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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 computationTue, 06 Dec 2011 10:20:29 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/06/t13231849236h700cu1jt72f0i.htm/, Retrieved Mon, 29 Apr 2024 00:54:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151664, Retrieved Mon, 29 Apr 2024 00:54:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [WS 9] [2011-12-06 15:20:29] [6e647d331a8f33aa61a2d78ef323178e] [Current]
-   PD    [(Partial) Autocorrelation Function] [WS 9] [2011-12-06 15:40:19] [43239ed98a62e091c70785d80176537f]
-   P       [(Partial) Autocorrelation Function] [WS 9 ] [2011-12-06 15:44:17] [43239ed98a62e091c70785d80176537f]
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Dataseries X:
411
410
415
414
411
408
410
411
416
479
498
502
498
499
506
510
509
502
495
490
490
553
570
573
572
575
580
580
574
563
556
546
545
605
628
631
626
614
606
602
589
574
558
552
546
607
636
631
623
618
605
619
596
570
546
528
506
555
568
564
553
541
542
540
521
505
491
482
478
523
531
532
540
525
533
531
508
495
482
470
466
515
518
516
511
500
498
494
476
458
443
430
424
476
481
470
460
451
450
444
429
421
400
389
384
432
446
431
423
416
416
413
399
386
374
365
365
418
428
424
421
417
423
423
419
406
398
390
391
444
460
455
456
452
459
461
451
443
439
430
436
488
506
502
501
501
515
521
520
512
509
505
511
570
592
594
586
586
592
594
586
572
563
555
554
601
622
617
606
595
599
600
592
575
567
555
555
608
631
629
624
610
616
621
604
584
574
555
545
599
620
608
590
579
580
579
572
560
551
537
541
588
607
599
578
563
566
561
554
540
526
512
505
554
584
569
540
522
526
527
516
503
489
479
475
524
552
532
511
492
492
493
481
462
457
442
439
488
521
501
485
464
460
467
460
448
443
436
431
484
510
513
503
471
471
476
475
470
461
455
456
517
525
523
519
509
512
519
517
510
509
501
507
569
580
578
565
547
555
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556
548
540
531
521
519
572
581
563
548




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151664&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151664&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151664&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.94936618.33530
20.87032216.80870
30.80813615.60770
40.77138614.89790
50.75609814.60270
60.73993814.29060
70.7113913.73920
80.68247513.18080
90.6748113.03280
100.69759913.47290
110.73943214.28080
120.75481814.5780
130.6863713.2560
140.59167111.42710
150.5143469.93370
160.4639248.95990
170.436278.42580
180.4085057.88950
190.3700447.14670
200.3320446.41280
210.3149936.08350
220.3282056.33870
230.3603596.95970
240.3671067.090
250.2962575.72170

