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*The author of this computation has been verified*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Wed, 09 Dec 2009 12:51:41 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/09/t1260388430saaz6z0tqq6226j.htm/, Retrieved Wed, 09 Dec 2009 20:53:52 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/09/t1260388430saaz6z0tqq6226j.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

595 591 612 595 597 589 584 573 567 569 621 629 628 593 588 566 557 590 580 574 573 573 620 626 620 561 527 510 514 549 532 526 511 499 555 565 542 517 506 502 516 508 493 490 469 478 528 534 518 528 533 536 537 524 536 587 597 581 564 558

Output produced by software:

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.850174	6.5854	0
2	0.647968	5.0191	2e-06
3	0.496422	3.8453	0.000147
4	0.450418	3.4889	0.000457
5	0.479241	3.7122	0.000226
6	0.469216	3.6345	0.00029
7	0.401713	3.1117	0.001424
8	0.332724	2.5773	0.006217
9	0.316679	2.453	0.008546
10	0.349535	2.7075	0.004409
11	0.371893	2.8807	0.002748
12	0.354086	2.7427	0.00401
13	0.202984	1.5723	0.060569
14	0.073104	0.5663	0.286665
15	-0.006385	-0.0495	0.48036
16	-0.030755	-0.2382	0.406259
17	-0.014444	-0.1119	0.455645
18	-0.055943	-0.4333	0.333164
19	-0.116683	-0.9038	0.184852
20	-0.150178	-1.1633	0.124662
21	-0.17494	-1.3551	0.090236
22	-0.186763	-1.4467	0.076598
23	-0.207447	-1.6069	0.056666
24	-0.236794	-1.8342	0.035792
25	-0.298018	-2.3084	0.012219
26	-0.332853	-2.5783	0.006201
27	-0.351195	-2.7203	0.00426
28	-0.358657	-2.7781	0.003643
29	-0.354707	-2.7475	0.003959
30	-0.361003	-2.7963	0.003467
31	-0.335275	-2.597	0.005905
32	-0.276682	-2.1432	0.018082
33	-0.238023	-1.8437	0.035082
34	-0.218797	-1.6948	0.04765
35	-0.217959	-1.6883	0.048272
36	-0.225248	-1.7448	0.043073
37	-0.23157	-1.7937	0.038948
38	-0.225327	-1.7454	0.043019
39	-0.225405	-1.746	0.042967
40	-0.223808	-1.7336	0.044062
41	-0.213604	-1.6546	0.051617
42	-0.190148	-1.4729	0.073005
43	-0.138898	-1.0759	0.14314
44	-0.07523	-0.5827	0.281131
45	-0.028832	-0.2233	0.412018
46	-0.023294	-0.1804	0.42871
47	-0.040258	-0.3118	0.378122
48	-0.049003	-0.3796	0.352799
49	-0.035942	-0.2784	0.390829
50	-0.019472	-0.1508	0.440308
51	-0.004402	-0.0341	0.486457
52	0.011101	0.086	0.465881
53	0.02874	0.2226	0.412294
54	0.041298	0.3199	0.37508
55	0.045998	0.3563	0.361432
56	0.031193	0.2416	0.404949
57	0.014386	0.1114	0.455822
58	0.004143	0.0321	0.487253
59	0.000923	0.0072	0.497159
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.850174	6.5854	0
2	-0.269939	-2.0909	0.020388
3	0.102436	0.7935	0.215316
4	0.236745	1.8338	0.035821
5	0.157495	1.2199	0.113629
6	-0.139546	-1.0809	0.14203
7	-0.045866	-0.3553	0.361815
8	0.104854	0.8122	0.209946
9	0.122291	0.9473	0.173652
10	0.033581	0.2601	0.397832
11	-0.037235	-0.2884	0.387008
12	0.021178	0.164	0.435123
13	-0.445502	-3.4508	0.000515
14	0.140203	1.086	0.14091
15	-0.109692	-0.8497	0.199442
16	-0.078869	-0.6109	0.271782
17	0.006798	0.0527	0.47909
18	-0.138147	-1.0701	0.144434
19	0.070014	0.5423	0.294801
20	-0.005916	-0.0458	0.4818
21	-0.184164	-1.4265	0.07945
22	-0.031596	-0.2447	0.403745
23	0.063938	0.4953	0.311112
24	-0.054071	-0.4188	0.338418
25	-0.000754	-0.0058	0.497681
26	-0.047574	-0.3685	0.356896
27	-0.007959	-0.0617	0.475522
28	-0.032041	-0.2482	0.402417
29	-0.120165	-0.9308	0.177846
30	0.160945	1.2467	0.108681
31	0.088752	0.6875	0.247218
32	0.007702	0.0597	0.476311
33	0.040572	0.3143	0.377203
34	0.004841	0.0375	0.485106
35	0.048474	0.3755	0.354313
36	-0.095914	-0.7429	0.230206
37	-0.074711	-0.5787	0.282475
38	0.050953	0.3947	0.34724
39	-0.049315	-0.382	0.351909
40	-0.094946	-0.7354	0.232467
41	0.004529	0.0351	0.486064
42	0.014778	0.1145	0.454625
43	-0.039955	-0.3095	0.379011
44	-0.017968	-0.1392	0.444886
45	0.064348	0.4984	0.309999
46	-0.060013	-0.4649	0.321859
47	-0.053399	-0.4136	0.340312
48	0.025353	0.1964	0.422487
49	0.037806	0.2928	0.385327
50	-0.07954	-0.6161	0.270074
51	0.056792	0.4399	0.330791
52	0.001333	0.0103	0.495897
53	0.044862	0.3475	0.364717
54	-0.090892	-0.704	0.242065
55	-0.123689	-0.9581	0.170931
56	-0.03067	-0.2376	0.406513
57	-0.002882	-0.0223	0.491131
58	0.046105	0.3571	0.361124
59	-0.063615	-0.4928	0.311991
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260388430saaz6z0tqq6226j/1ngeb1260388298.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260388430saaz6z0tqq6226j/1ngeb1260388298.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260388430saaz6z0tqq6226j/2dt4g1260388298.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260388430saaz6z0tqq6226j/2dt4g1260388298.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

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('http://www.xycoon.com/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('http://www.xycoon.com/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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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