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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

Mon, 19 Dec 2016 20:03:22 +0100

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/2016/Dec/19/t1482174280599br7ouog3qizi.htm/, Retrieved Sun, 10 Nov 2024 21:01:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301460, Retrieved Sun, 10 Nov 2024 21:01:31 +0000

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User-defined keywords

Estimated Impact

123

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

-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- RM D  [Spectral Analysis] [] [2016-12-18 13:27:55] [683f400e1b95307fc738e729f07c4fce]
- RMP       [(Partial) Autocorrelation Function] [] [2016-12-19 19:03:22] [404ac5ee4f7301873f6a96ef36861981] [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	1 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301460&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301460&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301460&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	1 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.158532	-1.6399	0.051985
2	-0.140322	-1.4515	0.074783
3	0.318332	3.2928	0.000672
4	-0.189498	-1.9602	0.026287
5	-0.28235	-2.9207	0.00213
6	0.221225	2.2884	0.012041
7	-0.078994	-0.8171	0.207837
8	-0.323055	-3.3417	0.000574
9	0.170417	1.7628	0.040394
10	-0.028123	-0.2909	0.385842
11	-0.175126	-1.8115	0.036433
12	0.267199	2.7639	0.003363
13	0.12671	1.3107	0.096382
14	-0.132524	-1.3708	0.086646
15	0.101612	1.0511	0.147793
16	-0.010056	-0.104	0.458674
17	-0.077722	-0.804	0.2116
18	0.030873	0.3194	0.375041
19	0.028737	0.2973	0.383423
20	-0.135031	-1.3968	0.082687

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.158532 & -1.6399 & 0.051985 \tabularnewline
2 & -0.140322 & -1.4515 & 0.074783 \tabularnewline
3 & 0.318332 & 3.2928 & 0.000672 \tabularnewline
4 & -0.189498 & -1.9602 & 0.026287 \tabularnewline
5 & -0.28235 & -2.9207 & 0.00213 \tabularnewline
6 & 0.221225 & 2.2884 & 0.012041 \tabularnewline
7 & -0.078994 & -0.8171 & 0.207837 \tabularnewline
8 & -0.323055 & -3.3417 & 0.000574 \tabularnewline
9 & 0.170417 & 1.7628 & 0.040394 \tabularnewline
10 & -0.028123 & -0.2909 & 0.385842 \tabularnewline
11 & -0.175126 & -1.8115 & 0.036433 \tabularnewline
12 & 0.267199 & 2.7639 & 0.003363 \tabularnewline
13 & 0.12671 & 1.3107 & 0.096382 \tabularnewline
14 & -0.132524 & -1.3708 & 0.086646 \tabularnewline
