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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 21 Dec 2018 19:25:21 +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/2018/Dec/21/t1545417016rrexapa1xm8izjt.htm/, Retrieved Sat, 04 May 2024 16:07:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=316202, Retrieved Sat, 04 May 2024 16:07:07 +0000

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User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [Autocorrelatie bo...] [2018-12-21 18:25:21] [8607e318ea7bb53061252e65c5c0fa8a] [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	3 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316202&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]

3 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=316202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316202&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.172468	-1.8171	0.035953
2	-0.004948	-0.0521	0.479259
3	0.046092	0.4856	0.314103
4	-0.289852	-3.0538	0.001415
5	-0.120202	-1.2664	0.10401
6	0.046685	0.4919	0.311895
7	-0.098781	-1.0407	0.150132
8	-0.031543	-0.3323	0.370135
9	0.123468	1.3008	0.098008
10	-0.012292	-0.1295	0.448595
11	-0.04475	-0.4715	0.319114
12	0.21424	2.2572	0.012978
13	-0.149474	-1.5748	0.059073
14	0.037992	0.4003	0.344864
15	0.035038	0.3691	0.356361
16	-0.173909	-1.8322	0.034798
17	0.019282	0.2031	0.419696
18	0.003731	0.0393	0.484358
19	-0.035042	-0.3692	0.356344
20	-0.033543	-0.3534	0.362232
21	0.160019	1.6859	0.047312
22	-0.049682	-0.5234	0.300859
23	-0.018047	-0.1901	0.424775
24	0.137771	1.4515	0.07473

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.172468 & -1.8171 & 0.035953 \tabularnewline
2 & -0.004948 & -0.0521 & 0.479259 \tabularnewline
3 & 0.046092 & 0.4856 & 0.314103 \tabularnewline
4 & -0.289852 & -3.0538 & 0.001415 \tabularnewline
5 & -0.120202 & -1.2664 & 0.10401 \tabularnewline
6 & 0.046685 & 0.4919 & 0.311895 \tabularnewline
7 & -0.098781 & -1.0407 & 0.150132 \tabularnewline
8 & -0.031543 & -0.3323 & 0.370135 \tabularnewline
9 & 0.123468 & 1.3008 & 0.098008 \tabularnewline
10 & -0.012292 & -0.1295 & 0.448595 \tabularnewline
11 & -0.04475 & -0.4715 & 0.319114 \tabularnewline
12 & 0.21424 & 2.2572 & 0.012978 \tabularnewline
13 & -0.149474 & -1.5748 & 0.059073 \tabularnewline
14 & 0.037992 & 0.4003 & 0.344864 \tabularnewline
15 & 0.035038 & 0.3691 & 0.356361 \tabularnewline
16 & -0.173909 & -1.8322 & 0.034798 \tabularnewline
17 & 0.019282 & 0.2031 & 0.419696 \tabularnewline
18 & 0.003731 & 0.0393 & 0.484358 \tabularnewline
19 & -0.035042 & -0.3692 & 0.356344 \tabularnewline
20 & -0.033543 & -0.3534 & 0.362232 \tabularnewline
