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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 07 Dec 2017 10:54:30 +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/2017/Dec/07/t15126406741ck0ynlpsa94ob6.htm/, Retrieved Thu, 16 May 2024 02:49:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308662, Retrieved Thu, 16 May 2024 02:49:55 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

111

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

-       [(Partial) Autocorrelation Function] [Autocorrelation 2] [2017-12-07 09:54:30] [6ed64e8c4e855e992fbbfd41bce49003] [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	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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308662&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308662&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308662&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.494789	-6.9799	0
2	-0.074031	-1.0443	0.148798
3	0.35129	4.9556	1e-06
4	-0.315774	-4.4545	7e-06
5	0.139547	1.9685	0.025197
6	0.157833	2.2265	0.013551
7	-0.251741	-3.5512	0.000239
8	0.106985	1.5092	0.066416
9	0.033185	0.4681	0.320101
10	-0.09418	-1.3286	0.092754
11	0.168643	2.379	0.009153
12	-0.221364	-3.1227	0.001029
13	0.011475	0.1619	0.435784
14	0.073057	1.0306	0.15199
15	-0.048044	-0.6777	0.249361
16	-0.053752	-0.7583	0.224596
17	0.054148	0.7638	0.222931
18	0.02154	0.3039	0.380775
19	-0.145134	-2.0474	0.020968
20	0.10151	1.432	0.07686
21	0.043186	0.6092	0.27154
22	-0.254849	-3.5951	0.000204
23	0.319139	4.502	6e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.494789 & -6.9799 & 0 \tabularnewline
2 & -0.074031 & -1.0443 & 0.148798 \tabularnewline
3 & 0.35129 & 4.9556 & 1e-06 \tabularnewline
4 & -0.315774 & -4.4545 & 7e-06 \tabularnewline
5 & 0.139547 & 1.9685 & 0.025197 \tabularnewline
6 & 0.157833 & 2.2265 & 0.013551 \tabularnewline
7 & -0.251741 & -3.5512 & 0.000239 \tabularnewline
8 & 0.106985 & 1.5092 & 0.066416 \tabularnewline
9 & 0.033185 & 0.4681 & 0.320101 \tabularnewline
10 & -0.09418 & -1.3286 & 0.092754 \tabularnewline
11 & 0.168643 & 2.379 & 0.009153 \tabularnewline
12 & -0.221364 & -3.1227 & 0.001029 \tabularnewline
13 & 0.011475 & 0.1619 & 0.435784 \tabularnewline
14 & 0.073057 & 1.0306 & 0.15199 \tabularnewline
15 & -0.048044 & -0.6777 & 0.249361 \tabularnewline
16 & -0.053752 & -0.7583 & 0.224596 \tabularnewline
17 & 0.054148 & 0.7638 & 0.222931 \tabularnewline
18 & 0.02154 & 0.3039 & 0.380775 \tabularnewline
19 & -0.145134 & -2.0474 & 0.020968 \tabularnewline
20 & 0.10151 & 1.432 & 0.07686 \tabularnewline
21 & 0.043186 & 0.6092 & 0.27154 \tabularnewline
22 & -0.254849 & -3.5951 & 0.000204 \tabularnewline
23 & 0.319139 & 4.502 & 6e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308662&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]-0.494789[/C][C]-6.9799[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.074031[/C][C]-1.0443[/C][C]0.148798[/C][/ROW]