15 & 0.101612 & 1.0511 & 0.147793 \tabularnewline
16 & -0.010056 & -0.104 & 0.458674 \tabularnewline
17 & -0.077722 & -0.804 & 0.2116 \tabularnewline
18 & 0.030873 & 0.3194 & 0.375041 \tabularnewline
19 & 0.028737 & 0.2973 & 0.383423 \tabularnewline
20 & -0.135031 & -1.3968 & 0.082687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301460&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]-0.158532[/C][C]-1.6399[/C][C]0.051985[/C][/ROW]
[ROW][C]2[/C][C]-0.140322[/C][C]-1.4515[/C][C]0.074783[/C][/ROW]
[ROW][C]3[/C][C]0.318332[/C][C]3.2928[/C][C]0.000672[/C][/ROW]
[ROW][C]4[/C][C]-0.189498[/C][C]-1.9602[/C][C]0.026287[/C][/ROW]
[ROW][C]5[/C][C]-0.28235[/C][C]-2.9207[/C][C]0.00213[/C][/ROW]
[ROW][C]6[/C][C]0.221225[/C][C]2.2884[/C][C]0.012041[/C][/ROW]
[ROW][C]7[/C][C]-0.078994[/C][C]-0.8171[/C][C]0.207837[/C][/ROW]
[ROW][C]8[/C][C]-0.323055[/C][C]-3.3417[/C][C]0.000574[/C][/ROW]
[ROW][C]9[/C][C]0.170417[/C][C]1.7628[/C][C]0.040394[/C][/ROW]
[ROW][C]10[/C][C]-0.028123[/C][C]-0.2909[/C][C]0.385842[/C][/ROW]
[ROW][C]11[/C][C]-0.175126[/C][C]-1.8115[/C][C]0.036433[/C][/ROW]
[ROW][C]12[/C][C]0.267199[/C][C]2.7639[/C][C]0.003363[/C][/ROW]
[ROW][C]13[/C][C]0.12671[/C][C]1.3107[/C][C]0.096382[/C][/ROW]
[ROW][C]14[/C][C]-0.132524[/C][C]-1.3708[/C][C]0.086646[/C][/ROW]
[ROW][C]15[/C][C]0.101612[/C][C]1.0511[/C][C]0.147793[/C][/ROW]
[ROW][C]16[/C][C]-0.010056[/C][C]-0.104[/C][C]0.458674[/C][/ROW]
[ROW][C]17[/C][C]-0.077722[/C][C]-0.804[/C][C]0.2116[/C][/ROW]
[ROW][C]18[/C][C]0.030873[/C][C]0.3194[/C][C]0.375041[/C][/ROW]
[ROW][C]19[/C][C]0.028737[/C][C]0.2973[/C][C]0.383423[/C][/ROW]
[ROW][C]20[/C][C]-0.135031[/C][C]-1.3968[/C][C]0.082687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301460&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301460&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	-0.158532	-1.6399	0.051985
2	-0.140322	-1.4515	0.074783
3	0.318332	3.2928	0.000672
4	-0.189498	-1.9602	0.026287
5	-0.28235	-2.9207	0.00213
6	0.221225	2.2884	0.012041
7	-0.078994	-0.8171	0.207837
8	-0.323055	-3.3417	0.000574
9	0.170417	1.7628	0.040394
10	-0.028123	-0.2909	0.385842
11	-0.175126	-1.8115	0.036433
12	0.267199	2.7639	0.003363
13	0.12671	1.3107	0.096382
14	-0.132524	-1.3708	0.086646
15	0.101612	1.0511	0.147793
16	-0.010056	-0.104	0.458674
17	-0.077722	-0.804	0.2116
18	0.030873	0.3194	0.375041
19	0.028737	0.2973	0.383423
20	-0.135031	-1.3968	0.082687

