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rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 22 Nov 2010 14:50:14 +0000

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/2010/Nov/22/t12904372986au93yvi747bssf.htm/, Retrieved Fri, 03 May 2024 21:29:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=98550, Retrieved Fri, 03 May 2024 21:29:04 +0000

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123

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-       [(Partial) Autocorrelation Function] [] [2010-11-22 14:50:14] [9b9a58c480cb5dafe4bfceb51e1cfd12] [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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98550&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98550&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98550&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.194303	-2.7479	0.003273
2	-0.163841	-2.3171	0.010756
3	-0.123138	-1.7414	0.041572
4	-0.061212	-0.8657	0.193854
5	-0.03455	-0.4886	0.312827
6	0.040706	0.5757	0.282744
7	0.015545	0.2198	0.413113
8	0.150714	2.1314	0.017138
9	-0.033789	-0.4778	0.31664
10	-0.107699	-1.5231	0.064657
11	-0.051672	-0.7308	0.232891
12	0.007322	0.1035	0.458817
13	0.122116	1.727	0.042857
14	-0.006038	-0.0854	0.466021
15	-0.046163	-0.6528	0.257304
16	-0.059258	-0.838	0.201506
17	0.091724	1.2972	0.098034
18	0.002165	0.0306	0.4878
19	0.039067	0.5525	0.290617
20	-0.113249	-1.6016	0.055412
21	0.048764	0.6896	0.245616
22	-0.021695	-0.3068	0.379653
23	-0.037141	-0.5253	0.299995

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.194303 & -2.7479 & 0.003273 \tabularnewline
2 & -0.163841 & -2.3171 & 0.010756 \tabularnewline
3 & -0.123138 & -1.7414 & 0.041572 \tabularnewline
4 & -0.061212 & -0.8657 & 0.193854 \tabularnewline
5 & -0.03455 & -0.4886 & 0.312827 \tabularnewline
6 & 0.040706 & 0.5757 & 0.282744 \tabularnewline
7 & 0.015545 & 0.2198 & 0.413113 \tabularnewline
8 & 0.150714 & 2.1314 & 0.017138 \tabularnewline
9 & -0.033789 & -0.4778 & 0.31664 \tabularnewline
10 & -0.107699 & -1.5231 & 0.064657 \tabularnewline
11 & -0.051672 & -0.7308 & 0.232891 \tabularnewline
12 & 0.007322 & 0.1035 & 0.458817 \tabularnewline
13 & 0.122116 & 1.727 & 0.042857 \tabularnewline
14 & -0.006038 & -0.0854 & 0.466021 \tabularnewline
15 & -0.046163 & -0.6528 & 0.257304 \tabularnewline
16 & -0.059258 & -0.838 & 0.201506 \tabularnewline
17 & 0.091724 & 1.2972 & 0.098034 \tabularnewline
18 & 0.002165 & 0.0306 & 0.4878 \tabularnewline
19 & 0.039067 & 0.5525 & 0.290617 \tabularnewline
20 & -0.113249 & -1.6016 & 0.055412 \tabularnewline
