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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: Tue, 01 Dec 2009 04:28:41 -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/01/t1259666954mstn9c452tw7jbk.htm/, Retrieved Tue, 01 Dec 2009 12:29:16 +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/01/t1259666954mstn9c452tw7jbk.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 «

115.47 103.34 102.6 100.69 105.67 123.61 113.08 106.46 123.38 109.87 95.74 123.06 123.39 120.28 115.33 110.4 114.49 132.03 123.16 118.82 128.32 112.24 104.53 132.57 122.52 131.8 124.55 120.96 122.6 145.52 118.57 134.25 136.7 121.37 111.63 134.42 137.65 137.86 119.77 130.69 128.28 147.45 128.42 136.9 143.95 135.64 122.48 136.83 153.04 142.71 123.46 144.37 146.15 147.61 158.51 147.4 165.05 154.64 126.2 157.36 154.15 123.21 113.07 110.45 113.57 122.44 114.93 111.85 126.04 121.34

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	-0.556035	-4.198	4.8e-05
2	0.063502	0.4794	0.316733
3	0.355724	2.6857	0.004733
4	-0.331469	-2.5025	0.007611
5	0.139995	1.0569	0.147499
6	0.162795	1.2291	0.112047
7	-0.376035	-2.839	0.003131
8	0.276417	2.0869	0.02069
9	-0.116754	-0.8815	0.190883
10	-0.067012	-0.5059	0.307428
11	0.107028	0.808	0.211214
12	-0.099207	-0.749	0.228469
13	0.001736	0.0131	0.494795
14	0.05664	0.4276	0.335269
15	0.035666	0.2693	0.394346
16	-0.172723	-1.304	0.098733
17	0.155404	1.1733	0.122783
18	-0.052305	-0.3949	0.347196
19	-0.098981	-0.7473	0.228979
20	0.176587	1.3332	0.093884
21	-0.08798	-0.6642	0.254609
22	-0.196978	-1.4871	0.071243
23	0.402392	3.038	0.001795
24	-0.342945	-2.5892	0.006094
25	0.110026	0.8307	0.204811
26	0.096893	0.7315	0.233728
27	-0.149319	-1.1273	0.132162
28	0.079808	0.6025	0.274604
29	0.055722	0.4207	0.337782
30	-0.141341	-1.0671	0.145213
31	0.127115	0.9597	0.17063
32	-0.087663	-0.6618	0.25537
33	0.037354	0.282	0.389475
34	0.030666	0.2315	0.408869
35	-0.087626	-0.6616	0.25546
36	0.023389	0.1766	0.43023
37	0.010815	0.0817	0.467605
38	-0.011077	-0.0836	0.466823
39	-0.023644	-0.1785	0.429479
40	0.024052	0.1816	0.428274
41	-0.00982	-0.0741	0.470579
42	-0.001542	-0.0116	0.495377
43	0.025556	0.1929	0.423844
44	-0.012292	-0.0928	0.463192
45	-0.033603	-0.2537	0.400321
46	0.058323	0.4403	0.330683
47	-0.0255	-0.1925	0.42401
48	-0.027056	-0.2043	0.419436
49	0.019697	0.1487	0.441154
50	-0.03397	-0.2565	0.399257
51	0.006713	0.0507	0.479879
52	0.018256	0.1378	0.445429
53	-0.029252	-0.2208	0.413
54	0.011848	0.0895	0.464518
55	-0.007267	-0.0549	0.478219
56	0.009277	0.07	0.472203
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.556035	-4.198	4.8e-05
2	-0.355623	-2.6849	0.004742
3	0.341119	2.5754	0.006316
4	0.167736	1.2664	0.105264
5	0.01045	0.0789	0.468696
6	0.127727	0.9643	0.16948
7	-0.235162	-1.7754	0.040583
8	-0.17047	-1.287	0.101645
9	-0.17425	-1.3156	0.096795
10	0.064659	0.4882	0.313653
11	0.065409	0.4938	0.311662
12	0.04642	0.3505	0.363641
13	0.016508	0.1246	0.450625
14	-0.076707	-0.5791	0.282392
15	0.189635	1.4317	0.078843
16	-0.188624	-1.4241	0.079938
17	-0.130683	-0.9866	0.163996
18	-0.097821	-0.7385	0.231611
19	-0.068201	-0.5149	0.304306
20	0.128513	0.9703	0.16801
21	0.216522	1.6347	0.053811
22	-0.152853	-1.154	0.126655
23	0.013397	0.1011	0.459897
24	-0.054037	-0.408	0.342413
25	-0.026891	-0.203	0.41992
26	-0.121152	-0.9147	0.182108
27	0.116291	0.878	0.191821
28	0.026044	0.1966	0.422409
29	-0.048566	-0.3667	0.357613
30	0.079867	0.603	0.274456
31	-0.002098	-0.0158	0.493709
32	-0.105609	-0.7973	0.214284
33	-0.056829	-0.429	0.334752
34	0.039309	0.2968	0.383859
35	-0.04324	-0.3265	0.372638
36	-0.058285	-0.44	0.330786
37	-0.026388	-0.1992	0.421397
38	-0.059354	-0.4481	0.327886
39	0.08694	0.6564	0.257109
40	0.021351	0.1612	0.436254
41	0.028834	0.2177	0.414222
42	0.039108	0.2953	0.384434
43	-0.045176	-0.3411	0.367151
44	-0.133411	-1.0072	0.15904
45	0.005285	0.0399	0.484155
46	-0.079849	-0.6028	0.274501
47	0.027462	0.2073	0.418244
48	0.004027	0.0304	0.487926
49	0.059126	0.4464	0.328502
50	-0.089687	-0.6771	0.250533
51	0.011392	0.086	0.465881
52	-0.005445	-0.0411	0.483676
53	-0.090088	-0.6802	0.249581
54	-0.013422	-0.1013	0.459821
55	0.020214	0.1526	0.439621
56	-0.02159	-0.163	0.435548
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259666954mstn9c452tw7jbk/1vfy71259666920.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259666954mstn9c452tw7jbk/1vfy71259666920.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259666954mstn9c452tw7jbk/2t98s1259666920.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259666954mstn9c452tw7jbk/2t98s1259666920.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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