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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 03 Dec 2010 14:19:39 +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/Dec/03/t12913858948216ilesmu33sea.htm/, Retrieved Wed, 08 May 2024 02:16:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104818, Retrieved Wed, 08 May 2024 02:16:24 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

106

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]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-   PD      [(Partial) Autocorrelation Function] [Stationarity in t...] [2010-12-03 14:19:39] [18ef3d986e8801a4b28404e69e5bf56b] [Current]
-   P         [(Partial) Autocorrelation Function] [Stationarity in t...] [2010-12-03 14:33:49] [aeb27d5c05332f2e597ad139ee63fbe4] 
-   P           [(Partial) Autocorrelation Function] [Stationarity in t...] [2010-12-03 14:41:54] [aeb27d5c05332f2e597ad139ee63fbe4] 

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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	'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104818&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104818&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104818&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.665719	-5.8036	0
2	0.17815	1.5531	0.06228
3	-0.020788	-0.1812	0.428336
4	0.060795	0.53	0.298829
5	-0.023575	-0.2055	0.418858
6	-0.098035	-0.8546	0.197717
7	0.120124	1.0472	0.149159
8	0.01171	0.1021	0.459477
9	-0.149915	-1.3069	0.097589
10	0.035029	0.3054	0.380459
11	0.350017	3.0514	0.001568
12	-0.632415	-5.5133	0
13	0.537455	4.6854	6e-06
14	-0.323478	-2.82	0.003061
15	0.217079	1.8925	0.03112
16	-0.156325	-1.3628	0.088484
17	0.010829	0.0944	0.462517
18	0.118358	1.0318	0.152714
19	-0.134347	-1.1712	0.122586
20	0.0459	0.4002	0.345084

