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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationSun, 18 Dec 2016 11:18:04 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/18/t1482056606y9bpddgbxevqutd.htm/, Retrieved Wed, 08 May 2024 05:26:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300995, Retrieved Wed, 08 May 2024 05:26:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [autocorr n2383] [2016-12-18 10:18:04] [afe7f6443461a2cd6ee0b843643e84a9] [Current]
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Dataseries X:
2119.9
2108.7
2092
2104.2
2110.1
2114
2138.8
2165.5
2155.1
2135.2
2163.1
2175.2
2183.3
2201.5
2212.3
2223.8
2241.9
2269.2
2261.4
2273.4
2299.3
2315.5
2338.7
2333
2311
2303.6
2310.5
2295.8
2265.5
2271.1
2231.9
2245
2249.7
2300.5
2280.4
2290.7
2261.5
2259.1
2249.8
2271.2
2259
2259.4
2250.2
2243.3
2234.3
2216.5
2197.6
2211.7
2206.7
2214.6
2229.8
2219.5
2213.8
2214.1
2224.1
2229.6
2251.7
2262.9
2268.9
2293.7
2312.4
2342
2327.4
2366.2
2371.8
2364.4
2370.5
2412.8
2447.3
2443.5
2459.3
2480.7
2504.4
2505.5
2534
2538.7
2538.1
2522
2566.4
2572.8
2557.3
2541
2540.7
2508.5
2567.1
2553.6
2522.4
2520.6
2499.4
2470.8
2479.3
2481.8
2470.3
2491
2479.1
2456.6
2456.1
2482.2
2444.7
2425.3
2389.3
2367.7
2339.3
2342.4
2343.6
2346.3
2363.5
2338.7
2369.4
2356
2348.6
2349.7
2371.9
2364.9
2394.1
2399.2
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig 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=300995&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=300995&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300995&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 Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.97378110.48790
20.94515110.17960
30.911469.81670
40.8766139.44140
50.8381629.02730
60.8022328.64030
70.7613518.20
80.7204317.75930
90.6792127.31530
100.6324336.81150
110.588466.33790
120.5446125.86570
130.499895.3840
140.456644.91821e-06
150.4158914.47939e-06
160.3745854.03444.9e-05
170.3349153.60710.000229
180.2979163.20870.000862
190.258932.78880.003093
200.2222172.39340.00915
210.1928722.07730.019991

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.973781 & 10.4879 & 0 \tabularnewline
2 & 0.945151 & 10.1796 & 0 \tabularnewline
3 & 0.91146 & 9.8167 & 0 \tabularnewline
4 & 0.876613 & 9.4414 & 0 \tabularnewline
5 & 0.838162 & 9.0273 & 0 \tabularnewline
6 & 0.802232 & 8.6403 & 0 \tabularnewline
7 & 0.761351 & 8.2 & 0 \tabularnewline
8 & 0.720431 & 7.7593 & 0 \tabularnewline
9 & 0.679212 & 7.3153 & 0 \tabularnewline
10 & 0.632433 & 6.8115 & 0 \tabularnewline
11 & 0.58846 & 6.3379 & 0 \tabularnewline
12 & 0.544612 & 5.8657 & 0 \tabularnewline
13 & 0.49989 & 5.384 & 0 \tabularnewline
14 & 0.45664 & 4.9182 & 1e-06 \tabularnewline
15 & 0.415891 & 4.4793 & 9e-06 \tabularnewline
16 & 0.374585 & 4.0344 & 4.9e-05 \tabularnewline
17 & 0.334915 & 3.6071 & 0.000229 \tabularnewline
18 & 0.297916 & 3.2087 & 0.000862 \tabularnewline
19 & 0.25893 & 2.7888 & 0.003093 \tabularnewline
20 & 0.222217 & 2.3934 & 0.00915 \tabularnewline
21 & 0.192872 & 2.0773 & 0.019991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300995&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]0.973781[/C][C]10.4879[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.945151[/C][C]10.1796[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.91146[/C][C]9.8167[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.876613[/C][C]9.4414[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.838162[/C][C]9.0273[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.802232[/C][C]8.6403[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.761351[/C][C]8.2[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.720431[/C][C]7.7593[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.679212[/C][C]7.3153[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.632433[/C][C]6.8115[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.58846[/C][C]6.3379[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.544612[/C][C]5.8657[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.49989[/C][C]5.384[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.45664[/C][C]4.9182[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.415891[/C][C]4.4793[/C][C]9e-06[/C][/ROW]
[ROW][C]16[/C][C]0.374585[/C][C]4.0344[/C][C]4.9e-05[/C][/ROW]
[ROW][C]17[/C][C]0.334915[/C][C]3.6071[/C][C]0.000229[/C][/ROW]
[ROW][C]18[/C][C]0.297916[/C][C]3.2087[/C][C]0.000862[/C][/ROW]
[ROW][C]19[/C][C]0.25893[/C][C]2.7888[/C][C]0.003093[/C][/ROW]
[ROW][C]20[/C][C]0.222217[/C][C]2.3934[/C][C]0.00915[/C][/ROW]
[ROW][C]21[/C][C]0.192872[/C][C]2.0773[/C][C]0.019991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300995&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300995&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 kACF(k)T-STATP-value
10.97378110.48790
20.94515110.17960
30.911469.81670
40.8766139.44140
50.8381629.02730
60.8022328.64030
70.7613518.20
80.7204317.75930
90.6792127.31530
100.6324336.81150
110.588466.33790
120.5446125.86570
130.499895.3840
140.456644.91821e-06
150.4158914.47939e-06
160.3745854.03444.9e-05
170.3349153.60710.000229
180.2979163.20870.000862
190.258932.78880.003093
200.2222172.39340.00915
210.1928722.07730.019991