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.949366 & 18.3353 & 0 \tabularnewline
2 & 0.870322 & 16.8087 & 0 \tabularnewline
3 & 0.808136 & 15.6077 & 0 \tabularnewline
4 & 0.771386 & 14.8979 & 0 \tabularnewline
5 & 0.756098 & 14.6027 & 0 \tabularnewline
6 & 0.739938 & 14.2906 & 0 \tabularnewline
7 & 0.71139 & 13.7392 & 0 \tabularnewline
8 & 0.682475 & 13.1808 & 0 \tabularnewline
9 & 0.67481 & 13.0328 & 0 \tabularnewline
10 & 0.697599 & 13.4729 & 0 \tabularnewline
11 & 0.739432 & 14.2808 & 0 \tabularnewline
12 & 0.754818 & 14.578 & 0 \tabularnewline
13 & 0.68637 & 13.256 & 0 \tabularnewline
14 & 0.591671 & 11.4271 & 0 \tabularnewline
15 & 0.514346 & 9.9337 & 0 \tabularnewline
16 & 0.463924 & 8.9599 & 0 \tabularnewline
17 & 0.43627 & 8.4258 & 0 \tabularnewline
18 & 0.408505 & 7.8895 & 0 \tabularnewline
19 & 0.370044 & 7.1467 & 0 \tabularnewline
20 & 0.332044 & 6.4128 & 0 \tabularnewline
21 & 0.314993 & 6.0835 & 0 \tabularnewline
22 & 0.328205 & 6.3387 & 0 \tabularnewline
23 & 0.360359 & 6.9597 & 0 \tabularnewline
24 & 0.367106 & 7.09 & 0 \tabularnewline
25 & 0.296257 & 5.7217 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151664&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]0.949366[/C][C]18.3353[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.870322[/C][C]16.8087[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.808136[/C][C]15.6077[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.771386[/C][C]14.8979[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.756098[/C][C]14.6027[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.739938[/C][C]14.2906[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.71139[/C][C]13.7392[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.682475[/C][C]13.1808[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.67481[/C][C]13.0328[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.697599[/C][C]13.4729[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.739432[/C][C]14.2808[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.754818[/C][C]14.578[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.68637[/C][C]13.256[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.591671[/C][C]11.4271[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.514346[/C][C]9.9337[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.463924[/C][C]8.9599[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.43627[/C][C]8.4258[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.408505[/C][C]7.8895[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.370044[/C][C]7.1467[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.332044[/C][C]6.4128[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.314993[/C][C]6.0835[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.328205[/C][C]6.3387[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.360359[/C][C]6.9597[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.367106[/C][C]7.09[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.296257[/C][C]5.7217[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151664&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151664&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
10.94936618.33530
20.87032216.80870
30.80813615.60770
40.77138614.89790
50.75609814.60270
60.73993814.29060
70.7113913.73920
80.68247513.18080
90.6748113.03280
100.69759913.47290
110.73943214.28080
120.75481814.5780
130.6863713.2560
140.59167111.42710
150.5143469.93370
160.4639248.95990
170.436278.42580
180.4085057.88950
190.3700447.14670
200.3320446.41280
210.3149936.08350
220.3282056.33870
230.3603596.95970
240.3671067.090
250.2962575.72170







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.94936618.33530
2-0.313793-6.06030
30.2305234.45216e-06
40.1122072.16710.015431
50.1353142.61340.004664
6-0.062924-1.21530.112519
7-0.027931-0.53940.294956
80.0860471.66180.048692
90.2065563.98934e-05
100.220734.2631.3e-05
110.1766483.41160.000358
12-0.218003-4.21031.6e-05
13-0.762063-14.71790
140.0405850.78380.216818
150.0602761.16410.122559
160.1203322.3240.010331
170.0207180.40010.344642
180.0040890.0790.468552
190.035440.68450.247053
200.0134080.2590.397907
21-0.008136-0.15710.437614
22-0.114982-2.22070.013487
23-0.025701-0.49640.309966
24-0.026714-0.51590.303104
25-0.224414-4.33429e-06