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.158532	-1.6399	0.051985
2	-0.16972	-1.7556	0.04101
3	0.280321	2.8997	0.002267
4	-0.13491	-1.3955	0.082874
5	-0.284216	-2.94	0.002011
6	0.040292	0.4168	0.338835
7	-0.008349	-0.0864	0.465668
8	-0.251636	-2.6029	0.005277
9	-0.080099	-0.8286	0.2046
10	-0.075867	-0.7848	0.217159
11	-0.030649	-0.317	0.375918
12	0.103236	1.0679	0.143988
13	0.089347	0.9242	0.178728
14	0.011033	0.1141	0.454674
15	-0.060556	-0.6264	0.266195
16	-0.119042	-1.2314	0.110439
17	0.098821	1.0222	0.154494
18	0.002132	0.022	0.491225
19	-0.015133	-0.1565	0.43795
20	-0.070276	-0.7269	0.234425

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.158532 & -1.6399 & 0.051985 \tabularnewline
2 & -0.16972 & -1.7556 & 0.04101 \tabularnewline
3 & 0.280321 & 2.8997 & 0.002267 \tabularnewline
4 & -0.13491 & -1.3955 & 0.082874 \tabularnewline
5 & -0.284216 & -2.94 & 0.002011 \tabularnewline
6 & 0.040292 & 0.4168 & 0.338835 \tabularnewline
7 & -0.008349 & -0.0864 & 0.465668 \tabularnewline
8 & -0.251636 & -2.6029 & 0.005277 \tabularnewline
9 & -0.080099 & -0.8286 & 0.2046 \tabularnewline
10 & -0.075867 & -0.7848 & 0.217159 \tabularnewline
11 & -0.030649 & -0.317 & 0.375918 \tabularnewline
12 & 0.103236 & 1.0679 & 0.143988 \tabularnewline
13 & 0.089347 & 0.9242 & 0.178728 \tabularnewline
14 & 0.011033 & 0.1141 & 0.454674 \tabularnewline
15 & -0.060556 & -0.6264 & 0.266195 \tabularnewline
16 & -0.119042 & -1.2314 & 0.110439 \tabularnewline
17 & 0.098821 & 1.0222 & 0.154494 \tabularnewline
18 & 0.002132 & 0.022 & 0.491225 \tabularnewline
19 & -0.015133 & -0.1565 & 0.43795 \tabularnewline
20 & -0.070276 & -0.7269 & 0.234425 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301460&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]-0.158532[/C][C]-1.6399[/C][C]0.051985[/C][/ROW]
[ROW][C]2[/C][C]-0.16972[/C][C]-1.7556[/C][C]0.04101[/C][/ROW]
[ROW][C]3[/C][C]0.280321[/C][C]2.8997[/C][C]0.002267[/C][/ROW]
[ROW][C]4[/C][C]-0.13491[/C][C]-1.3955[/C][C]0.082874[/C][/ROW]
[ROW][C]5[/C][C]-0.284216[/C][C]-2.94[/C][C]0.002011[/C][/ROW]
[ROW][C]6[/C][C]0.040292[/C][C]0.4168[/C][C]0.338835[/C][/ROW]
[ROW][C]7[/C][C]-0.008349[/C][C]-0.0864[/C][C]0.465668[/C][/ROW]
[ROW][C]8[/C][C]-0.251636[/C][C]-2.6029[/C][C]0.005277[/C][/ROW]
[ROW][C]9[/C][C]-0.080099[/C][C]-0.8286[/C][C]0.2046[/C][/ROW]
[ROW][C]10[/C][C]-0.075867[/C][C]-0.7848[/C][C]0.217159[/C][/ROW]
[ROW][C]11[/C][C]-0.030649[/C][C]-0.317[/C][C]0.375918[/C][/ROW]
[ROW][C]12[/C][C]0.103236[/C][C]1.0679[/C][C]0.143988[/C][/ROW]
[ROW][C]13[/C][C]0.089347[/C][C]0.9242[/C][C]0.178728[/C][/ROW]
[ROW][C]14[/C][C]0.011033[/C][C]0.1141[/C][C]0.454674[/C][/ROW]
[ROW][C]15[/C][C]-0.060556[/C][C]-0.6264[/C][C]0.266195[/C][/ROW]
[ROW][C]16[/C][C]-0.119042[/C][C]-1.2314[/C][C]0.110439[/C][/ROW]
[ROW][C]17[/C][C]0.098821[/C][C]1.0222[/C][C]0.154494[/C][/ROW]
[ROW][C]18[/C][C]0.002132[/C][C]0.022[/C][C]0.491225[/C][/ROW]
[ROW][C]19[/C][C]-0.015133[/C][C]-0.1565[/C][C]0.43795[/C][/ROW]
[ROW][C]20[/C][C]-0.070276[/C][C]-0.7269[/C][C]0.234425[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301460&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301460&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	-0.158532	-1.6399	0.051985
2	-0.16972	-1.7556	0.04101
3	0.280321	2.8997	0.002267
4	-0.13491	-1.3955	0.082874
5	-0.284216	-2.94	0.002011
6	0.040292	0.4168	0.338835
7	-0.008349	-0.0864	0.465668
8	-0.251636	-2.6029	0.005277
9	-0.080099	-0.8286	0.2046
10	-0.075867	-0.7848	0.217159
11	-0.030649	-0.317	0.375918
12	0.103236	1.0679	0.143988
13	0.089347	0.9242	0.178728
14	0.011033	0.1141	0.454674
15	-0.060556	-0.6264	0.266195
16	-0.119042	-1.2314	0.110439
17	0.098821	1.0222	0.154494
18	0.002132	0.022	0.491225
19	-0.015133	-0.1565	0.43795
20	-0.070276	-0.7269	0.234425

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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,'ACF(k)',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,'PACF(k)',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