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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

Sun, 25 Nov 2007 07:15:47 -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/Nov/25/t11959996096y664gxf3agx2q1.htm/, Retrieved Sat, 04 May 2024 13:47:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6459, Retrieved Sat, 04 May 2024 13:47:03 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

194

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

-       [(Partial) Autocorrelation Function] [WS10Q2-b] [2007-11-25 14:15:47] [f15e5fe6fe718a2cea2c195ef11f432f] [Current]

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Dataseries X:

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Histogram

Boxplots

7.3
7
6.6
6.4
6.3
6.4
6.3
6
5.3
5.2
5.1
5.4
5.8
5.6
5.6
5.4
5.4
5.5
5.5
5.3
5.7
5.6
5.5
5.6
5.9
6
7
6.6
6.6
6.3
6.3
6.3
6.3
6.2
6.2
6.3
6.4
6.4
7.8
7.7
7.7
7.7
7.7
7.6
7.5
7.4
7.4
7.5
7.6
7.6
8.1
7.8
8
7.9
7.9
7.8
6.7
6.6
6.6
7.7
7.9
8
7.7
7.5
7.6
7.8
7.8
7.7
7.4
7.5
7.2
7.5
7.6
7.6
7.8
7.7
7.7
8.2
8.2
8.1
7.8
7.8
7.7
6.7
6.7
6.7
7.2
6.9
6.8
7.2
7.1
6.9
6.9
6.7
6.5
6.6
6.6
6.5
6.3

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=6459&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=6459&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6459&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	9.8995	0
1	0.019787	0.1959	0.422553
2	0.037662	0.3728	0.355039
3	-0.197905	-1.9592	0.973532
4	-0.080038	-0.7923	0.78496
5	0.015705	0.1555	0.438386
6	-0.003334	-0.033	0.51313
7	0.004682	0.0463	0.481564
8	-0.026326	-0.2606	0.60253
9	-0.088942	-0.8805	0.809623
10	0.010271	0.1017	0.459609
11	-0.045976	-0.4551	0.674991
12	0.315275	3.1211	0.001184
13	0.003852	0.0381	0.484828
14	0.142009	1.4058	0.08147
15	0.04461	0.4416	0.32987
16	-0.109007	-1.0791	0.858406
17	-0.029788	-0.2949	0.615648
18	-0.169898	-1.6819	0.952114