[ROW][C]3[/C][C]0.35129[/C][C]4.9556[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.315774[/C][C]-4.4545[/C][C]7e-06[/C][/ROW]
[ROW][C]5[/C][C]0.139547[/C][C]1.9685[/C][C]0.025197[/C][/ROW]
[ROW][C]6[/C][C]0.157833[/C][C]2.2265[/C][C]0.013551[/C][/ROW]
[ROW][C]7[/C][C]-0.251741[/C][C]-3.5512[/C][C]0.000239[/C][/ROW]
[ROW][C]8[/C][C]0.106985[/C][C]1.5092[/C][C]0.066416[/C][/ROW]
[ROW][C]9[/C][C]0.033185[/C][C]0.4681[/C][C]0.320101[/C][/ROW]
[ROW][C]10[/C][C]-0.09418[/C][C]-1.3286[/C][C]0.092754[/C][/ROW]
[ROW][C]11[/C][C]0.168643[/C][C]2.379[/C][C]0.009153[/C][/ROW]
[ROW][C]12[/C][C]-0.221364[/C][C]-3.1227[/C][C]0.001029[/C][/ROW]
[ROW][C]13[/C][C]0.011475[/C][C]0.1619[/C][C]0.435784[/C][/ROW]
[ROW][C]14[/C][C]0.073057[/C][C]1.0306[/C][C]0.15199[/C][/ROW]
[ROW][C]15[/C][C]-0.048044[/C][C]-0.6777[/C][C]0.249361[/C][/ROW]
[ROW][C]16[/C][C]-0.053752[/C][C]-0.7583[/C][C]0.224596[/C][/ROW]
[ROW][C]17[/C][C]0.054148[/C][C]0.7638[/C][C]0.222931[/C][/ROW]
[ROW][C]18[/C][C]0.02154[/C][C]0.3039[/C][C]0.380775[/C][/ROW]
[ROW][C]19[/C][C]-0.145134[/C][C]-2.0474[/C][C]0.020968[/C][/ROW]
[ROW][C]20[/C][C]0.10151[/C][C]1.432[/C][C]0.07686[/C][/ROW]
[ROW][C]21[/C][C]0.043186[/C][C]0.6092[/C][C]0.27154[/C][/ROW]
[ROW][C]22[/C][C]-0.254849[/C][C]-3.5951[/C][C]0.000204[/C][/ROW]
[ROW][C]23[/C][C]0.319139[/C][C]4.502[/C][C]6e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308662&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308662&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	-0.494789	-6.9799	0
2	-0.074031	-1.0443	0.148798
3	0.35129	4.9556	1e-06
4	-0.315774	-4.4545	7e-06
5	0.139547	1.9685	0.025197
6	0.157833	2.2265	0.013551
7	-0.251741	-3.5512	0.000239
8	0.106985	1.5092	0.066416
9	0.033185	0.4681	0.320101
10	-0.09418	-1.3286	0.092754
11	0.168643	2.379	0.009153
12	-0.221364	-3.1227	0.001029
13	0.011475	0.1619	0.435784
14	0.073057	1.0306	0.15199
15	-0.048044	-0.6777	0.249361
16	-0.053752	-0.7583	0.224596
17	0.054148	0.7638	0.222931
18	0.02154	0.3039	0.380775
19	-0.145134	-2.0474	0.020968
20	0.10151	1.432	0.07686
21	0.043186	0.6092	0.27154
22	-0.254849	-3.5951	0.000204
23	0.319139	4.502	6e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.494789	-6.9799	0
2	-0.422212	-5.956	0
3	0.145495	2.0525	0.020717
4	-0.068883	-0.9717	0.166187
5	0.055257	0.7795	0.218306
6	0.196507	2.7721	0.003049
7	0.044184	0.6233	0.266903
8	-0.059575	-0.8404	0.200843
9	-0.071459	-1.0081	0.157327
10	-0.0203	-0.2864	0.387449
11	0.129675	1.8293	0.034426
12	-0.162079	-2.2864	0.011642
13	-0.182418	-2.5733	0.0054
14	-0.182717	-2.5775	0.005337
15	0.022335	0.3151	0.376517
16	-0.123662	-1.7445	0.041311
17	-0.045633	-0.6437	0.260246
18	0.176568	2.4908	0.006782
19	-0.043359	-0.6117	0.270732
20	-0.129333	-1.8245	0.034791
21	0.022114	0.312	0.377699
22	-0.199647	-2.8164	0.002673
23	0.150615	2.1247	0.017424

