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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

Sat, 13 Dec 2008 03:17:59 -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/13/t1229163525od1wy5xelmsjydk.htm/, Retrieved Sat, 25 May 2024 03:19:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32936, Retrieved Sat, 25 May 2024 03:19:46 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

207

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F   P   [Univariate Data Series] [unemployement] [2008-12-09 14:17:32] [74be16979710d4c4e7c6647856088456]
- RMPD      [(Partial) Autocorrelation Function] [EEEEE] [2008-12-13 10:17:59] [59094f58b9d90d3694e930ebd2901ecd] [Current]

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Dataseries X:

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Histogram

Boxplots

7.5
7.2
6.9
6.7
6.4
6.3
6.8
7.3
7.1
7.1
6.8
6.5
6.3
6.1
6.1
6.3
6.3
6
6.2
6.4
6.8
7.5
7.5
7.6
7.6
7.4
7.3
7.1
6.9
6.8
7.5
7.6
7.8
8.0
8.1
8.2
8.3
8.2
8.0
7.9
7.6
7.6
8.2
8.3
8.4
8.4
8.4
8.6
8.9
8.8
8.3
7.5
7.2
7.5
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.6
8.2
8.1
8.0
8.6
8.7
8.8
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8.1
8.2
8.1
8.1
7.9
7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.6
6.2
6.2
6.8
6.9
6.8

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32936&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32936&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32936&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.373759	3.8116	0.000117
2	-0.110772	-1.1297	0.13061
3	-0.377581	-3.8506	0.000102
4	-0.380593	-3.8813	9.1e-05
5	-0.071809	-0.7323	0.232812
6	0.213828	2.1806	0.015733
7	0.107287	1.0941	0.138216
8	-0.097688	-0.9962	0.160726
9	-0.150424	-1.534	0.06403
10	-0.118116	-1.2046	0.115555
11	0.138939	1.4169	0.07975
12	0.488343	4.9801	1e-06
13	0.139436	1.422	0.079014
14	-0.006578	-0.0671	0.473322
15	-0.141277	-1.4407	0.07633
16	-0.161339	-1.6453	0.05146
17	-0.051294	-0.5231	0.301008
18	0.083891	0.8555	0.197115
19	-0.03225	-0.3289	0.371453
20	-0.136786	-1.3949	0.083002

