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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 computationThu, 16 Dec 2010 20:12:46 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/16/t1292530262dn2mj1bvcay8emu.htm/, Retrieved Fri, 03 May 2024 13:10:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111253, Retrieved Fri, 03 May 2024 13:10:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Bouwvergunningen] [2009-11-02 16:57:06] [11ac052cc87d77b9933b02bea117068e]
-   P   [Univariate Data Series] [Bouwvergunningen ...] [2009-11-11 14:29:30] [11ac052cc87d77b9933b02bea117068e]
- RMPD      [(Partial) Autocorrelation Function] [Workshop 6] [2010-12-16 20:12:46] [f149abcac50db27facd6576b094a0cd9] [Current]
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Dataseries X:
2259703
2444005
2576401
2309146
2493971
2188754
2128515
2248771
2125552
2204434
1765972
1835861
2087121
2170744
2577245
2500625
2370817
2033775
2162554
1943964
1917423
2260681
1828487
1673658
1746814
2197119
2050797
2272390
2079219
2242532
2392286
2056150
2108444
2060266
1747495
2059217
1921030
1895979
2369584
2506099
2156596
2522368
2460648
2173272
2304310
2239807
1961006
2675929
2683265
2407253
3045566
2365409
2379364
3150342
2341189
2254773
2337912
2712988
2185444
2420840
2380842
2523958
2983983
2865389
3490844
3198770
2484559
2890255
3007413
2713443
2656410
3232194
3615139
2905958
3383619
2865686
3185367
3110915
2665099
2763832
2887458
3076986
2626692
2782998
2628939
2454307
2844926
2548952
2429593
3052758
2610175
2618184
2363387
3699616
2563593
2215478
2639036
2859271
2554225
2809697
2481829
2812053
2519658
2305688
2640975
2535552
2285721
2811647




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111253&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111253&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.5909096.14090
20.5387795.59920
30.6123486.36370
40.5130085.33130
50.4539664.71784e-06
60.4622664.8043e-06
70.4529824.70754e-06
80.4677944.86152e-06
90.4880135.07161e-06
100.4522284.69974e-06
110.4522114.69954e-06
120.5201745.40580
130.3525773.66410.000193
140.3987434.14393.4e-05
150.3747053.8948.6e-05
160.2576822.67790.004283
170.3061043.18110.000958
180.2722492.82930.002781
190.2195572.28170.012234
200.1873871.94740.027042

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.590909 & 6.1409 & 0 \tabularnewline
2 & 0.538779 & 5.5992 & 0 \tabularnewline
3 & 0.612348 & 6.3637 & 0 \tabularnewline
4 & 0.513008 & 5.3313 & 0 \tabularnewline
5 & 0.453966 & 4.7178 & 4e-06 \tabularnewline
6 & 0.462266 & 4.804 & 3e-06 \tabularnewline
7 & 0.452982 & 4.7075 & 4e-06 \tabularnewline
8 & 0.467794 & 4.8615 & 2e-06 \tabularnewline
9 & 0.488013 & 5.0716 & 1e-06 \tabularnewline
10 & 0.452228 & 4.6997 & 4e-06 \tabularnewline
11 & 0.452211 & 4.6995 & 4e-06 \tabularnewline
12 & 0.520174 & 5.4058 & 0 \tabularnewline
13 & 0.352577 & 3.6641 & 0.000193 \tabularnewline
14 & 0.398743 & 4.1439 & 3.4e-05 \tabularnewline
15 & 0.374705 & 3.894 & 8.6e-05 \tabularnewline
16 & 0.257682 & 2.6779 & 0.004283 \tabularnewline
17 & 0.306104 & 3.1811 & 0.000958 \tabularnewline
18 & 0.272249 & 2.8293 & 0.002781 \tabularnewline
19 & 0.219557 & 2.2817 & 0.012234 \tabularnewline
20 & 0.187387 & 1.9474 & 0.027042 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111253&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]0.590909[/C][C]6.1409[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.538779[/C][C]5.5992[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.612348[/C][C]6.3637[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.513008[/C][C]5.3313[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.453966[/C][C]4.7178[/C][C]4e-06[/C][/ROW]
[ROW][C]6[/C][C]0.462266[/C][C]4.804[/C][C]3e-06[/C][/ROW]
[ROW][C]7[/C][C]0.452982[/C][C]4.7075[/C][C]4e-06[/C][/ROW]
[ROW][C]8[/C][C]0.467794[/C][C]4.8615[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.488013[/C][C]5.0716[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.452228[/C][C]4.6997[/C][C]4e-06[/C][/ROW]
[ROW][C]11[/C][C]0.452211[/C][C]4.6995[/C][C]4e-06[/C][/ROW]
[ROW][C]12[/C][C]0.520174[/C][C]5.4058[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.352577[/C][C]3.6641[/C][C]0.000193[/C][/ROW]
[ROW][C]14[/C][C]0.398743[/C][C]4.1439[/C][C]3.4e-05[/C][/ROW]
[ROW][C]15[/C][C]0.374705[/C][C]3.894[/C][C]8.6e-05[/C][/ROW]
[ROW][C]16[/C][C]0.257682[/C][C]2.6779[/C][C]0.004283[/C][/ROW]
[ROW][C]17[/C][C]0.306104[/C][C]3.1811[/C][C]0.000958[/C][/ROW]
[ROW][C]18[/C][C]0.272249[/C][C]2.8293[/C][C]0.002781[/C][/ROW]
[ROW][C]19[/C][C]0.219557[/C][C]2.2817[/C][C]0.012234[/C][/ROW]
[ROW][C]20[/C][C]0.187387[/C][C]1.9474[/C][C]0.027042[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111253&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
10.5909096.14090
20.5387795.59920
30.6123486.36370
40.5130085.33130
50.4539664.71784e-06
60.4622664.8043e-06
70.4529824.70754e-06
80.4677944.86152e-06
90.4880135.07161e-06
100.4522284.69974e-06
110.4522114.69954e-06
120.5201745.40580
130.3525773.66410.000193
140.3987434.14393.4e-05
150.3747053.8948.6e-05
160.2576822.67790.004283
170.3061043.18110.000958
180.2722492.82930.002781
190.2195572.28170.012234
200.1873871.94740.027042