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.949366 & 18.3353 & 0 \tabularnewline
2 & -0.313793 & -6.0603 & 0 \tabularnewline
3 & 0.230523 & 4.4521 & 6e-06 \tabularnewline
4 & 0.112207 & 2.1671 & 0.015431 \tabularnewline
5 & 0.135314 & 2.6134 & 0.004664 \tabularnewline
6 & -0.062924 & -1.2153 & 0.112519 \tabularnewline
7 & -0.027931 & -0.5394 & 0.294956 \tabularnewline
8 & 0.086047 & 1.6618 & 0.048692 \tabularnewline
9 & 0.206556 & 3.9893 & 4e-05 \tabularnewline
10 & 0.22073 & 4.263 & 1.3e-05 \tabularnewline
11 & 0.176648 & 3.4116 & 0.000358 \tabularnewline
12 & -0.218003 & -4.2103 & 1.6e-05 \tabularnewline
13 & -0.762063 & -14.7179 & 0 \tabularnewline
14 & 0.040585 & 0.7838 & 0.216818 \tabularnewline
15 & 0.060276 & 1.1641 & 0.122559 \tabularnewline
16 & 0.120332 & 2.324 & 0.010331 \tabularnewline
17 & 0.020718 & 0.4001 & 0.344642 \tabularnewline
18 & 0.004089 & 0.079 & 0.468552 \tabularnewline
19 & 0.03544 & 0.6845 & 0.247053 \tabularnewline
20 & 0.013408 & 0.259 & 0.397907 \tabularnewline
21 & -0.008136 & -0.1571 & 0.437614 \tabularnewline
22 & -0.114982 & -2.2207 & 0.013487 \tabularnewline
23 & -0.025701 & -0.4964 & 0.309966 \tabularnewline
24 & -0.026714 & -0.5159 & 0.303104 \tabularnewline
25 & -0.224414 & -4.3342 & 9e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151664&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]0.949366[/C][C]18.3353[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.313793[/C][C]-6.0603[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.230523[/C][C]4.4521[/C][C]6e-06[/C][/ROW]
[ROW][C]4[/C][C]0.112207[/C][C]2.1671[/C][C]0.015431[/C][/ROW]
[ROW][C]5[/C][C]0.135314[/C][C]2.6134[/C][C]0.004664[/C][/ROW]
[ROW][C]6[/C][C]-0.062924[/C][C]-1.2153[/C][C]0.112519[/C][/ROW]
[ROW][C]7[/C][C]-0.027931[/C][C]-0.5394[/C][C]0.294956[/C][/ROW]
[ROW][C]8[/C][C]0.086047[/C][C]1.6618[/C][C]0.048692[/C][/ROW]
[ROW][C]9[/C][C]0.206556[/C][C]3.9893[/C][C]4e-05[/C][/ROW]
[ROW][C]10[/C][C]0.22073[/C][C]4.263[/C][C]1.3e-05[/C][/ROW]
[ROW][C]11[/C][C]0.176648[/C][C]3.4116[/C][C]0.000358[/C][/ROW]
[ROW][C]12[/C][C]-0.218003[/C][C]-4.2103[/C][C]1.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.762063[/C][C]-14.7179[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.040585[/C][C]0.7838[/C][C]0.216818[/C][/ROW]
[ROW][C]15[/C][C]0.060276[/C][C]1.1641[/C][C]0.122559[/C][/ROW]
[ROW][C]16[/C][C]0.120332[/C][C]2.324[/C][C]0.010331[/C][/ROW]
[ROW][C]17[/C][C]0.020718[/C][C]0.4001[/C][C]0.344642[/C][/ROW]
[ROW][C]18[/C][C]0.004089[/C][C]0.079[/C][C]0.468552[/C][/ROW]
[ROW][C]19[/C][C]0.03544[/C][C]0.6845[/C][C]0.247053[/C][/ROW]
[ROW][C]20[/C][C]0.013408[/C][C]0.259[/C][C]0.397907[/C][/ROW]
[ROW][C]21[/C][C]-0.008136[/C][C]-0.1571[/C][C]0.437614[/C][/ROW]
[ROW][C]22[/C][C]-0.114982[/C][C]-2.2207[/C][C]0.013487[/C][/ROW]
[ROW][C]23[/C][C]-0.025701[/C][C]-0.4964[/C][C]0.309966[/C][/ROW]
[ROW][C]24[/C][C]-0.026714[/C][C]-0.5159[/C][C]0.303104[/C][/ROW]
[ROW][C]25[/C][C]-0.224414[/C][C]-4.3342[/C][C]9e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151664&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151664&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
10.94936618.33530
2-0.313793-6.06030
30.2305234.45216e-06
40.1122072.16710.015431
50.1353142.61340.004664
6-0.062924-1.21530.112519
7-0.027931-0.53940.294956
80.0860471.66180.048692
90.2065563.98934e-05
100.220734.2631.3e-05
110.1766483.41160.000358
12-0.218003-4.21031.6e-05
13-0.762063-14.71790
140.0405850.78380.216818
150.0602761.16410.122559
160.1203322.3240.010331
170.0207180.40010.344642
180.0040890.0790.468552
190.035440.68450.247053
200.0134080.2590.397907
21-0.008136-0.15710.437614
22-0.114982-2.22070.013487
23-0.025701-0.49640.309966
24-0.026714-0.51590.303104
25-0.224414-4.33429e-06



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')