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.665719 & -5.8036 & 0 \tabularnewline
2 & 0.17815 & 1.5531 & 0.06228 \tabularnewline
3 & -0.020788 & -0.1812 & 0.428336 \tabularnewline
4 & 0.060795 & 0.53 & 0.298829 \tabularnewline
5 & -0.023575 & -0.2055 & 0.418858 \tabularnewline
6 & -0.098035 & -0.8546 & 0.197717 \tabularnewline
7 & 0.120124 & 1.0472 & 0.149159 \tabularnewline
8 & 0.01171 & 0.1021 & 0.459477 \tabularnewline
9 & -0.149915 & -1.3069 & 0.097589 \tabularnewline
10 & 0.035029 & 0.3054 & 0.380459 \tabularnewline
11 & 0.350017 & 3.0514 & 0.001568 \tabularnewline
12 & -0.632415 & -5.5133 & 0 \tabularnewline
13 & 0.537455 & 4.6854 & 6e-06 \tabularnewline
14 & -0.323478 & -2.82 & 0.003061 \tabularnewline
15 & 0.217079 & 1.8925 & 0.03112 \tabularnewline
16 & -0.156325 & -1.3628 & 0.088484 \tabularnewline
17 & 0.010829 & 0.0944 & 0.462517 \tabularnewline
18 & 0.118358 & 1.0318 & 0.152714 \tabularnewline
19 & -0.134347 & -1.1712 & 0.122586 \tabularnewline
20 & 0.0459 & 0.4002 & 0.345084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104818&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]-0.665719[/C][C]-5.8036[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.17815[/C][C]1.5531[/C][C]0.06228[/C][/ROW]
[ROW][C]3[/C][C]-0.020788[/C][C]-0.1812[/C][C]0.428336[/C][/ROW]
[ROW][C]4[/C][C]0.060795[/C][C]0.53[/C][C]0.298829[/C][/ROW]
[ROW][C]5[/C][C]-0.023575[/C][C]-0.2055[/C][C]0.418858[/C][/ROW]
[ROW][C]6[/C][C]-0.098035[/C][C]-0.8546[/C][C]0.197717[/C][/ROW]
[ROW][C]7[/C][C]0.120124[/C][C]1.0472[/C][C]0.149159[/C][/ROW]
[ROW][C]8[/C][C]0.01171[/C][C]0.1021[/C][C]0.459477[/C][/ROW]
[ROW][C]9[/C][C]-0.149915[/C][C]-1.3069[/C][C]0.097589[/C][/ROW]
[ROW][C]10[/C][C]0.035029[/C][C]0.3054[/C][C]0.380459[/C][/ROW]
[ROW][C]11[/C][C]0.350017[/C][C]3.0514[/C][C]0.001568[/C][/ROW]
[ROW][C]12[/C][C]-0.632415[/C][C]-5.5133[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.537455[/C][C]4.6854[/C][C]6e-06[/C][/ROW]
[ROW][C]14[/C][C]-0.323478[/C][C]-2.82[/C][C]0.003061[/C][/ROW]
[ROW][C]15[/C][C]0.217079[/C][C]1.8925[/C][C]0.03112[/C][/ROW]
[ROW][C]16[/C][C]-0.156325[/C][C]-1.3628[/C][C]0.088484[/C][/ROW]
[ROW][C]17[/C][C]0.010829[/C][C]0.0944[/C][C]0.462517[/C][/ROW]
[ROW][C]18[/C][C]0.118358[/C][C]1.0318[/C][C]0.152714[/C][/ROW]
[ROW][C]19[/C][C]-0.134347[/C][C]-1.1712[/C][C]0.122586[/C][/ROW]
[ROW][C]20[/C][C]0.0459[/C][C]0.4002[/C][C]0.345084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104818&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104818&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	-0.665719	-5.8036	0
2	0.17815	1.5531	0.06228
3	-0.020788	-0.1812	0.428336
4	0.060795	0.53	0.298829
5	-0.023575	-0.2055	0.418858
6	-0.098035	-0.8546	0.197717
7	0.120124	1.0472	0.149159
8	0.01171	0.1021	0.459477
9	-0.149915	-1.3069	0.097589
10	0.035029	0.3054	0.380459
11	0.350017	3.0514	0.001568
12	-0.632415	-5.5133	0
13	0.537455	4.6854	6e-06
14	-0.323478	-2.82	0.003061
15	0.217079	1.8925	0.03112
16	-0.156325	-1.3628	0.088484
17	0.010829	0.0944	0.462517
18	0.118358	1.0318	0.152714
19	-0.134347	-1.1712	0.122586
20	0.0459	0.4002	0.345084

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.665719	-5.8036	0
2	-0.475975	-4.1495	4.3e-05
3	-0.377566	-3.2915	0.000757
4	-0.17286	-1.507	0.067983
5	0.05132	0.4474	0.327931
6	-0.071109	-0.6199	0.268584
7	-0.09085	-0.792	0.215409
8	0.091998	0.802	0.212521
9	-0.06192	-0.5398	0.295453
10	-0.361157	-3.1485	0.001173
11	0.42628	3.7162	0.000192
12	-0.215226	-1.8763	0.032227
13	-0.031117	-0.2713	0.393459
14	-0.163938	-1.4292	0.078526
15	-0.188027	-1.6392	0.052654
16	-0.062358	-0.5436	0.294146
17	-0.073923	-0.6444	0.260613
18	-0.245734	-2.1423	0.017688
19	-0.194072	-1.6919	0.047383
20	-0.05499	-0.4794	0.316517

