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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, 02 Dec 2009 11:27:30 -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/02/t12597784962rwewez0vk2nrho.htm/, Retrieved Wed, 02 Dec 2009 19:28:19 +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/02/t12597784962rwewez0vk2nrho.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 «

79.8 83.4 113.6 112.9 104 109.9 99 106.3 128.9 111.1 102.9 130 87 87.5 117.6 103.4 110.8 112.6 102.5 112.4 135.6 105.1 127.7 137 91 90.5 122.4 123.3 124.3 120 118.1 119 142.7 123.6 129.6 151.6 110.4 99.2 130.5 136.2 129.7 128 121.6 135.8 143.8 147.5 136.2 156.6 123.3 104.5 139.8 136.5 112.1 118.5 94.4 102.3 111.4 99.2 87.8 115.8

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	0.387767	3.0036	0.001944
2	0.117697	0.9117	0.182793
3	0.402151	3.115	0.00141
4	0.193957	1.5024	0.069121
5	0.170787	1.3229	0.095443
6	0.35124	2.7207	0.004256
7	0.024765	0.1918	0.424262
8	0.006118	0.0474	0.481181
9	0.171175	1.3259	0.094947
10	-0.126376	-0.9789	0.165778
11	0.003641	0.0282	0.488796
12	0.442677	3.429	0.000551
13	0.060682	0.47	0.320015
14	-0.167091	-1.2943	0.100264
15	0.088876	0.6884	0.246916
16	-0.028071	-0.2174	0.414303
17	-0.06139	-0.4755	0.318069
18	0.084296	0.653	0.258139
19	-0.113004	-0.8753	0.192444
20	-0.162647	-1.2599	0.1063
21	-0.01042	-0.0807	0.46797
22	-0.252338	-1.9546	0.027647
23	-0.179518	-1.3905	0.084751
24	0.170058	1.3173	0.096379
25	-0.039296	-0.3044	0.380943
26	-0.286355	-2.2181	0.015172
27	-0.085202	-0.66	0.255899
28	-0.125289	-0.9705	0.167851
29	-0.173228	-1.3418	0.092356
30	-0.050436	-0.3907	0.348711
31	-0.146779	-1.1369	0.130041
32	-0.222261	-1.7216	0.045145
33	-0.080369	-0.6225	0.267975
34	-0.205774	-1.5939	0.058105
35	-0.236709	-1.8335	0.035842
36	0.035697	0.2765	0.391554
37	-0.045397	-0.3516	0.363167
38	-0.211277	-1.6365	0.053481
39	-0.061449	-0.476	0.317909
40	-0.074515	-0.5772	0.282984
41	-0.094401	-0.7312	0.233744
42	0.011162	0.0865	0.465694
43	-0.077691	-0.6018	0.27479
44	-0.114966	-0.8905	0.18837
45	-0.032534	-0.252	0.400948
46	-0.099402	-0.77	0.222171
47	-0.108444	-0.84	0.20212
48	0.054141	0.4194	0.33822
49	0.0013	0.0101	0.495999
50	-0.064251	-0.4977	0.310261
51	0.016433	0.1273	0.44957
52	0.049417	0.3828	0.351616
53	0.061983	0.4801	0.316446
54	0.0931	0.7212	0.236808
55	0.046554	0.3606	0.359829
56	0.046005	0.3564	0.361413
57	0.085455	0.6619	0.255274
58	0.0581	0.45	0.327151
59	0.001643	0.0127	0.494945
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.387767	3.0036	0.001944
2	-0.038447	-0.2978	0.383438
3	0.435731	3.3752	0.000649
4	-0.172415	-1.3355	0.093375
5	0.274084	2.123	0.018942
6	0.052479	0.4065	0.342911
7	-0.221568	-1.7163	0.045637
8	0.094544	0.7323	0.233407
9	-0.120663	-0.9347	0.176857
10	-0.173509	-1.344	0.092006
11	0.22576	1.7487	0.042726
12	0.407249	3.1545	0.001256
13	-0.220117	-1.705	0.046682
14	-0.167244	-1.2955	0.10006
15	-0.064698	-0.5011	0.30905
16	-0.031012	-0.2402	0.405491
17	-0.118646	-0.919	0.18088
18	-0.063987	-0.4956	0.310979
19	0.16614	1.2869	0.101534
20	-0.092221	-0.7143	0.238894
21	-0.009037	-0.07	0.472213
22	-0.110387	-0.8551	0.197961
23	0.094577	0.7326	0.233331
24	-0.066436	-0.5146	0.304359
25	0.052777	0.4088	0.342068
26	-0.151325	-1.1722	0.122883
27	0.004612	0.0357	0.485811
28	-0.101444	-0.7858	0.217545
29	-0.041181	-0.319	0.375422
30	-0.029578	-0.2291	0.409782
31	0.047273	0.3662	0.357761
32	-0.030709	-0.2379	0.406396
33	-0.00147	-0.0114	0.495476
34	0.055993	0.4337	0.333025
35	-0.141333	-1.0948	0.138998
36	-0.047327	-0.3666	0.357605
37	-0.070495	-0.5461	0.293527
38	0.188393	1.4593	0.074851
39	-0.087594	-0.6785	0.250032
40	-0.0267	-0.2068	0.418425
41	0.130527	1.0111	0.158024
42	-0.099614	-0.7716	0.221689
43	-0.107249	-0.8307	0.204705
44	-0.043779	-0.3391	0.367854
45	0.01631	0.1263	0.449942
46	-0.031295	-0.2424	0.404644
47	0.084411	0.6538	0.257855
48	-0.031122	-0.2411	0.40516
49	0.01745	0.1352	0.446466
50	-0.024171	-0.1872	0.426057
51	0.025832	0.2001	0.421042
52	0.0895	0.6933	0.24541
53	-0.024242	-0.1878	0.425841
54	-0.030978	-0.24	0.405591
55	-0.012021	-0.0931	0.463062
56	0.005756	0.0446	0.482293
57	-0.013411	-0.1039	0.458805
58	0.005406	0.0419	0.483369
59	-0.114786	-0.8891	0.188743
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t12597784962rwewez0vk2nrho/1vnah1259778449.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t12597784962rwewez0vk2nrho/1vnah1259778449.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t12597784962rwewez0vk2nrho/2e58v1259778449.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t12597784962rwewez0vk2nrho/2e58v1259778449.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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