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.494789 & -6.9799 & 0 \tabularnewline
2 & -0.422212 & -5.956 & 0 \tabularnewline
3 & 0.145495 & 2.0525 & 0.020717 \tabularnewline
4 & -0.068883 & -0.9717 & 0.166187 \tabularnewline
5 & 0.055257 & 0.7795 & 0.218306 \tabularnewline
6 & 0.196507 & 2.7721 & 0.003049 \tabularnewline
7 & 0.044184 & 0.6233 & 0.266903 \tabularnewline
8 & -0.059575 & -0.8404 & 0.200843 \tabularnewline
9 & -0.071459 & -1.0081 & 0.157327 \tabularnewline
10 & -0.0203 & -0.2864 & 0.387449 \tabularnewline
11 & 0.129675 & 1.8293 & 0.034426 \tabularnewline
12 & -0.162079 & -2.2864 & 0.011642 \tabularnewline
13 & -0.182418 & -2.5733 & 0.0054 \tabularnewline
14 & -0.182717 & -2.5775 & 0.005337 \tabularnewline
15 & 0.022335 & 0.3151 & 0.376517 \tabularnewline
16 & -0.123662 & -1.7445 & 0.041311 \tabularnewline
17 & -0.045633 & -0.6437 & 0.260246 \tabularnewline
18 & 0.176568 & 2.4908 & 0.006782 \tabularnewline
19 & -0.043359 & -0.6117 & 0.270732 \tabularnewline
20 & -0.129333 & -1.8245 & 0.034791 \tabularnewline
21 & 0.022114 & 0.312 & 0.377699 \tabularnewline
22 & -0.199647 & -2.8164 & 0.002673 \tabularnewline
23 & 0.150615 & 2.1247 & 0.017424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308662&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]-0.494789[/C][C]-6.9799[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.422212[/C][C]-5.956[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.145495[/C][C]2.0525[/C][C]0.020717[/C][/ROW]
[ROW][C]4[/C][C]-0.068883[/C][C]-0.9717[/C][C]0.166187[/C][/ROW]
[ROW][C]5[/C][C]0.055257[/C][C]0.7795[/C][C]0.218306[/C][/ROW]
[ROW][C]6[/C][C]0.196507[/C][C]2.7721[/C][C]0.003049[/C][/ROW]
[ROW][C]7[/C][C]0.044184[/C][C]0.6233[/C][C]0.266903[/C][/ROW]
[ROW][C]8[/C][C]-0.059575[/C][C]-0.8404[/C][C]0.200843[/C][/ROW]
[ROW][C]9[/C][C]-0.071459[/C][C]-1.0081[/C][C]0.157327[/C][/ROW]
[ROW][C]10[/C][C]-0.0203[/C][C]-0.2864[/C][C]0.387449[/C][/ROW]
[ROW][C]11[/C][C]0.129675[/C][C]1.8293[/C][C]0.034426[/C][/ROW]
[ROW][C]12[/C][C]-0.162079[/C][C]-2.2864[/C][C]0.011642[/C][/ROW]
[ROW][C]13[/C][C]-0.182418[/C][C]-2.5733[/C][C]0.0054[/C][/ROW]
[ROW][C]14[/C][C]-0.182717[/C][C]-2.5775[/C][C]0.005337[/C][/ROW]
[ROW][C]15[/C][C]0.022335[/C][C]0.3151[/C][C]0.376517[/C][/ROW]
[ROW][C]16[/C][C]-0.123662[/C][C]-1.7445[/C][C]0.041311[/C][/ROW]
[ROW][C]17[/C][C]-0.045633[/C][C]-0.6437[/C][C]0.260246[/C][/ROW]
[ROW][C]18[/C][C]0.176568[/C][C]2.4908[/C][C]0.006782[/C][/ROW]
[ROW][C]19[/C][C]-0.043359[/C][C]-0.6117[/C][C]0.270732[/C][/ROW]
[ROW][C]20[/C][C]-0.129333[/C][C]-1.8245[/C][C]0.034791[/C][/ROW]
[ROW][C]21[/C][C]0.022114[/C][C]0.312[/C][C]0.377699[/C][/ROW]
[ROW][C]22[/C][C]-0.199647[/C][C]-2.8164[/C][C]0.002673[/C][/ROW]
[ROW][C]23[/C][C]0.150615[/C][C]2.1247[/C][C]0.017424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308662&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308662&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	-0.494789	-6.9799	0
2	-0.422212	-5.956	0
3	0.145495	2.0525	0.020717
4	-0.068883	-0.9717	0.166187
5	0.055257	0.7795	0.218306
6	0.196507	2.7721	0.003049
7	0.044184	0.6233	0.266903
8	-0.059575	-0.8404	0.200843
9	-0.071459	-1.0081	0.157327
10	-0.0203	-0.2864	0.387449
11	0.129675	1.8293	0.034426
12	-0.162079	-2.2864	0.011642
13	-0.182418	-2.5733	0.0054
14	-0.182717	-2.5775	0.005337
15	0.022335	0.3151	0.376517
16	-0.123662	-1.7445	0.041311
17	-0.045633	-0.6437	0.260246
18	0.176568	2.4908	0.006782
19	-0.043359	-0.6117	0.270732
20	-0.129333	-1.8245	0.034791
21	0.022114	0.312	0.377699
22	-0.199647	-2.8164	0.002673
23	0.150615	2.1247	0.017424

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

par1 = Default ; par2 = 0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; 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