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.373759 & 3.8116 & 0.000117 \tabularnewline
2 & -0.110772 & -1.1297 & 0.13061 \tabularnewline
3 & -0.377581 & -3.8506 & 0.000102 \tabularnewline
4 & -0.380593 & -3.8813 & 9.1e-05 \tabularnewline
5 & -0.071809 & -0.7323 & 0.232812 \tabularnewline
6 & 0.213828 & 2.1806 & 0.015733 \tabularnewline
7 & 0.107287 & 1.0941 & 0.138216 \tabularnewline
8 & -0.097688 & -0.9962 & 0.160726 \tabularnewline
9 & -0.150424 & -1.534 & 0.06403 \tabularnewline
10 & -0.118116 & -1.2046 & 0.115555 \tabularnewline
11 & 0.138939 & 1.4169 & 0.07975 \tabularnewline
12 & 0.488343 & 4.9801 & 1e-06 \tabularnewline
13 & 0.139436 & 1.422 & 0.079014 \tabularnewline
14 & -0.006578 & -0.0671 & 0.473322 \tabularnewline
15 & -0.141277 & -1.4407 & 0.07633 \tabularnewline
16 & -0.161339 & -1.6453 & 0.05146 \tabularnewline
17 & -0.051294 & -0.5231 & 0.301008 \tabularnewline
18 & 0.083891 & 0.8555 & 0.197115 \tabularnewline
19 & -0.03225 & -0.3289 & 0.371453 \tabularnewline
20 & -0.136786 & -1.3949 & 0.083002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32936&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]0.373759[/C][C]3.8116[/C][C]0.000117[/C][/ROW]
[ROW][C]2[/C][C]-0.110772[/C][C]-1.1297[/C][C]0.13061[/C][/ROW]
[ROW][C]3[/C][C]-0.377581[/C][C]-3.8506[/C][C]0.000102[/C][/ROW]
[ROW][C]4[/C][C]-0.380593[/C][C]-3.8813[/C][C]9.1e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.071809[/C][C]-0.7323[/C][C]0.232812[/C][/ROW]
[ROW][C]6[/C][C]0.213828[/C][C]2.1806[/C][C]0.015733[/C][/ROW]
[ROW][C]7[/C][C]0.107287[/C][C]1.0941[/C][C]0.138216[/C][/ROW]
[ROW][C]8[/C][C]-0.097688[/C][C]-0.9962[/C][C]0.160726[/C][/ROW]
[ROW][C]9[/C][C]-0.150424[/C][C]-1.534[/C][C]0.06403[/C][/ROW]
[ROW][C]10[/C][C]-0.118116[/C][C]-1.2046[/C][C]0.115555[/C][/ROW]
[ROW][C]11[/C][C]0.138939[/C][C]1.4169[/C][C]0.07975[/C][/ROW]
[ROW][C]12[/C][C]0.488343[/C][C]4.9801[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.139436[/C][C]1.422[/C][C]0.079014[/C][/ROW]
[ROW][C]14[/C][C]-0.006578[/C][C]-0.0671[/C][C]0.473322[/C][/ROW]
[ROW][C]15[/C][C]-0.141277[/C][C]-1.4407[/C][C]0.07633[/C][/ROW]
[ROW][C]16[/C][C]-0.161339[/C][C]-1.6453[/C][C]0.05146[/C][/ROW]
[ROW][C]17[/C][C]-0.051294[/C][C]-0.5231[/C][C]0.301008[/C][/ROW]
[ROW][C]18[/C][C]0.083891[/C][C]0.8555[/C][C]0.197115[/C][/ROW]
[ROW][C]19[/C][C]-0.03225[/C][C]-0.3289[/C][C]0.371453[/C][/ROW]
[ROW][C]20[/C][C]-0.136786[/C][C]-1.3949[/C][C]0.083002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32936&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32936&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	0.373759	3.8116	0.000117
2	-0.110772	-1.1297	0.13061
3	-0.377581	-3.8506	0.000102
4	-0.380593	-3.8813	9.1e-05
5	-0.071809	-0.7323	0.232812
6	0.213828	2.1806	0.015733
7	0.107287	1.0941	0.138216
8	-0.097688	-0.9962	0.160726
9	-0.150424	-1.534	0.06403
10	-0.118116	-1.2046	0.115555
11	0.138939	1.4169	0.07975
12	0.488343	4.9801	1e-06
13	0.139436	1.422	0.079014
14	-0.006578	-0.0671	0.473322
15	-0.141277	-1.4407	0.07633
16	-0.161339	-1.6453	0.05146
17	-0.051294	-0.5231	0.301008
18	0.083891	0.8555	0.197115
19	-0.03225	-0.3289	0.371453
20	-0.136786	-1.3949	0.083002

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.373759	3.8116	0.000117
2	-0.291138	-2.969	0.001854
3	-0.27345	-2.7887	0.003148
4	-0.197486	-2.014	0.023297
5	0.059088	0.6026	0.27405
6	0.080763	0.8236	0.20602
7	-0.213602	-2.1783	0.01582
8	-0.174433	-1.7789	0.039091
9	0.005024	0.0512	0.47962
10	-0.042519	-0.4336	0.332733
11	0.115396	1.1768	0.120978
12	0.382836	3.9042	8.4e-05
13	-0.279044	-2.8457	0.002669
14	0.268879	2.742	0.003595
15	0.120075	1.2245	0.11176
16	0.112366	1.1459	0.127232
17	-0.045809	-0.4672	0.32068
18	0.031767	0.324	0.37331
19	-0.048008	-0.4896	0.31273
20	-0.083047	-0.8469	0.199493