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.665719 & -5.8036 & 0 \tabularnewline
2 & -0.475975 & -4.1495 & 4.3e-05 \tabularnewline
3 & -0.377566 & -3.2915 & 0.000757 \tabularnewline
4 & -0.17286 & -1.507 & 0.067983 \tabularnewline
5 & 0.05132 & 0.4474 & 0.327931 \tabularnewline
6 & -0.071109 & -0.6199 & 0.268584 \tabularnewline
7 & -0.09085 & -0.792 & 0.215409 \tabularnewline
8 & 0.091998 & 0.802 & 0.212521 \tabularnewline
9 & -0.06192 & -0.5398 & 0.295453 \tabularnewline
10 & -0.361157 & -3.1485 & 0.001173 \tabularnewline
11 & 0.42628 & 3.7162 & 0.000192 \tabularnewline
12 & -0.215226 & -1.8763 & 0.032227 \tabularnewline
13 & -0.031117 & -0.2713 & 0.393459 \tabularnewline
14 & -0.163938 & -1.4292 & 0.078526 \tabularnewline
15 & -0.188027 & -1.6392 & 0.052654 \tabularnewline
16 & -0.062358 & -0.5436 & 0.294146 \tabularnewline
17 & -0.073923 & -0.6444 & 0.260613 \tabularnewline
18 & -0.245734 & -2.1423 & 0.017688 \tabularnewline
19 & -0.194072 & -1.6919 & 0.047383 \tabularnewline
20 & -0.05499 & -0.4794 & 0.316517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104818&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]-0.665719[/C][C]-5.8036[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.475975[/C][C]-4.1495[/C][C]4.3e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.377566[/C][C]-3.2915[/C][C]0.000757[/C][/ROW]
[ROW][C]4[/C][C]-0.17286[/C][C]-1.507[/C][C]0.067983[/C][/ROW]
[ROW][C]5[/C][C]0.05132[/C][C]0.4474[/C][C]0.327931[/C][/ROW]
[ROW][C]6[/C][C]-0.071109[/C][C]-0.6199[/C][C]0.268584[/C][/ROW]
[ROW][C]7[/C][C]-0.09085[/C][C]-0.792[/C][C]0.215409[/C][/ROW]
[ROW][C]8[/C][C]0.091998[/C][C]0.802[/C][C]0.212521[/C][/ROW]
[ROW][C]9[/C][C]-0.06192[/C][C]-0.5398[/C][C]0.295453[/C][/ROW]
[ROW][C]10[/C][C]-0.361157[/C][C]-3.1485[/C][C]0.001173[/C][/ROW]
[ROW][C]11[/C][C]0.42628[/C][C]3.7162[/C][C]0.000192[/C][/ROW]
[ROW][C]12[/C][C]-0.215226[/C][C]-1.8763[/C][C]0.032227[/C][/ROW]
[ROW][C]13[/C][C]-0.031117[/C][C]-0.2713[/C][C]0.393459[/C][/ROW]
[ROW][C]14[/C][C]-0.163938[/C][C]-1.4292[/C][C]0.078526[/C][/ROW]
[ROW][C]15[/C][C]-0.188027[/C][C]-1.6392[/C][C]0.052654[/C][/ROW]
[ROW][C]16[/C][C]-0.062358[/C][C]-0.5436[/C][C]0.294146[/C][/ROW]
[ROW][C]17[/C][C]-0.073923[/C][C]-0.6444[/C][C]0.260613[/C][/ROW]
[ROW][C]18[/C][C]-0.245734[/C][C]-2.1423[/C][C]0.017688[/C][/ROW]
[ROW][C]19[/C][C]-0.194072[/C][C]-1.6919[/C][C]0.047383[/C][/ROW]
[ROW][C]20[/C][C]-0.05499[/C][C]-0.4794[/C][C]0.316517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104818&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104818&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	-0.665719	-5.8036	0
2	-0.475975	-4.1495	4.3e-05
3	-0.377566	-3.2915	0.000757
4	-0.17286	-1.507	0.067983
5	0.05132	0.4474	0.327931
6	-0.071109	-0.6199	0.268584
7	-0.09085	-0.792	0.215409
8	0.091998	0.802	0.212521
9	-0.06192	-0.5398	0.295453
10	-0.361157	-3.1485	0.001173
11	0.42628	3.7162	0.000192
12	-0.215226	-1.8763	0.032227
13	-0.031117	-0.2713	0.393459
14	-0.163938	-1.4292	0.078526
15	-0.188027	-1.6392	0.052654
16	-0.062358	-0.5436	0.294146
17	-0.073923	-0.6444	0.260613
18	-0.245734	-2.1423	0.017688
19	-0.194072	-1.6919	0.047383
20	-0.05499	-0.4794	0.316517

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 2 ; 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