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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 22 Dec 2009 06:29:08 -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/2009/Dec/22/t1261488939qvuce064kimb654.htm/, Retrieved Sat, 04 May 2024 05:41:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70439, Retrieved Sat, 04 May 2024 05:41:21 +0000

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No (this computation is public)

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Estimated Impact

158

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

-       [(Partial) Autocorrelation Function] [ACF, PACF] [2009-12-22 13:29:08] [b08f24ccf7d7e0757793cda532be96b3] [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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70439&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70439&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70439&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.982319	12.6944	0
2	0.964762	12.4675	0
3	0.947616	12.2459	0
4	0.930547	12.0253	0
5	0.913998	11.8115	0
6	0.896418	11.5843	0
7	0.878241	11.3494	0
8	0.860001	11.1137	0
9	0.84238	10.886	0
10	0.825131	10.663	0
11	0.808437	10.4473	0
12	0.790618	10.217	0
13	0.77173	9.9729	0
14	0.752125	9.7196	0
15	0.732503	9.466	0
16	0.713083	9.2151	0
17	0.693698	8.9646	0
18	0.673886	8.7085	0
19	0.653929	8.4506	0
20	0.634777	8.2031	0
21	0.616265	7.9639	0
22	0.598896	7.7394	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.982319 & 12.6944 & 0 \tabularnewline
2 & 0.964762 & 12.4675 & 0 \tabularnewline
3 & 0.947616 & 12.2459 & 0 \tabularnewline
4 & 0.930547 & 12.0253 & 0 \tabularnewline
5 & 0.913998 & 11.8115 & 0 \tabularnewline
6 & 0.896418 & 11.5843 & 0 \tabularnewline
7 & 0.878241 & 11.3494 & 0 \tabularnewline
8 & 0.860001 & 11.1137 & 0 \tabularnewline
9 & 0.84238 & 10.886 & 0 \tabularnewline
10 & 0.825131 & 10.663 & 0 \tabularnewline
11 & 0.808437 & 10.4473 & 0 \tabularnewline
12 & 0.790618 & 10.217 & 0 \tabularnewline
13 & 0.77173 & 9.9729 & 0 \tabularnewline
14 & 0.752125 & 9.7196 & 0 \tabularnewline
15 & 0.732503 & 9.466 & 0 \tabularnewline
16 & 0.713083 & 9.2151 & 0 \tabularnewline
17 & 0.693698 & 8.9646 & 0 \tabularnewline
18 & 0.673886 & 8.7085 & 0 \tabularnewline
19 & 0.653929 & 8.4506 & 0 \tabularnewline
20 & 0.634777 & 8.2031 & 0 \tabularnewline
21 & 0.616265 & 7.9639 & 0 \tabularnewline
22 & 0.598896 & 7.7394 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70439&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]0.982319[/C][C]12.6944[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.964762[/C][C]12.4675[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.947616[/C][C]12.2459[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.930547[/C][C]12.0253[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.913998[/C][C]11.8115[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.896418[/C][C]11.5843[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.878241[/C][C]11.3494[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.860001[/C][C]11.1137[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.84238[/C][C]10.886[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.825131[/C][C]10.663[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.808437[/C][C]10.4473[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.790618[/C][C]10.217[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.77173[/C][C]9.9729[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.752125[/C][C]9.7196[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.732503[/C][C]9.466[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.713083[/C][C]9.2151[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.693698[/C][C]8.9646[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.673886[/C][C]8.7085[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.653929[/C][C]8.4506[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.634777[/C][C]8.2031[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.616265[/C][C]7.9639[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.598896[/C][C]7.7394[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70439&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70439&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	0.982319	12.6944	0
2	0.964762	12.4675	0
3	0.947616	12.2459	0
4	0.930547	12.0253	0
5	0.913998	11.8115	0
6	0.896418	11.5843	0
7	0.878241	11.3494	0
8	0.860001	11.1137	0
9	0.84238	10.886	0
10	0.825131	10.663	0
11	0.808437	10.4473	0
12	0.790618	10.217	0
13	0.77173	9.9729	0
14	0.752125	9.7196	0
15	0.732503	9.466	0
16	0.713083	9.2151	0
17	0.693698	8.9646	0
18	0.673886	8.7085	0
19	0.653929	8.4506	0
20	0.634777	8.2031	0
21	0.616265	7.9639	0
22	0.598896	7.7394	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.982319	12.6944	0
2	-0.005398	-0.0698	0.472234
3	0.002808	0.0363	0.485546
4	-0.006538	-0.0845	0.466382
5	0.00618	0.0799	0.468223
6	-0.037943	-0.4903	0.312272
7	-0.026175	-0.3383	0.3678
8	-0.012203	-0.1577	0.437441
9	0.007579	0.0979	0.461048
10	0.000192	0.0025	0.499009
11	0.007246	0.0936	0.462753
12	-0.040126	-0.5185	0.302383
13	-0.039455	-0.5099	0.305409
14	-0.032781	-0.4236	0.33619
15	-0.013366	-0.1727	0.431536
16	-0.008441	-0.1091	0.456634
17	-0.009745	-0.1259	0.449967
18	-0.021268	-0.2748	0.391886
19	-0.013224	-0.1709	0.432258
20	0.010898	0.1408	0.444087
21	0.005301	0.0685	0.472732
22	0.019276	0.2491	0.401796