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.8995 & 0 \tabularnewline
1 & 0.019787 & 0.1959 & 0.422553 \tabularnewline
2 & 0.037662 & 0.3728 & 0.355039 \tabularnewline
3 & -0.197905 & -1.9592 & 0.973532 \tabularnewline
4 & -0.080038 & -0.7923 & 0.78496 \tabularnewline
5 & 0.015705 & 0.1555 & 0.438386 \tabularnewline
6 & -0.003334 & -0.033 & 0.51313 \tabularnewline
7 & 0.004682 & 0.0463 & 0.481564 \tabularnewline
8 & -0.026326 & -0.2606 & 0.60253 \tabularnewline
9 & -0.088942 & -0.8805 & 0.809623 \tabularnewline
10 & 0.010271 & 0.1017 & 0.459609 \tabularnewline
11 & -0.045976 & -0.4551 & 0.674991 \tabularnewline
12 & 0.315275 & 3.1211 & 0.001184 \tabularnewline
13 & 0.003852 & 0.0381 & 0.484828 \tabularnewline
14 & 0.142009 & 1.4058 & 0.08147 \tabularnewline
15 & 0.04461 & 0.4416 & 0.32987 \tabularnewline
16 & -0.109007 & -1.0791 & 0.858406 \tabularnewline
17 & -0.029788 & -0.2949 & 0.615648 \tabularnewline
18 & -0.169898 & -1.6819 & 0.952114 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6459&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]9.8995[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.019787[/C][C]0.1959[/C][C]0.422553[/C][/ROW]
[ROW][C]2[/C][C]0.037662[/C][C]0.3728[/C][C]0.355039[/C][/ROW]
[ROW][C]3[/C][C]-0.197905[/C][C]-1.9592[/C][C]0.973532[/C][/ROW]
[ROW][C]4[/C][C]-0.080038[/C][C]-0.7923[/C][C]0.78496[/C][/ROW]
[ROW][C]5[/C][C]0.015705[/C][C]0.1555[/C][C]0.438386[/C][/ROW]
[ROW][C]6[/C][C]-0.003334[/C][C]-0.033[/C][C]0.51313[/C][/ROW]
[ROW][C]7[/C][C]0.004682[/C][C]0.0463[/C][C]0.481564[/C][/ROW]
[ROW][C]8[/C][C]-0.026326[/C][C]-0.2606[/C][C]0.60253[/C][/ROW]
[ROW][C]9[/C][C]-0.088942[/C][C]-0.8805[/C][C]0.809623[/C][/ROW]
[ROW][C]10[/C][C]0.010271[/C][C]0.1017[/C][C]0.459609[/C][/ROW]
[ROW][C]11[/C][C]-0.045976[/C][C]-0.4551[/C][C]0.674991[/C][/ROW]
[ROW][C]12[/C][C]0.315275[/C][C]3.1211[/C][C]0.001184[/C][/ROW]
[ROW][C]13[/C][C]0.003852[/C][C]0.0381[/C][C]0.484828[/C][/ROW]
[ROW][C]14[/C][C]0.142009[/C][C]1.4058[/C][C]0.08147[/C][/ROW]
[ROW][C]15[/C][C]0.04461[/C][C]0.4416[/C][C]0.32987[/C][/ROW]
[ROW][C]16[/C][C]-0.109007[/C][C]-1.0791[/C][C]0.858406[/C][/ROW]
[ROW][C]17[/C][C]-0.029788[/C][C]-0.2949[/C][C]0.615648[/C][/ROW]
[ROW][C]18[/C][C]-0.169898[/C][C]-1.6819[/C][C]0.952114[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6459&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6459&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	9.8995	0
1	0.019787	0.1959	0.422553
2	0.037662	0.3728	0.355039
3	-0.197905	-1.9592	0.973532
4	-0.080038	-0.7923	0.78496
5	0.015705	0.1555	0.438386
6	-0.003334	-0.033	0.51313
7	0.004682	0.0463	0.481564
8	-0.026326	-0.2606	0.60253
9	-0.088942	-0.8805	0.809623
10	0.010271	0.1017	0.459609
11	-0.045976	-0.4551	0.674991
12	0.315275	3.1211	0.001184
13	0.003852	0.0381	0.484828
14	0.142009	1.4058	0.08147
15	0.04461	0.4416	0.32987
16	-0.109007	-1.0791	0.858406
17	-0.029788	-0.2949	0.615648
18	-0.169898	-1.6819	0.952114

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.019787	0.1959	0.422553
1	0.037285	0.3691	0.356424
2	-0.199715	-1.9771	0.974579
3	-0.075532	-0.7477	0.771792
4	0.035999	0.3564	0.361164
5	-0.038609	-0.3822	0.648434
6	-0.029301	-0.2901	0.613809
7	-0.020874	-0.2066	0.58164
8	-0.096276	-0.9531	0.828553
9	0.006492	0.0643	0.474445
10	-0.051595	-0.5108	0.694668
11	0.292464	2.8952	0.002336
12	-0.015962	-0.158	0.562614
13	0.119256	1.1806	0.120314
14	0.166878	1.652	0.050867
15	-0.092182	-0.9126	0.818141
16	0.003949	0.0391	0.484448
17	-0.121169	-1.1995	0.88339
18	-0.097345	-0.9637	0.831209