21 & 0.160019 & 1.6859 & 0.047312 \tabularnewline
22 & -0.049682 & -0.5234 & 0.300859 \tabularnewline
23 & -0.018047 & -0.1901 & 0.424775 \tabularnewline
24 & 0.137771 & 1.4515 & 0.07473 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316202&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]-0.172468[/C][C]-1.8171[/C][C]0.035953[/C][/ROW]
[ROW][C]2[/C][C]-0.004948[/C][C]-0.0521[/C][C]0.479259[/C][/ROW]
[ROW][C]3[/C][C]0.046092[/C][C]0.4856[/C][C]0.314103[/C][/ROW]
[ROW][C]4[/C][C]-0.289852[/C][C]-3.0538[/C][C]0.001415[/C][/ROW]
[ROW][C]5[/C][C]-0.120202[/C][C]-1.2664[/C][C]0.10401[/C][/ROW]
[ROW][C]6[/C][C]0.046685[/C][C]0.4919[/C][C]0.311895[/C][/ROW]
[ROW][C]7[/C][C]-0.098781[/C][C]-1.0407[/C][C]0.150132[/C][/ROW]
[ROW][C]8[/C][C]-0.031543[/C][C]-0.3323[/C][C]0.370135[/C][/ROW]
[ROW][C]9[/C][C]0.123468[/C][C]1.3008[/C][C]0.098008[/C][/ROW]
[ROW][C]10[/C][C]-0.012292[/C][C]-0.1295[/C][C]0.448595[/C][/ROW]
[ROW][C]11[/C][C]-0.04475[/C][C]-0.4715[/C][C]0.319114[/C][/ROW]
[ROW][C]12[/C][C]0.21424[/C][C]2.2572[/C][C]0.012978[/C][/ROW]
[ROW][C]13[/C][C]-0.149474[/C][C]-1.5748[/C][C]0.059073[/C][/ROW]
[ROW][C]14[/C][C]0.037992[/C][C]0.4003[/C][C]0.344864[/C][/ROW]
[ROW][C]15[/C][C]0.035038[/C][C]0.3691[/C][C]0.356361[/C][/ROW]
[ROW][C]16[/C][C]-0.173909[/C][C]-1.8322[/C][C]0.034798[/C][/ROW]
[ROW][C]17[/C][C]0.019282[/C][C]0.2031[/C][C]0.419696[/C][/ROW]
[ROW][C]18[/C][C]0.003731[/C][C]0.0393[/C][C]0.484358[/C][/ROW]
[ROW][C]19[/C][C]-0.035042[/C][C]-0.3692[/C][C]0.356344[/C][/ROW]
[ROW][C]20[/C][C]-0.033543[/C][C]-0.3534[/C][C]0.362232[/C][/ROW]
[ROW][C]21[/C][C]0.160019[/C][C]1.6859[/C][C]0.047312[/C][/ROW]
[ROW][C]22[/C][C]-0.049682[/C][C]-0.5234[/C][C]0.300859[/C][/ROW]
[ROW][C]23[/C][C]-0.018047[/C][C]-0.1901[/C][C]0.424775[/C][/ROW]
[ROW][C]24[/C][C]0.137771[/C][C]1.4515[/C][C]0.07473[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316202&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	-0.172468	-1.8171	0.035953
2	-0.004948	-0.0521	0.479259
3	0.046092	0.4856	0.314103
4	-0.289852	-3.0538	0.001415
5	-0.120202	-1.2664	0.10401
6	0.046685	0.4919	0.311895
7	-0.098781	-1.0407	0.150132
8	-0.031543	-0.3323	0.370135
9	0.123468	1.3008	0.098008
10	-0.012292	-0.1295	0.448595
11	-0.04475	-0.4715	0.319114
12	0.21424	2.2572	0.012978
13	-0.149474	-1.5748	0.059073
14	0.037992	0.4003	0.344864
15	0.035038	0.3691	0.356361
16	-0.173909	-1.8322	0.034798
17	0.019282	0.2031	0.419696
18	0.003731	0.0393	0.484358
19	-0.035042	-0.3692	0.356344
20	-0.033543	-0.3534	0.362232
21	0.160019	1.6859	0.047312
22	-0.049682	-0.5234	0.300859
23	-0.018047	-0.1901	0.424775
24	0.137771	1.4515	0.07473