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.5909096.14090
20.291333.02760.001542
30.3602823.74420.000146
40.0622910.64730.259391
50.0066960.06960.472324
60.0372230.38680.349821
70.0761240.79110.215308
80.1394661.44940.075066
90.1381211.43540.077032
100.0242180.25170.400884
110.0213160.22150.412554
120.1517261.57680.058885
13-0.207255-2.15390.016737
140.0546070.56750.285779
15-0.096124-0.99890.160026
16-0.134509-1.39790.08251
170.0330160.34310.366091
18-0.075574-0.78540.216972
19-0.048933-0.50850.306062
20-0.145945-1.51670.066131

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.590909 & 6.1409 & 0 \tabularnewline
2 & 0.29133 & 3.0276 & 0.001542 \tabularnewline
3 & 0.360282 & 3.7442 & 0.000146 \tabularnewline
4 & 0.062291 & 0.6473 & 0.259391 \tabularnewline
5 & 0.006696 & 0.0696 & 0.472324 \tabularnewline
6 & 0.037223 & 0.3868 & 0.349821 \tabularnewline
7 & 0.076124 & 0.7911 & 0.215308 \tabularnewline
8 & 0.139466 & 1.4494 & 0.075066 \tabularnewline
9 & 0.138121 & 1.4354 & 0.077032 \tabularnewline
10 & 0.024218 & 0.2517 & 0.400884 \tabularnewline
11 & 0.021316 & 0.2215 & 0.412554 \tabularnewline
12 & 0.151726 & 1.5768 & 0.058885 \tabularnewline
13 & -0.207255 & -2.1539 & 0.016737 \tabularnewline
14 & 0.054607 & 0.5675 & 0.285779 \tabularnewline
15 & -0.096124 & -0.9989 & 0.160026 \tabularnewline
16 & -0.134509 & -1.3979 & 0.08251 \tabularnewline
17 & 0.033016 & 0.3431 & 0.366091 \tabularnewline
18 & -0.075574 & -0.7854 & 0.216972 \tabularnewline
19 & -0.048933 & -0.5085 & 0.306062 \tabularnewline
20 & -0.145945 & -1.5167 & 0.066131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111253&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]0.590909[/C][C]6.1409[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.29133[/C][C]3.0276[/C][C]0.001542[/C][/ROW]
[ROW][C]3[/C][C]0.360282[/C][C]3.7442[/C][C]0.000146[/C][/ROW]
[ROW][C]4[/C][C]0.062291[/C][C]0.6473[/C][C]0.259391[/C][/ROW]
[ROW][C]5[/C][C]0.006696[/C][C]0.0696[/C][C]0.472324[/C][/ROW]
[ROW][C]6[/C][C]0.037223[/C][C]0.3868[/C][C]0.349821[/C][/ROW]
[ROW][C]7[/C][C]0.076124[/C][C]0.7911[/C][C]0.215308[/C][/ROW]
[ROW][C]8[/C][C]0.139466[/C][C]1.4494[/C][C]0.075066[/C][/ROW]
[ROW][C]9[/C][C]0.138121[/C][C]1.4354[/C][C]0.077032[/C][/ROW]
[ROW][C]10[/C][C]0.024218[/C][C]0.2517[/C][C]0.400884[/C][/ROW]
[ROW][C]11[/C][C]0.021316[/C][C]0.2215[/C][C]0.412554[/C][/ROW]
[ROW][C]12[/C][C]0.151726[/C][C]1.5768[/C][C]0.058885[/C][/ROW]
[ROW][C]13[/C][C]-0.207255[/C][C]-2.1539[/C][C]0.016737[/C][/ROW]
[ROW][C]14[/C][C]0.054607[/C][C]0.5675[/C][C]0.285779[/C][/ROW]
[ROW][C]15[/C][C]-0.096124[/C][C]-0.9989[/C][C]0.160026[/C][/ROW]
[ROW][C]16[/C][C]-0.134509[/C][C]-1.3979[/C][C]0.08251[/C][/ROW]
[ROW][C]17[/C][C]0.033016[/C][C]0.3431[/C][C]0.366091[/C][/ROW]
[ROW][C]18[/C][C]-0.075574[/C][C]-0.7854[/C][C]0.216972[/C][/ROW]
[ROW][C]19[/C][C]-0.048933[/C][C]-0.5085[/C][C]0.306062[/C][/ROW]
[ROW][C]20[/C][C]-0.145945[/C][C]-1.5167[/C][C]0.066131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111253&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111253&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
10.5909096.14090
20.291333.02760.001542
30.3602823.74420.000146
40.0622910.64730.259391
50.0066960.06960.472324
60.0372230.38680.349821
70.0761240.79110.215308
80.1394661.44940.075066
90.1381211.43540.077032
100.0242180.25170.400884
110.0213160.22150.412554
120.1517261.57680.058885
13-0.207255-2.15390.016737
140.0546070.56750.285779
15-0.096124-0.99890.160026
16-0.134509-1.39790.08251
170.0330160.34310.366091
18-0.075574-0.78540.216972
19-0.048933-0.50850.306062
20-0.145945-1.51670.066131



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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)
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,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')