21 & 0.048764 & 0.6896 & 0.245616 \tabularnewline
22 & -0.021695 & -0.3068 & 0.379653 \tabularnewline
23 & -0.037141 & -0.5253 & 0.299995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98550&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]-0.194303[/C][C]-2.7479[/C][C]0.003273[/C][/ROW]
[ROW][C]2[/C][C]-0.163841[/C][C]-2.3171[/C][C]0.010756[/C][/ROW]
[ROW][C]3[/C][C]-0.123138[/C][C]-1.7414[/C][C]0.041572[/C][/ROW]
[ROW][C]4[/C][C]-0.061212[/C][C]-0.8657[/C][C]0.193854[/C][/ROW]
[ROW][C]5[/C][C]-0.03455[/C][C]-0.4886[/C][C]0.312827[/C][/ROW]
[ROW][C]6[/C][C]0.040706[/C][C]0.5757[/C][C]0.282744[/C][/ROW]
[ROW][C]7[/C][C]0.015545[/C][C]0.2198[/C][C]0.413113[/C][/ROW]
[ROW][C]8[/C][C]0.150714[/C][C]2.1314[/C][C]0.017138[/C][/ROW]
[ROW][C]9[/C][C]-0.033789[/C][C]-0.4778[/C][C]0.31664[/C][/ROW]
[ROW][C]10[/C][C]-0.107699[/C][C]-1.5231[/C][C]0.064657[/C][/ROW]
[ROW][C]11[/C][C]-0.051672[/C][C]-0.7308[/C][C]0.232891[/C][/ROW]
[ROW][C]12[/C][C]0.007322[/C][C]0.1035[/C][C]0.458817[/C][/ROW]
[ROW][C]13[/C][C]0.122116[/C][C]1.727[/C][C]0.042857[/C][/ROW]
[ROW][C]14[/C][C]-0.006038[/C][C]-0.0854[/C][C]0.466021[/C][/ROW]
[ROW][C]15[/C][C]-0.046163[/C][C]-0.6528[/C][C]0.257304[/C][/ROW]
[ROW][C]16[/C][C]-0.059258[/C][C]-0.838[/C][C]0.201506[/C][/ROW]
[ROW][C]17[/C][C]0.091724[/C][C]1.2972[/C][C]0.098034[/C][/ROW]
[ROW][C]18[/C][C]0.002165[/C][C]0.0306[/C][C]0.4878[/C][/ROW]
[ROW][C]19[/C][C]0.039067[/C][C]0.5525[/C][C]0.290617[/C][/ROW]
[ROW][C]20[/C][C]-0.113249[/C][C]-1.6016[/C][C]0.055412[/C][/ROW]
[ROW][C]21[/C][C]0.048764[/C][C]0.6896[/C][C]0.245616[/C][/ROW]
[ROW][C]22[/C][C]-0.021695[/C][C]-0.3068[/C][C]0.379653[/C][/ROW]
[ROW][C]23[/C][C]-0.037141[/C][C]-0.5253[/C][C]0.299995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98550&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98550&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	-0.194303	-2.7479	0.003273
2	-0.163841	-2.3171	0.010756
3	-0.123138	-1.7414	0.041572
4	-0.061212	-0.8657	0.193854
5	-0.03455	-0.4886	0.312827
6	0.040706	0.5757	0.282744
7	0.015545	0.2198	0.413113
8	0.150714	2.1314	0.017138
9	-0.033789	-0.4778	0.31664
10	-0.107699	-1.5231	0.064657
11	-0.051672	-0.7308	0.232891
12	0.007322	0.1035	0.458817
13	0.122116	1.727	0.042857
14	-0.006038	-0.0854	0.466021
15	-0.046163	-0.6528	0.257304
16	-0.059258	-0.838	0.201506
17	0.091724	1.2972	0.098034
18	0.002165	0.0306	0.4878
19	0.039067	0.5525	0.290617
20	-0.113249	-1.6016	0.055412
21	0.048764	0.6896	0.245616
22	-0.021695	-0.3068	0.379653
23	-0.037141	-0.5253	0.299995

