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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, 17 Dec 2009 07:49:59 -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/17/t1261061445xddqhesmj7nzsmq.htm/, Retrieved Thu, 17 Dec 2009 15:50:48 +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/17/t1261061445xddqhesmj7nzsmq.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 «

9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9 7.7 8 8 7.7 7.3 7.4 8.1 8.3 8.3

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	0.854304	6.7268	0
2	0.634494	4.996	3e-06
3	0.509475	4.0116	8.2e-05
4	0.531651	4.1862	4.6e-05
5	0.626606	4.9339	3e-06
6	0.674671	5.3124	1e-06
7	0.59722	4.7025	7e-06
8	0.447405	3.5229	0.000404
9	0.327787	2.581	0.006116
10	0.296698	2.3362	0.011364
11	0.34814	2.7413	0.003993
12	0.364387	2.8692	0.00281
13	0.287927	2.2671	0.01344
14	0.187107	1.4733	0.072867
15	0.111648	0.8791	0.191365
16	0.073629	0.5798	0.282089
17	0.054548	0.4295	0.33452
18	0.021375	0.1683	0.433444
19	-0.038828	-0.3057	0.380415
20	-0.104869	-0.8257	0.206059
21	-0.158305	-1.2465	0.108637
22	-0.188462	-1.484	0.071444
23	-0.189838	-1.4948	0.070021
24	-0.211074	-1.662	0.050781
25	-0.26361	-2.0757	0.02104
26	-0.297692	-2.344	0.011148
27	-0.299473	-2.3581	0.01077
28	-0.276893	-2.1803	0.016522
29	-0.258389	-2.0346	0.023089
30	-0.26725	-2.1043	0.019705
31	-0.303072	-2.3864	0.01004
32	-0.344236	-2.7105	0.004339
33	-0.364448	-2.8697	0.002806
34	-0.332591	-2.6188	0.005538
35	-0.277961	-2.1887	0.016198
36	-0.276069	-2.1738	0.016775
37	-0.316829	-2.4947	0.007642
38	-0.337983	-2.6613	0.00495
39	-0.321827	-2.5341	0.006908
40	-0.260774	-2.0533	0.022132
41	-0.205133	-1.6152	0.055671
42	-0.192132	-1.5128	0.0677
43	-0.22846	-1.7989	0.038451
44	-0.266964	-2.1021	0.019808
45	-0.244384	-1.9243	0.029456
46	-0.147286	-1.1597	0.125302
47	-0.053435	-0.4207	0.337697
48	-0.047101	-0.3709	0.355999
49	-0.098177	-0.773	0.221215
50	-0.140585	-1.107	0.136292
51	-0.130347	-1.0264	0.154357
52	-0.063548	-0.5004	0.30929
53	-0.000158	-0.0012	0.499506
54	0.01777	0.1399	0.444589
55	-0.001177	-0.0093	0.496317
56	-0.031555	-0.2485	0.402297
57	-0.033233	-0.2617	0.397218
58	0.0043	0.0339	0.48655
59	0.0425	0.3346	0.36951
60	0.040338	0.3176	0.37592

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.854304	6.7268	0
2	-0.352902	-2.7788	0.003606
3	0.328174	2.584	0.006067
4	0.322292	2.5377	0.006843
5	0.190737	1.5019	0.069104
6	0.028742	0.2263	0.410851
7	-0.171783	-1.3526	0.090544
8	-0.089088	-0.7015	0.242815
9	-0.074104	-0.5835	0.280838
10	-0.048661	-0.3832	0.351456
11	0.083712	0.6592	0.25612
12	-0.186286	-1.4668	0.07374
13	-0.084157	-0.6626	0.255006
14	0.131272	1.0336	0.152661
15	-0.083896	-0.6606	0.255657
16	-0.106659	-0.8398	0.202115
17	-0.105043	-0.8271	0.205673
18	-0.065518	-0.5159	0.303882
19	-0.032692	-0.2574	0.398854
20	-0.057598	-0.4535	0.325877
21	-0.042627	-0.3356	0.369137
22	-0.037527	-0.2955	0.384306
23	0.077486	0.6101	0.272003
24	-0.040158	-0.3162	0.376456
25	-0.072423	-0.5703	0.285282
26	0.092744	0.7303	0.233988
27	0.031712	0.2497	0.401821
28	0.068389	0.5385	0.296081
29	0.007601	0.0598	0.476235
30	-0.013933	-0.1097	0.456498
31	-0.02829	-0.2228	0.41223
32	-0.101291	-0.7976	0.214083
33	-0.034763	-0.2737	0.392602
34	0.050077	0.3943	0.347355
35	-0.045247	-0.3563	0.361423
36	-0.117013	-0.9214	0.180217
37	0.005343	0.0421	0.483289
38	0.087053	0.6855	0.247807
39	-0.037473	-0.2951	0.384465
40	0.07499	0.5905	0.27851
41	-0.056669	-0.4462	0.328498
42	-0.031611	-0.2489	0.40213
43	-0.093302	-0.7347	0.232657
44	-0.032976	-0.2597	0.397996
45	0.118244	0.9311	0.177718
46	0.071243	0.561	0.28842
47	0.021648	0.1705	0.432603
48	-0.030617	-0.2411	0.405145
49	0.013993	0.1102	0.456311
50	-0.003532	-0.0278	0.48895
51	-0.08828	-0.6951	0.244788
52	-0.019635	-0.1546	0.438817
53	-0.071821	-0.5655	0.286882
54	-0.000762	-0.006	0.497616
55	0.076729	0.6042	0.273969
56	-0.059001	-0.4646	0.321932
57	-0.014353	-0.113	0.455191
58	-0.06668	-0.525	0.300714
59	-0.00325	-0.0256	0.489834
60	-0.040296	-0.3173	0.376044

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261061445xddqhesmj7nzsmq/1djvm1261061397.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261061445xddqhesmj7nzsmq/1djvm1261061397.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261061445xddqhesmj7nzsmq/2fdsw1261061397.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261061445xddqhesmj7nzsmq/2fdsw1261061397.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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