6552[/C][C]0.74345[/C][/ROW]
[ROW][C]19[/C][C]-0.143226[/C][C]-2.0356[/C][C]0.978453[/C][/ROW]
[ROW][C]20[/C][C]0.01953[/C][C]0.2776[/C][C]0.390812[/C][/ROW]
[ROW][C]21[/C][C]0.069731[/C][C]0.9911[/C][C]0.161419[/C][/ROW]
[ROW][C]22[/C][C]0.004514[/C][C]0.0642[/C][C]0.474456[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4403&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4403&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	14.2127	0
1	0.057136	0.8121	0.208859
2	-0.051112	-0.7264	0.765795
3	-0.038007	-0.5402	0.705166
4	-0.058479	-0.8311	0.796562
5	0.141099	2.0054	0.023128
6	-0.041338	-0.5875	0.721245
7	-0.119512	-1.6986	0.954531
8	-0.064647	-0.9188	0.820355
9	0.025562	0.3633	0.358381
10	0.19708	2.801	0.002794
11	-0.056515	-0.8032	0.788609
12	0.061979	0.8809	0.189713
13	0.035704	0.5075	0.306196
14	-0.088661	-1.2601	0.895459
15	-0.037561	-0.5338	0.70298
16	-0.01874	-0.2663	0.604876
17	0.056459	0.8024	0.211622
18	-0.046098	-0.6552	0.74345
19	-0.143226	-2.0356	0.978453
20	0.01953	0.2776	0.390812
21	0.069731	0.9911	0.161419
22	0.004514	0.0642	0.474456

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.057136	0.8121	0.208859
1	-0.054555	-0.7754	0.780485
2	-0.03201	-0.4549	0.675181
3	-0.057533	-0.8177	0.792754
4	0.145655	2.0701	0.019855
5	-0.06814	-0.9684	0.83301
6	-0.104637	-1.4872	0.930736
7	-0.052331	-0.7438	0.771059
8	0.039899	0.5671	0.285646
9	0.16247	2.3091	0.010974
10	-0.085716	-1.2183	0.887725
11	0.114663	1.6297	0.052364
12	0.037319	0.5304	0.298208
13	-0.099459	-1.4136	0.920487
14	-0.094906	-1.3489	0.910555
15	0.038872	0.5525	0.290618
16	0.079383	1.1282	0.130278
17	-0.083069	-1.1806	0.880432
18	-0.128359	-1.8243	0.96521
19	0.050116	0.7123	0.238555
20	0.081986	1.1652	0.122649
21	-0.12377	-1.7591	0.959962
22	-0.068829	-0.9782	0.835438

