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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 15 Dec 2008 07:31:46 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/15/t12293515486znxi8brmrc4tev.htm/, Retrieved Mon, 15 Dec 2008 15:32:30 +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/2008/Dec/15/t12293515486znxi8brmrc4tev.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

6,3 6,1 6,1 6,3 6,3 6 6,2 6,4 6,8 7,5 7,5 7,6 7,6 7,4 7,3 7,1 6,9 6,8 7,5 7,6 7,8 8 8,1 8,2 8,3 8,2 8 7,9 7,6 7,6 8,2 8,3 8,4 8,4 8,4 8,6 8,9 8,8 8,3 7,5 7,2 7,5 8,8 9,3 9,3 8,7 8,2 8,3 8,5 8,6 8,6 8,2 8,1 8 8,6 8,7 8,8 8,5 8,4 8,5 8,7

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	0.887313	6.9301	0
2	0.709612	5.5422	0
3	0.552216	4.3129	3e-05
4	0.477161	3.7267	0.000213
5	0.459462	3.5885	0.000332
6	0.435428	3.4008	0.000595
7	0.377564	2.9489	0.002258
8	0.322074	2.5155	0.007268
9	0.306021	2.3901	0.009974
10	0.348481	2.7217	0.004227
11	0.395901	3.0921	0.001498
12	0.414075	3.234	0.000986
13	0.350556	2.7379	0.004046
14	0.253654	1.9811	0.026046
15	0.163441	1.2765	0.103306
16	0.094598	0.7388	0.231422
17	0.041487	0.324	0.373515
18	-0.006217	-0.0486	0.480717
19	-0.037917	-0.2961	0.384065
20	-0.041405	-0.3234	0.373757
21	-0.021148	-0.1652	0.434677
22	0.010121	0.0791	0.468626
23	0.025275	0.1974	0.422084
24	0.013028	0.1018	0.459644
25	-0.038914	-0.3039	0.381108
26	-0.095129	-0.743	0.230173
27	-0.148968	-1.1635	0.124583
28	-0.192129	-1.5006	0.069312
29	-0.229612	-1.7933	0.038939
30	-0.25527	-1.9937	0.02533
31	-0.248597	-1.9416	0.028404
32	-0.216264	-1.6891	0.048155
33	-0.181086	-1.4143	0.081175
34	-0.170611	-1.3325	0.093824
35	-0.18388	-1.4361	0.078034
36	-0.20365	-1.5906	0.05844
37	-0.219834	-1.717	0.04553
38	-0.219933	-1.7177	0.045459
39	-0.232744	-1.8178	0.037004
40	-0.271842	-2.1232	0.018903
41	-0.321725	-2.5128	0.007319
42	-0.356845	-2.787	0.00354
43	-0.337201	-2.6336	0.005345
44	-0.278779	-2.1773	0.016667
45	-0.22095	-1.7257	0.044734
46	-0.197421	-1.5419	0.064134
47	-0.202826	-1.5841	0.059169
48	-0.210105	-1.641	0.052975
49	-0.212195	-1.6573	0.051297
50	-0.203189	-1.587	0.058846
51	-0.192672	-1.5048	0.068765
52	-0.201098	-1.5706	0.060721
53	-0.204086	-1.594	0.058057
54	-0.202501	-1.5816	0.059458
55	-0.174181	-1.3604	0.089355
56	-0.136099	-1.063	0.145993
57	-0.102225	-0.7984	0.213866
58	-0.080323	-0.6273	0.266387
59	-0.057557	-0.4495	0.32732
60	-0.030342	-0.237	0.406735

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.887313	6.9301	0
2	-0.365402	-2.8539	0.002946
3	0.090734	0.7087	0.240619
4	0.255038	1.9919	0.025431
5	0.03923	0.3064	0.380174
6	-0.121748	-0.9509	0.172708
7	-0.040244	-0.3143	0.377176
8	0.146313	1.1427	0.128805
9	0.117915	0.9209	0.180354
10	0.14254	1.1133	0.13498
11	-0.048118	-0.3758	0.354179
12	0.02758	0.2154	0.415085
13	-0.237853	-1.8577	0.034021
14	-0.005274	-0.0412	0.483639
15	-0.060085	-0.4693	0.320273
16	-0.144954	-1.1321	0.131006
17	-0.066387	-0.5185	0.302994
18	0.016202	0.1265	0.449859
19	0.104531	0.8164	0.208721
20	0.010442	0.0816	0.467633
21	0.000351	0.0027	0.498912
22	-0.016855	-0.1316	0.447851
23	-0.009041	-0.0706	0.471969
24	-0.079317	-0.6195	0.268952
25	-0.130472	-1.019	0.156109
26	0.037076	0.2896	0.386562
27	-0.072275	-0.5645	0.287246
28	0.005164	0.0403	0.483979
29	-0.015885	-0.1241	0.450835
30	0.047768	0.3731	0.35519
31	0.08647	0.6754	0.251001
32	-0.036713	-0.2867	0.387643
33	-0.063402	-0.4952	0.311123
34	-0.132507	-1.0349	0.152397
35	-0.001416	-0.0111	0.495607
36	-0.027624	-0.2157	0.414953
37	0.028538	0.2229	0.412184
38	0.053836	0.4205	0.337808
39	-0.056177	-0.4388	0.331194
40	-0.060591	-0.4732	0.31887
41	-0.039077	-0.3052	0.380627
42	-0.041687	-0.3256	0.372927
43	0.018089	0.1413	0.444058
44	-0.001219	-0.0095	0.496218
45	-0.012895	-0.1007	0.460054
46	-0.0012	-0.0094	0.496278
47	0.034449	0.2691	0.394398
48	0.005316	0.0415	0.48351
49	-0.051478	-0.4021	0.344524
50	-0.011684	-0.0913	0.463795
51	0.061519	0.4805	0.316303
52	-0.059954	-0.4683	0.320636
53	0.067818	0.5297	0.29913
54	-0.050634	-0.3955	0.346939
55	0.02559	0.1999	0.421126
56	-0.036889	-0.2881	0.387118
57	0.002643	0.0206	0.491798
58	0.023093	0.1804	0.428735
59	0.04326	0.3379	0.368311
60	0.018229	0.1424	0.443627

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t12293515486znxi8brmrc4tev/1gl9k1229351504.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t12293515486znxi8brmrc4tev/1gl9k1229351504.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t12293515486znxi8brmrc4tev/21y661229351504.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t12293515486znxi8brmrc4tev/21y661229351504.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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

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 (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='lags',ylab='ACF')

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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