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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: Thu, 26 Nov 2009 03:19:32 -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/Nov/26/t1259230831za2qn8hz0zrawl6.htm/, Retrieved Thu, 26 Nov 2009 11:20:33 +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/Nov/26/t1259230831za2qn8hz0zrawl6.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 «

785.8 819.3 849.4 880.4 900.1 937.2 948.9 952.6 947.3 974.2 1000.8 1032.8 1050.7 1057.3 1075.4 1118.4 1179.8 1227 1257.8 1251.5 1236.3 1170.6 1213.1 1265.5 1300.8 1348.4 1371.9 1403.3 1451.8 1474.2 1438.2 1513.6 1562.2 1546.2 1527.5 1418.7 1448.5 1492.1 1395.4 1403.7 1316.6 1274.5 1264.4 1323.9 1332.1 1250.2 1096.7 1080.8 1039.2 792 746.6 688.8 715.8 672.9 629.5 681.2 755.4 760.6 765.9 836.8 904.9

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.324571	2.5141	0.007317
2	0.13958	1.0812	0.141972
3	0.233297	1.8071	0.037879
4	0.248655	1.9261	0.029419
5	0.238771	1.8495	0.034655
6	-0.020655	-0.16	0.436711
7	-0.011905	-0.0922	0.463416
8	0.158733	1.2295	0.111835
9	0.037902	0.2936	0.385043
10	-0.150881	-1.1687	0.12357
11	0.096274	0.7457	0.229369
12	0.014168	0.1097	0.456488
13	0.00444	0.0344	0.48634
14	0.055541	0.4302	0.334289
15	-0.01043	-0.0808	0.467938
16	0.057927	0.4487	0.327631
17	-0.122494	-0.9488	0.173256
18	-0.195882	-1.5173	0.067221
19	-0.000556	-0.0043	0.498288
20	-0.077906	-0.6035	0.274241
21	-0.131977	-1.0223	0.155373
22	-0.178449	-1.3823	0.086008
23	-0.127103	-0.9845	0.164403
24	-0.115911	-0.8978	0.186429
25	-0.073005	-0.5655	0.286923
26	-0.094817	-0.7344	0.232768
27	-0.010736	-0.0832	0.466999
28	0.08067	0.6249	0.267214
29	-0.041953	-0.325	0.373169
30	-0.053962	-0.418	0.338724
31	-0.078307	-0.6066	0.273214
32	-0.047702	-0.3695	0.356528
33	-0.069252	-0.5364	0.296826
34	-0.08689	-0.673	0.25175
35	-0.104996	-0.8133	0.209632
36	-0.068829	-0.5331	0.297952
37	-0.066013	-0.5113	0.305495
38	-0.062583	-0.4848	0.314805
39	-0.077032	-0.5967	0.276481
40	-0.044416	-0.344	0.366008
41	-0.006171	-0.0478	0.481016
42	-0.00265	-0.0205	0.491847
43	-0.019991	-0.1549	0.438729
44	-0.052375	-0.4057	0.343206
45	-0.033724	-0.2612	0.397407
46	-0.034243	-0.2652	0.395865
47	-0.036814	-0.2852	0.388251
48	-0.047817	-0.3704	0.356199
49	-0.00243	-0.0188	0.492524
50	0.012315	0.0954	0.46216
51	0.013912	0.1078	0.457273
52	-0.000927	-0.0072	0.497147
53	0.014956	0.1158	0.45408
54	0.033743	0.2614	0.39735
55	0.029748	0.2304	0.409272
56	0.016672	0.1291	0.44884
57	0.019619	0.152	0.43986
58	0.019968	0.1547	0.4388
59	0.010322	0.08	0.46827
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.324571	2.5141	0.007317
2	0.038264	0.2964	0.383977
3	0.198477	1.5374	0.064727
4	0.135744	1.0515	0.14863
5	0.128839	0.998	0.161148
6	-0.200019	-1.5493	0.063279
7	-0.038324	-0.2969	0.3838
8	0.109938	0.8516	0.198918
9	-0.058704	-0.4547	0.325475
10	-0.17395	-1.3474	0.091457
11	0.256068	1.9835	0.025947
12	-0.119781	-0.9278	0.17861
13	0.008496	0.0658	0.473874
14	0.132179	1.0239	0.155008
15	-0.018036	-0.1397	0.444681
16	-0.096472	-0.7473	0.22891
17	-0.13957	-1.0811	0.141989
18	-0.108842	-0.8431	0.201263
19	0.029194	0.2261	0.410932
20	-0.070557	-0.5465	0.293364
21	0.086808	0.6724	0.251951
22	-0.154706	-1.1983	0.117747
23	0.023588	0.1827	0.427821
24	-0.1002	-0.7761	0.220356
25	0.091753	0.7107	0.240008
26	0.016984	0.1316	0.447887
27	0.037234	0.2884	0.387012
28	0.099155	0.768	0.222735
29	-0.030477	-0.2361	0.407091
30	-0.163901	-1.2696	0.104569
31	0.002759	0.0214	0.491509
32	-0.071596	-0.5546	0.290622
33	-0.038839	-0.3008	0.382285
34	-0.018983	-0.147	0.441796
35	-0.00333	-0.0258	0.489752
36	-0.033563	-0.26	0.397887
37	0.020452	0.1584	0.437329
38	0.075567	0.5853	0.280257
39	-0.144446	-1.1189	0.133827
40	-0.0215	-0.1665	0.434147
41	0.013826	0.1071	0.457536
42	-0.073287	-0.5677	0.286185
43	0.0175	0.1356	0.446315
44	-0.027667	-0.2143	0.415517
45	0.008287	0.0642	0.474517
46	-0.034633	-0.2683	0.394708
47	-0.024703	-0.1913	0.424449
48	-0.003317	-0.0257	0.489794
49	0.022156	0.1716	0.432158
50	0.077984	0.6041	0.274039
51	0.010013	0.0776	0.469219
52	-0.022668	-0.1756	0.430605
53	-0.030401	-0.2355	0.407317
54	-0.074577	-0.5777	0.282825
55	0.00982	0.0761	0.469809
56	-0.064584	-0.5003	0.309359
57	-0.035485	-0.2749	0.392181
58	0.059544	0.4612	0.323153
59	-0.013815	-0.107	0.45757
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259230831za2qn8hz0zrawl6/1bqvx1259230771.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259230831za2qn8hz0zrawl6/1bqvx1259230771.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259230831za2qn8hz0zrawl6/20m9h1259230771.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/26/t1259230831za2qn8hz0zrawl6/20m9h1259230771.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; 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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