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.057136 & 0.8121 & 0.208859 \tabularnewline
1 & -0.054555 & -0.7754 & 0.780485 \tabularnewline
2 & -0.03201 & -0.4549 & 0.675181 \tabularnewline
3 & -0.057533 & -0.8177 & 0.792754 \tabularnewline
4 & 0.145655 & 2.0701 & 0.019855 \tabularnewline
5 & -0.06814 & -0.9684 & 0.83301 \tabularnewline
6 & -0.104637 & -1.4872 & 0.930736 \tabularnewline
7 & -0.052331 & -0.7438 & 0.771059 \tabularnewline
8 & 0.039899 & 0.5671 & 0.285646 \tabularnewline
9 & 0.16247 & 2.3091 & 0.010974 \tabularnewline
10 & -0.085716 & -1.2183 & 0.887725 \tabularnewline
11 & 0.114663 & 1.6297 & 0.052364 \tabularnewline
12 & 0.037319 & 0.5304 & 0.298208 \tabularnewline
13 & -0.099459 & -1.4136 & 0.920487 \tabularnewline
14 & -0.094906 & -1.3489 & 0.910555 \tabularnewline
15 & 0.038872 & 0.5525 & 0.290618 \tabularnewline
16 & 0.079383 & 1.1282 & 0.130278 \tabularnewline
17 & -0.083069 & -1.1806 & 0.880432 \tabularnewline
18 & -0.128359 & -1.8243 & 0.96521 \tabularnewline
19 & 0.050116 & 0.7123 & 0.238555 \tabularnewline
20 & 0.081986 & 1.1652 & 0.122649 \tabularnewline
21 & -0.12377 & -1.7591 & 0.959962 \tabularnewline
22 & -0.068829 & -0.9782 & 0.835438 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4403&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]0.057136[/C][C]0.8121[/C][C]0.208859[/C][/ROW]
[ROW][C]1[/C][C]-0.054555[/C][C]-0.7754[/C][C]0.780485[/C][/ROW]
[ROW][C]2[/C][C]-0.03201[/C][C]-0.4549[/C][C]0.675181[/C][/ROW]
[ROW][C]3[/C][C]-0.057533[/C][C]-0.8177[/C][C]0.792754[/C][/ROW]
[ROW][C]4[/C][C]0.145655[/C][C]2.0701[/C][C]0.019855[/C][/ROW]
[ROW][C]5[/C][C]-0.06814[/C][C]-0.9684[/C][C]0.83301[/C][/ROW]
[ROW][C]6[/C][C]-0.104637[/C][C]-1.4872[/C][C]0.930736[/C][/ROW]
[ROW][C]7[/C][C]-0.052331[/C][C]-0.7438[/C][C]0.771059[/C][/ROW]
[ROW][C]8[/C][C]0.039899[/C][C]0.5671[/C][C]0.285646[/C][/ROW]
[ROW][C]9[/C][C]0.16247[/C][C]2.3091[/C][C]0.010974[/C][/ROW]
[ROW][C]10[/C][C]-0.085716[/C][C]-1.2183[/C][C]0.887725[/C][/ROW]
[ROW][C]11[/C][C]0.114663[/C][C]1.6297[/C][C]0.052364[/C][/ROW]
[ROW][C]12[/C][C]0.037319[/C][C]0.5304[/C][C]0.298208[/C][/ROW]
[ROW][C]13[/C][C]-0.099459[/C][C]-1.4136[/C][C]0.920487[/C][/ROW]
[ROW][C]14[/C][C]-0.094906[/C][C]-1.3489[/C][C]0.910555[/C][/ROW]
[ROW][C]15[/C][C]0.038872[/C][C]0.5525[/C][C]0.290618[/C][/ROW]
[ROW][C]16[/C][C]0.079383[/C][C]1.1282[/C][C]0.130278[/C][/ROW]
[ROW][C]17[/C][C]-0.083069[/C][C]-1.1806[/C][C]0.880432[/C][/ROW]
[ROW][C]18[/C][C]-0.128359[/C][C]-1.8243[/C][C]0.96521[/C][/ROW]
[ROW][C]19[/C][C]0.050116[/C][C]0.7123[/C][C]0.238555[/C][/ROW]
[ROW][C]20[/C][C]0.081986[/C][C]1.1652[/C][C]0.122649[/C][/ROW]
[ROW][C]21[/C][C]-0.12377[/C][C]-1.7591[/C][C]0.959962[/C][/ROW]
[ROW][C]22[/C][C]-0.068829[/C][C]-0.9782[/C][C]0.835438[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4403&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4403&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	0.057136	0.8121	0.208859
1	-0.054555	-0.7754	0.780485
2	-0.03201	-0.4549	0.675181
3	-0.057533	-0.8177	0.792754
4	0.145655	2.0701	0.019855
5	-0.06814	-0.9684	0.83301
6	-0.104637	-1.4872	0.930736
7	-0.052331	-0.7438	0.771059
8	0.039899	0.5671	0.285646
9	0.16247	2.3091	0.010974
10	-0.085716	-1.2183	0.887725
11	0.114663	1.6297	0.052364
12	0.037319	0.5304	0.298208
13	-0.099459	-1.4136	0.920487
14	-0.094906	-1.3489	0.910555
15	0.038872	0.5525	0.290618
16	0.079383	1.1282	0.130278
17	-0.083069	-1.1806	0.880432
18	-0.128359	-1.8243	0.96521
19	0.050116	0.7123	0.238555
20	0.081986	1.1652	0.122649
21	-0.12377	-1.7591	0.959962
22	-0.068829	-0.9782	0.835438

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.8 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -1.8 ; par3 = 1 ; 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