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.194303	-2.7479	0.003273
2	-0.209505	-2.9628	0.001709
3	-0.219943	-3.1105	0.00107
4	-0.207143	-2.9294	0.001895
5	-0.213851	-3.0243	0.001409
6	-0.155754	-2.2027	0.014379
7	-0.157588	-2.2286	0.013476
8	0.036791	0.5203	0.301715
9	-0.025024	-0.3539	0.361896
10	-0.097791	-1.383	0.084108
11	-0.099852	-1.4121	0.079734
12	-0.088188	-1.2472	0.106898
13	0.05148	0.728	0.233722
14	-0.012594	-0.1781	0.429412
15	-0.047945	-0.678	0.249266
16	-0.113494	-1.605	0.055031
17	0.042288	0.598	0.275243
18	0.043387	0.6136	0.270093
19	0.100565	1.4222	0.078262
20	-0.06224	-0.8802	0.189901
21	0.009124	0.129	0.448731
22	-0.012069	-0.1707	0.432321
23	-0.034351	-0.4858	0.313821

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.194303 & -2.7479 & 0.003273 \tabularnewline
2 & -0.209505 & -2.9628 & 0.001709 \tabularnewline
3 & -0.219943 & -3.1105 & 0.00107 \tabularnewline
4 & -0.207143 & -2.9294 & 0.001895 \tabularnewline
5 & -0.213851 & -3.0243 & 0.001409 \tabularnewline
6 & -0.155754 & -2.2027 & 0.014379 \tabularnewline
7 & -0.157588 & -2.2286 & 0.013476 \tabularnewline
8 & 0.036791 & 0.5203 & 0.301715 \tabularnewline
9 & -0.025024 & -0.3539 & 0.361896 \tabularnewline
10 & -0.097791 & -1.383 & 0.084108 \tabularnewline
11 & -0.099852 & -1.4121 & 0.079734 \tabularnewline
12 & -0.088188 & -1.2472 & 0.106898 \tabularnewline
13 & 0.05148 & 0.728 & 0.233722 \tabularnewline
14 & -0.012594 & -0.1781 & 0.429412 \tabularnewline
15 & -0.047945 & -0.678 & 0.249266 \tabularnewline
16 & -0.113494 & -1.605 & 0.055031 \tabularnewline
17 & 0.042288 & 0.598 & 0.275243 \tabularnewline
18 & 0.043387 & 0.6136 & 0.270093 \tabularnewline
19 & 0.100565 & 1.4222 & 0.078262 \tabularnewline
20 & -0.06224 & -0.8802 & 0.189901 \tabularnewline
21 & 0.009124 & 0.129 & 0.448731 \tabularnewline
22 & -0.012069 & -0.1707 & 0.432321 \tabularnewline
23 & -0.034351 & -0.4858 & 0.313821 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=98550&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]-0.194303[/C][C]-2.7479[/C][C]0.003273[/C][/ROW]
[ROW][C]2[/C][C]-0.209505[/C][C]-2.9628[/C][C]0.001709[/C][/ROW]
[ROW][C]3[/C][C]-0.219943[/C][C]-3.1105[/C][C]0.00107[/C][/ROW]
[ROW][C]4[/C][C]-0.207143[/C][C]-2.9294[/C][C]0.001895[/C][/ROW]
[ROW][C]5[/C][C]-0.213851[/C][C]-3.0243[/C][C]0.001409[/C][/ROW]
[ROW][C]6[/C][C]-0.155754[/C][C]-2.2027[/C][C]0.014379[/C][/ROW]
[ROW][C]7[/C][C]-0.157588[/C][C]-2.2286[/C][C]0.013476[/C][/ROW]
[ROW][C]8[/C][C]0.036791[/C][C]0.5203[/C][C]0.301715[/C][/ROW]
[ROW][C]9[/C][C]-0.025024[/C][C]-0.3539[/C][C]0.361896[/C][/ROW]
[ROW][C]10[/C][C]-0.097791[/C][C]-1.383[/C][C]0.084108[/C][/ROW]
[ROW][C]11[/C][C]-0.099852[/C][C]-1.4121[/C][C]0.079734[/C][/ROW]
[ROW][C]12[/C][C]-0.088188[/C][C]-1.2472[/C][C]0.106898[/C][/ROW]
[ROW][C]13[/C][C]0.05148[/C][C]0.728[/C][C]0.233722[/C][/ROW]
[ROW][C]14[/C][C]-0.012594[/C][C]-0.1781[/C][C]0.429412[/C][/ROW]
[ROW][C]15[/C][C]-0.047945[/C][C]-0.678[/C][C]0.249266[/C][/ROW]
[ROW][C]16[/C][C]-0.113494[/C][C]-1.605[/C][C]0.055031[/C][/ROW]
[ROW][C]17[/C][C]0.042288[/C][C]0.598[/C][C]0.275243[/C][/ROW]
[ROW][C]18[/C][C]0.043387[/C][C]0.6136[/C][C]0.270093[/C][/ROW]
[ROW][C]19[/C][C]0.100565[/C][C]1.4222[/C][C]0.078262[/C][/ROW]
[ROW][C]20[/C][C]-0.06224[/C][C]-0.8802[/C][C]0.189901[/C][/ROW]
[ROW][C]21[/C][C]0.009124[/C][C]0.129[/C][C]0.448731[/C][/ROW]
[ROW][C]22[/C][C]-0.012069[/C][C]-0.1707[/C][C]0.432321[/C][/ROW]
[ROW][C]23[/C][C]-0.034351[/C][C]-0.4858[/C][C]0.313821[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=98550&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=98550&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	-0.194303	-2.7479	0.003273
2	-0.209505	-2.9628	0.001709
3	-0.219943	-3.1105	0.00107
4	-0.207143	-2.9294	0.001895
5	-0.213851	-3.0243	0.001409
6	-0.155754	-2.2027	0.014379
7	-0.157588	-2.2286	0.013476
8	0.036791	0.5203	0.301715
9	-0.025024	-0.3539	0.361896
10	-0.097791	-1.383	0.084108
11	-0.099852	-1.4121	0.079734
12	-0.088188	-1.2472	0.106898
13	0.05148	0.728	0.233722
14	-0.012594	-0.1781	0.429412
15	-0.047945	-0.678	0.249266
16	-0.113494	-1.605	0.055031
17	0.042288	0.598	0.275243
18	0.043387	0.6136	0.270093
19	0.100565	1.4222	0.078262
20	-0.06224	-0.8802	0.189901
21	0.009124	0.129	0.448731
22	-0.012069	-0.1707	0.432321
23	-0.034351	-0.4858	0.313821

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code