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.172468	-1.8171	0.035953
2	-0.035757	-0.3767	0.353549
3	0.040289	0.4245	0.336022
4	-0.284128	-2.9935	0.0017
5	-0.242434	-2.5542	0.005999
6	-0.042288	-0.4455	0.328402
7	-0.11123	-1.1719	0.121877
8	-0.196182	-2.0669	0.020535
9	-0.057168	-0.6023	0.2741
10	-0.04741	-0.4995	0.30921
11	-0.159473	-1.6802	0.04787
12	0.077554	0.8171	0.207817
13	-0.115989	-1.222	0.112144
14	-0.026122	-0.2752	0.391833
15	-0.041919	-0.4416	0.329804
16	-0.138208	-1.4561	0.074092
17	-0.083036	-0.8748	0.191776
18	-0.098384	-1.0365	0.151102
19	-0.076216	-0.803	0.21185
20	-0.206804	-2.1788	0.01573
21	-0.018621	-0.1962	0.422411
22	-0.101474	-1.0691	0.143673
23	-0.169788	-1.7888	0.038185
24	-0.082009	-0.864	0.194722

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.172468 & -1.8171 & 0.035953 \tabularnewline
2 & -0.035757 & -0.3767 & 0.353549 \tabularnewline
3 & 0.040289 & 0.4245 & 0.336022 \tabularnewline
4 & -0.284128 & -2.9935 & 0.0017 \tabularnewline
5 & -0.242434 & -2.5542 & 0.005999 \tabularnewline
6 & -0.042288 & -0.4455 & 0.328402 \tabularnewline
7 & -0.11123 & -1.1719 & 0.121877 \tabularnewline
8 & -0.196182 & -2.0669 & 0.020535 \tabularnewline
9 & -0.057168 & -0.6023 & 0.2741 \tabularnewline
10 & -0.04741 & -0.4995 & 0.30921 \tabularnewline
11 & -0.159473 & -1.6802 & 0.04787 \tabularnewline
12 & 0.077554 & 0.8171 & 0.207817 \tabularnewline
13 & -0.115989 & -1.222 & 0.112144 \tabularnewline
14 & -0.026122 & -0.2752 & 0.391833 \tabularnewline
15 & -0.041919 & -0.4416 & 0.329804 \tabularnewline
16 & -0.138208 & -1.4561 & 0.074092 \tabularnewline
17 & -0.083036 & -0.8748 & 0.191776 \tabularnewline
18 & -0.098384 & -1.0365 & 0.151102 \tabularnewline
19 & -0.076216 & -0.803 & 0.21185 \tabularnewline
20 & -0.206804 & -2.1788 & 0.01573 \tabularnewline
21 & -0.018621 & -0.1962 & 0.422411 \tabularnewline
22 & -0.101474 & -1.0691 & 0.143673 \tabularnewline
23 & -0.169788 & -1.7888 & 0.038185 \tabularnewline
24 & -0.082009 & -0.864 & 0.194722 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316202&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]-0.172468[/C][C]-1.8171[/C][C]0.035953[/C][/ROW]
[ROW][C]2[/C][C]-0.035757[/C][C]-0.3767[/C][C]0.353549[/C][/ROW]
[ROW][C]3[/C][C]0.040289[/C][C]0.4245[/C][C]0.336022[/C][/ROW]
[ROW][C]4[/C][C]-0.284128[/C][C]-2.9935[/C][C]0.0017[/C][/ROW]
[ROW][C]5[/C][C]-0.242434[/C][C]-2.5542[/C][C]0.005999[/C][/ROW]
[ROW][C]6[/C][C]-0.042288[/C][C]-0.4455[/C][C]0.328402[/C][/ROW]
[ROW][C]7[/C][C]-0.11123[/C][C]-1.1719[/C][C]0.121877[/C][/ROW]
[ROW][C]8[/C][C]-0.196182[/C][C]-2.0669[/C][C]0.020535[/C][/ROW]
[ROW][C]9[/C][C]-0.057168[/C][C]-0.6023[/C][C]0.2741[/C][/ROW]
[ROW][C]10[/C][C]-0.04741[/C][C]-0.4995[/C][C]0.30921[/C][/ROW]
[ROW][C]11[/C][C]-0.159473[/C][C]-1.6802[/C][C]0.04787[/C][/ROW]
[ROW][C]12[/C][C]0.077554[/C][C]0.8171[/C][C]0.207817[/C][/ROW]
[ROW][C]13[/C][C]-0.115989[/C][C]-1.222[/C][C]0.112144[/C][/ROW]
[ROW][C]14[/C][C]-0.026122[/C][C]-0.2752[/C][C]0.391833[/C][/ROW]
[ROW][C]15[/C][C]-0.041919[/C][C]-0.4416[/C][C]0.329804[/C][/ROW]
[ROW][C]16[/C][C]-0.138208[/C][C]-1.4561[/C][C]0.074092[/C][/ROW]
[ROW][C]17[/C][C]-0.083036[/C][C]-0.8748[/C][C]0.191776[/C][/ROW]
[ROW][C]18[/C][C]-0.098384[/C][C]-1.0365[/C][C]0.151102[/C][/ROW]
[ROW][C]19[/C][C]-0.076216[/C][C]-0.803[/C][C]0.21185[/C][/ROW]
[ROW][C]20[/C][C]-0.206804[/C][C]-2.1788[/C][C]0.01573[/C][/ROW]
[ROW][C]21[/C][C]-0.018621[/C][C]-0.1962[/C][C]0.422411[/C][/ROW]
[ROW][C]22[/C][C]-0.101474[/C][C]-1.0691[/C][C]0.143673[/C][/ROW]
[ROW][C]23[/C][C]-0.169788[/C][C]-1.7888[/C][C]0.038185[/C][/ROW]
[ROW][C]24[/C][C]-0.082009[/C][C]-0.864[/C][C]0.194722[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316202&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316202&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	-0.172468	-1.8171	0.035953
2	-0.035757	-0.3767	0.353549
3	0.040289	0.4245	0.336022
4	-0.284128	-2.9935	0.0017
5	-0.242434	-2.5542	0.005999
6	-0.042288	-0.4455	0.328402
7	-0.11123	-1.1719	0.121877
8	-0.196182	-2.0669	0.020535
9	-0.057168	-0.6023	0.2741
10	-0.04741	-0.4995	0.30921
11	-0.159473	-1.6802	0.04787
12	0.077554	0.8171	0.207817
13	-0.115989	-1.222	0.112144
14	-0.026122	-0.2752	0.391833
15	-0.041919	-0.4416	0.329804
16	-0.138208	-1.4561	0.074092
17	-0.083036	-0.8748	0.191776
18	-0.098384	-1.0365	0.151102
19	-0.076216	-0.803	0.21185
20	-0.206804	-2.1788	0.01573
21	-0.018621	-0.1962	0.422411
22	-0.101474	-1.0691	0.143673
23	-0.169788	-1.7888	0.038185
24	-0.082009	-0.864	0.194722

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- '24'
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