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.982319 & 12.6944 & 0 \tabularnewline
2 & -0.005398 & -0.0698 & 0.472234 \tabularnewline
3 & 0.002808 & 0.0363 & 0.485546 \tabularnewline
4 & -0.006538 & -0.0845 & 0.466382 \tabularnewline
5 & 0.00618 & 0.0799 & 0.468223 \tabularnewline
6 & -0.037943 & -0.4903 & 0.312272 \tabularnewline
7 & -0.026175 & -0.3383 & 0.3678 \tabularnewline
8 & -0.012203 & -0.1577 & 0.437441 \tabularnewline
9 & 0.007579 & 0.0979 & 0.461048 \tabularnewline
10 & 0.000192 & 0.0025 & 0.499009 \tabularnewline
11 & 0.007246 & 0.0936 & 0.462753 \tabularnewline
12 & -0.040126 & -0.5185 & 0.302383 \tabularnewline
13 & -0.039455 & -0.5099 & 0.305409 \tabularnewline
14 & -0.032781 & -0.4236 & 0.33619 \tabularnewline
15 & -0.013366 & -0.1727 & 0.431536 \tabularnewline
16 & -0.008441 & -0.1091 & 0.456634 \tabularnewline
17 & -0.009745 & -0.1259 & 0.449967 \tabularnewline
18 & -0.021268 & -0.2748 & 0.391886 \tabularnewline
19 & -0.013224 & -0.1709 & 0.432258 \tabularnewline
20 & 0.010898 & 0.1408 & 0.444087 \tabularnewline
21 & 0.005301 & 0.0685 & 0.472732 \tabularnewline
22 & 0.019276 & 0.2491 & 0.401796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70439&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]0.982319[/C][C]12.6944[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.005398[/C][C]-0.0698[/C][C]0.472234[/C][/ROW]
[ROW][C]3[/C][C]0.002808[/C][C]0.0363[/C][C]0.485546[/C][/ROW]
[ROW][C]4[/C][C]-0.006538[/C][C]-0.0845[/C][C]0.466382[/C][/ROW]
[ROW][C]5[/C][C]0.00618[/C][C]0.0799[/C][C]0.468223[/C][/ROW]
[ROW][C]6[/C][C]-0.037943[/C][C]-0.4903[/C][C]0.312272[/C][/ROW]
[ROW][C]7[/C][C]-0.026175[/C][C]-0.3383[/C][C]0.3678[/C][/ROW]
[ROW][C]8[/C][C]-0.012203[/C][C]-0.1577[/C][C]0.437441[/C][/ROW]
[ROW][C]9[/C][C]0.007579[/C][C]0.0979[/C][C]0.461048[/C][/ROW]
[ROW][C]10[/C][C]0.000192[/C][C]0.0025[/C][C]0.499009[/C][/ROW]
[ROW][C]11[/C][C]0.007246[/C][C]0.0936[/C][C]0.462753[/C][/ROW]
[ROW][C]12[/C][C]-0.040126[/C][C]-0.5185[/C][C]0.302383[/C][/ROW]
[ROW][C]13[/C][C]-0.039455[/C][C]-0.5099[/C][C]0.305409[/C][/ROW]
[ROW][C]14[/C][C]-0.032781[/C][C]-0.4236[/C][C]0.33619[/C][/ROW]
[ROW][C]15[/C][C]-0.013366[/C][C]-0.1727[/C][C]0.431536[/C][/ROW]
[ROW][C]16[/C][C]-0.008441[/C][C]-0.1091[/C][C]0.456634[/C][/ROW]
[ROW][C]17[/C][C]-0.009745[/C][C]-0.1259[/C][C]0.449967[/C][/ROW]
[ROW][C]18[/C][C]-0.021268[/C][C]-0.2748[/C][C]0.391886[/C][/ROW]
[ROW][C]19[/C][C]-0.013224[/C][C]-0.1709[/C][C]0.432258[/C][/ROW]
[ROW][C]20[/C][C]0.010898[/C][C]0.1408[/C][C]0.444087[/C][/ROW]
[ROW][C]21[/C][C]0.005301[/C][C]0.0685[/C][C]0.472732[/C][/ROW]
[ROW][C]22[/C][C]0.019276[/C][C]0.2491[/C][C]0.401796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70439&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70439&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	0.982319	12.6944	0
2	-0.005398	-0.0698	0.472234
3	0.002808	0.0363	0.485546
4	-0.006538	-0.0845	0.466382
5	0.00618	0.0799	0.468223
6	-0.037943	-0.4903	0.312272
7	-0.026175	-0.3383	0.3678
8	-0.012203	-0.1577	0.437441
9	0.007579	0.0979	0.461048
10	0.000192	0.0025	0.499009
11	0.007246	0.0936	0.462753
12	-0.040126	-0.5185	0.302383
13	-0.039455	-0.5099	0.305409
14	-0.032781	-0.4236	0.33619
15	-0.013366	-0.1727	0.431536
16	-0.008441	-0.1091	0.456634
17	-0.009745	-0.1259	0.449967
18	-0.021268	-0.2748	0.391886
19	-0.013224	-0.1709	0.432258
20	0.010898	0.1408	0.444087
21	0.005301	0.0685	0.472732
22	0.019276	0.2491	0.401796

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 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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