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.97378110.48790
2-0.059852-0.64460.260222
3-0.110793-1.19330.117597
4-0.032283-0.34770.36435
5-0.078953-0.85030.198442
60.0367280.39560.346574
7-0.109988-1.18460.119296
8-0.024241-0.26110.397246
9-0.01197-0.12890.448821
10-0.14032-1.51130.066716
110.0508140.54730.292617
12-0.024402-0.26280.396579
13-0.047754-0.51430.304
140.014620.15750.437577
15-0.003704-0.03990.484125
16-0.020441-0.22020.413068
17-0.013352-0.14380.442951
180.0143990.15510.438513
19-0.061474-0.66210.254611
20-0.00517-0.05570.477846
210.1182251.27330.102724

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.973781 & 10.4879 & 0 \tabularnewline
2 & -0.059852 & -0.6446 & 0.260222 \tabularnewline
3 & -0.110793 & -1.1933 & 0.117597 \tabularnewline
4 & -0.032283 & -0.3477 & 0.36435 \tabularnewline
5 & -0.078953 & -0.8503 & 0.198442 \tabularnewline
6 & 0.036728 & 0.3956 & 0.346574 \tabularnewline
7 & -0.109988 & -1.1846 & 0.119296 \tabularnewline
8 & -0.024241 & -0.2611 & 0.397246 \tabularnewline
9 & -0.01197 & -0.1289 & 0.448821 \tabularnewline
10 & -0.14032 & -1.5113 & 0.066716 \tabularnewline
11 & 0.050814 & 0.5473 & 0.292617 \tabularnewline
12 & -0.024402 & -0.2628 & 0.396579 \tabularnewline
13 & -0.047754 & -0.5143 & 0.304 \tabularnewline
14 & 0.01462 & 0.1575 & 0.437577 \tabularnewline
15 & -0.003704 & -0.0399 & 0.484125 \tabularnewline
16 & -0.020441 & -0.2202 & 0.413068 \tabularnewline
17 & -0.013352 & -0.1438 & 0.442951 \tabularnewline
18 & 0.014399 & 0.1551 & 0.438513 \tabularnewline
19 & -0.061474 & -0.6621 & 0.254611 \tabularnewline
20 & -0.00517 & -0.0557 & 0.477846 \tabularnewline
21 & 0.118225 & 1.2733 & 0.102724 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300995&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]0.973781[/C][C]10.4879[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.059852[/C][C]-0.6446[/C][C]0.260222[/C][/ROW]
[ROW][C]3[/C][C]-0.110793[/C][C]-1.1933[/C][C]0.117597[/C][/ROW]
[ROW][C]4[/C][C]-0.032283[/C][C]-0.3477[/C][C]0.36435[/C][/ROW]
[ROW][C]5[/C][C]-0.078953[/C][C]-0.8503[/C][C]0.198442[/C][/ROW]
[ROW][C]6[/C][C]0.036728[/C][C]0.3956[/C][C]0.346574[/C][/ROW]
[ROW][C]7[/C][C]-0.109988[/C][C]-1.1846[/C][C]0.119296[/C][/ROW]
[ROW][C]8[/C][C]-0.024241[/C][C]-0.2611[/C][C]0.397246[/C][/ROW]
[ROW][C]9[/C][C]-0.01197[/C][C]-0.1289[/C][C]0.448821[/C][/ROW]
[ROW][C]10[/C][C]-0.14032[/C][C]-1.5113[/C][C]0.066716[/C][/ROW]
[ROW][C]11[/C][C]0.050814[/C][C]0.5473[/C][C]0.292617[/C][/ROW]
[ROW][C]12[/C][C]-0.024402[/C][C]-0.2628[/C][C]0.396579[/C][/ROW]
[ROW][C]13[/C][C]-0.047754[/C][C]-0.5143[/C][C]0.304[/C][/ROW]
[ROW][C]14[/C][C]0.01462[/C][C]0.1575[/C][C]0.437577[/C][/ROW]
[ROW][C]15[/C][C]-0.003704[/C][C]-0.0399[/C][C]0.484125[/C][/ROW]
[ROW][C]16[/C][C]-0.020441[/C][C]-0.2202[/C][C]0.413068[/C][/ROW]
[ROW][C]17[/C][C]-0.013352[/C][C]-0.1438[/C][C]0.442951[/C][/ROW]
[ROW][C]18[/C][C]0.014399[/C][C]0.1551[/C][C]0.438513[/C][/ROW]
[ROW][C]19[/C][C]-0.061474[/C][C]-0.6621[/C][C]0.254611[/C][/ROW]
[ROW][C]20[/C][C]-0.00517[/C][C]-0.0557[/C][C]0.477846[/C][/ROW]
[ROW][C]21[/C][C]0.118225[/C][C]1.2733[/C][C]0.102724[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300995&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300995&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 kPACF(k)T-STATP-value
10.97378110.48790
2-0.059852-0.64460.260222
3-0.110793-1.19330.117597
4-0.032283-0.34770.36435
5-0.078953-0.85030.198442
60.0367280.39560.346574
7-0.109988-1.18460.119296
8-0.024241-0.26110.397246
9-0.01197-0.12890.448821
10-0.14032-1.51130.066716
110.0508140.54730.292617
12-0.024402-0.26280.396579
13-0.047754-0.51430.304
140.014620.15750.437577
15-0.003704-0.03990.484125
16-0.020441-0.22020.413068
17-0.013352-0.14380.442951
180.0143990.15510.438513
19-0.061474-0.66210.254611
20-0.00517-0.05570.477846
210.1182251.27330.102724



Parameters (Session):
par1 = n1862 ; par4 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 0.4 ; par3 = 0 ; 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 <- '1'
par2 <- '0.4'
par1 <- 'Default'
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')