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.373759 & 3.8116 & 0.000117 \tabularnewline
2 & -0.291138 & -2.969 & 0.001854 \tabularnewline
3 & -0.27345 & -2.7887 & 0.003148 \tabularnewline
4 & -0.197486 & -2.014 & 0.023297 \tabularnewline
5 & 0.059088 & 0.6026 & 0.27405 \tabularnewline
6 & 0.080763 & 0.8236 & 0.20602 \tabularnewline
7 & -0.213602 & -2.1783 & 0.01582 \tabularnewline
8 & -0.174433 & -1.7789 & 0.039091 \tabularnewline
9 & 0.005024 & 0.0512 & 0.47962 \tabularnewline
10 & -0.042519 & -0.4336 & 0.332733 \tabularnewline
11 & 0.115396 & 1.1768 & 0.120978 \tabularnewline
12 & 0.382836 & 3.9042 & 8.4e-05 \tabularnewline
13 & -0.279044 & -2.8457 & 0.002669 \tabularnewline
14 & 0.268879 & 2.742 & 0.003595 \tabularnewline
15 & 0.120075 & 1.2245 & 0.11176 \tabularnewline
16 & 0.112366 & 1.1459 & 0.127232 \tabularnewline
17 & -0.045809 & -0.4672 & 0.32068 \tabularnewline
18 & 0.031767 & 0.324 & 0.37331 \tabularnewline
19 & -0.048008 & -0.4896 & 0.31273 \tabularnewline
20 & -0.083047 & -0.8469 & 0.199493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32936&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]0.373759[/C][C]3.8116[/C][C]0.000117[/C][/ROW]
[ROW][C]2[/C][C]-0.291138[/C][C]-2.969[/C][C]0.001854[/C][/ROW]
[ROW][C]3[/C][C]-0.27345[/C][C]-2.7887[/C][C]0.003148[/C][/ROW]
[ROW][C]4[/C][C]-0.197486[/C][C]-2.014[/C][C]0.023297[/C][/ROW]
[ROW][C]5[/C][C]0.059088[/C][C]0.6026[/C][C]0.27405[/C][/ROW]
[ROW][C]6[/C][C]0.080763[/C][C]0.8236[/C][C]0.20602[/C][/ROW]
[ROW][C]7[/C][C]-0.213602[/C][C]-2.1783[/C][C]0.01582[/C][/ROW]
[ROW][C]8[/C][C]-0.174433[/C][C]-1.7789[/C][C]0.039091[/C][/ROW]
[ROW][C]9[/C][C]0.005024[/C][C]0.0512[/C][C]0.47962[/C][/ROW]
[ROW][C]10[/C][C]-0.042519[/C][C]-0.4336[/C][C]0.332733[/C][/ROW]
[ROW][C]11[/C][C]0.115396[/C][C]1.1768[/C][C]0.120978[/C][/ROW]
[ROW][C]12[/C][C]0.382836[/C][C]3.9042[/C][C]8.4e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.279044[/C][C]-2.8457[/C][C]0.002669[/C][/ROW]
[ROW][C]14[/C][C]0.268879[/C][C]2.742[/C][C]0.003595[/C][/ROW]
[ROW][C]15[/C][C]0.120075[/C][C]1.2245[/C][C]0.11176[/C][/ROW]
[ROW][C]16[/C][C]0.112366[/C][C]1.1459[/C][C]0.127232[/C][/ROW]
[ROW][C]17[/C][C]-0.045809[/C][C]-0.4672[/C][C]0.32068[/C][/ROW]
[ROW][C]18[/C][C]0.031767[/C][C]0.324[/C][C]0.37331[/C][/ROW]
[ROW][C]19[/C][C]-0.048008[/C][C]-0.4896[/C][C]0.31273[/C][/ROW]
[ROW][C]20[/C][C]-0.083047[/C][C]-0.8469[/C][C]0.199493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32936&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32936&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	0.373759	3.8116	0.000117
2	-0.291138	-2.969	0.001854
3	-0.27345	-2.7887	0.003148
4	-0.197486	-2.014	0.023297
5	0.059088	0.6026	0.27405
6	0.080763	0.8236	0.20602
7	-0.213602	-2.1783	0.01582
8	-0.174433	-1.7789	0.039091
9	0.005024	0.0512	0.47962
10	-0.042519	-0.4336	0.332733
11	0.115396	1.1768	0.120978
12	0.382836	3.9042	8.4e-05
13	-0.279044	-2.8457	0.002669
14	0.268879	2.742	0.003595
15	0.120075	1.2245	0.11176
16	0.112366	1.1459	0.127232
17	-0.045809	-0.4672	0.32068
18	0.031767	0.324	0.37331
19	-0.048008	-0.4896	0.31273
20	-0.083047	-0.8469	0.199493

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 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