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.019787 & 0.1959 & 0.422553 \tabularnewline
1 & 0.037285 & 0.3691 & 0.356424 \tabularnewline
2 & -0.199715 & -1.9771 & 0.974579 \tabularnewline
3 & -0.075532 & -0.7477 & 0.771792 \tabularnewline
4 & 0.035999 & 0.3564 & 0.361164 \tabularnewline
5 & -0.038609 & -0.3822 & 0.648434 \tabularnewline
6 & -0.029301 & -0.2901 & 0.613809 \tabularnewline
7 & -0.020874 & -0.2066 & 0.58164 \tabularnewline
8 & -0.096276 & -0.9531 & 0.828553 \tabularnewline
9 & 0.006492 & 0.0643 & 0.474445 \tabularnewline
10 & -0.051595 & -0.5108 & 0.694668 \tabularnewline
11 & 0.292464 & 2.8952 & 0.002336 \tabularnewline
12 & -0.015962 & -0.158 & 0.562614 \tabularnewline
13 & 0.119256 & 1.1806 & 0.120314 \tabularnewline
14 & 0.166878 & 1.652 & 0.050867 \tabularnewline
15 & -0.092182 & -0.9126 & 0.818141 \tabularnewline
16 & 0.003949 & 0.0391 & 0.484448 \tabularnewline
17 & -0.121169 & -1.1995 & 0.88339 \tabularnewline
18 & -0.097345 & -0.9637 & 0.831209 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6459&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]0.019787[/C][C]0.1959[/C][C]0.422553[/C][/ROW]
[ROW][C]1[/C][C]0.037285[/C][C]0.3691[/C][C]0.356424[/C][/ROW]
[ROW][C]2[/C][C]-0.199715[/C][C]-1.9771[/C][C]0.974579[/C][/ROW]
[ROW][C]3[/C][C]-0.075532[/C][C]-0.7477[/C][C]0.771792[/C][/ROW]
[ROW][C]4[/C][C]0.035999[/C][C]0.3564[/C][C]0.361164[/C][/ROW]
[ROW][C]5[/C][C]-0.038609[/C][C]-0.3822[/C][C]0.648434[/C][/ROW]
[ROW][C]6[/C][C]-0.029301[/C][C]-0.2901[/C][C]0.613809[/C][/ROW]
[ROW][C]7[/C][C]-0.020874[/C][C]-0.2066[/C][C]0.58164[/C][/ROW]
[ROW][C]8[/C][C]-0.096276[/C][C]-0.9531[/C][C]0.828553[/C][/ROW]
[ROW][C]9[/C][C]0.006492[/C][C]0.0643[/C][C]0.474445[/C][/ROW]
[ROW][C]10[/C][C]-0.051595[/C][C]-0.5108[/C][C]0.694668[/C][/ROW]
[ROW][C]11[/C][C]0.292464[/C][C]2.8952[/C][C]0.002336[/C][/ROW]
[ROW][C]12[/C][C]-0.015962[/C][C]-0.158[/C][C]0.562614[/C][/ROW]
[ROW][C]13[/C][C]0.119256[/C][C]1.1806[/C][C]0.120314[/C][/ROW]
[ROW][C]14[/C][C]0.166878[/C][C]1.652[/C][C]0.050867[/C][/ROW]
[ROW][C]15[/C][C]-0.092182[/C][C]-0.9126[/C][C]0.818141[/C][/ROW]
[ROW][C]16[/C][C]0.003949[/C][C]0.0391[/C][C]0.484448[/C][/ROW]
[ROW][C]17[/C][C]-0.121169[/C][C]-1.1995[/C][C]0.88339[/C][/ROW]
[ROW][C]18[/C][C]-0.097345[/C][C]-0.9637[/C][C]0.831209[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6459&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6459&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	0.019787	0.1959	0.422553
1	0.037285	0.3691	0.356424
2	-0.199715	-1.9771	0.974579
3	-0.075532	-0.7477	0.771792
4	0.035999	0.3564	0.361164
5	-0.038609	-0.3822	0.648434
6	-0.029301	-0.2901	0.613809
7	-0.020874	-0.2066	0.58164
8	-0.096276	-0.9531	0.828553
9	0.006492	0.0643	0.474445
10	-0.051595	-0.5108	0.694668
11	0.292464	2.8952	0.002336
12	-0.015962	-0.158	0.562614
13	0.119256	1.1806	0.120314
14	0.166878	1.652	0.050867
15	-0.092182	-0.9126	0.818141
16	0.003949	0.0391	0.484448
17	-0.121169	-1.1995	0.88339
18	-0.097345	-0.9637	0.831209

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; 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