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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, 16 Dec 2010 14:55:48 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/16/t1292511209rn7sq08f8kq94p1.htm/, Retrieved Thu, 16 Dec 2010 15:53:29 +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/2010/Dec/16/t1292511209rn7sq08f8kq94p1.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

112,3 117,3 111,1 102,2 104,3 122,9 107,6 121,3 131,5 89 104,4 128,9 135,9 133,3 121,3 120,5 120,4 137,9 126,1 133,2 151,1 105 119 140,4 156,6 137,1 122,7 125,8 139,3 134,9 149,2 132,3 149 117,2 119,6 152 149,4 127,3 114,1 102,1 107,7 104,4 102,1 96 109,3 90 83,9 112 114,3 103,6 91,7 80,8 87,2 109,2 102,7 95,1 117,5 85,1 92,1 113,5

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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.832219	5.7658	0
2	0.821241	5.6897	0
3	0.764357	5.2956	1e-06
4	0.667186	4.6224	1.4e-05
5	0.605091	4.1922	5.9e-05
6	0.489299	3.39	0.000703
7	0.378155	2.6199	0.00587
8	0.311945	2.1612	0.017849
9	0.190318	1.3186	0.096787
10	0.130336	0.903	0.185519
11	0.036205	0.2508	0.401506
12	-0.041596	-0.2882	0.387224
13	-0.090314	-0.6257	0.267234
14	-0.161797	-1.121	0.13394
15	-0.135224	-0.9369	0.176761
16	-0.198754	-1.377	0.087449
17	-0.223266	-1.5468	0.064236
18	-0.219452	-1.5204	0.067485
19	-0.275388	-1.9079	0.031195
20	-0.270189	-1.8719	0.033659
21	-0.269441	-1.8667	0.034026
22	-0.323745	-2.243	0.014776
23	-0.294608	-2.0411	0.02338
24	-0.365013	-2.5289	0.007392
25	-0.337585	-2.3389	0.011777
26	-0.342974	-2.3762	0.010765
27	-0.379845	-2.6316	0.005696
28	-0.338505	-2.3452	0.011598
29	-0.320671	-2.2217	0.015527
30	-0.297508	-2.0612	0.022362
31	-0.253231	-1.7544	0.042869
32	-0.215418	-1.4925	0.071062
33	-0.172861	-1.1976	0.118473
34	-0.144792	-1.0031	0.16041
35	-0.113883	-0.789	0.216994
36	-0.07554	-0.5234	0.301567
37	-0.041771	-0.2894	0.38676
38	-0.010996	-0.0762	0.469796
39	-0.005728	-0.0397	0.484254
40	0.016814	0.1165	0.453874
41	0.045175	0.313	0.377826
42	0.030737	0.213	0.416132
43	0.031931	0.2212	0.412929
44	0.028284	0.196	0.422736
45	0.012871	0.0892	0.464657
46	0.021126	0.1464	0.442124
47	0.006806	0.0472	0.481294
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
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	0.832219	5.7658	0
2	0.418503	2.8995	0.002811
3	0.073533	0.5095	0.306386
4	-0.217495	-1.5069	0.069201
5	-0.102344	-0.7091	0.24086
6	-0.200034	-1.3859	0.086095
7	-0.201713	-1.3975	0.084343
8	0.052054	0.3606	0.359975
9	-0.059438	-0.4118	0.34116
10	0.065281	0.4523	0.326551
11	-0.044458	-0.308	0.379702
12	-0.044591	-0.3089	0.379353
13	-0.007927	-0.0549	0.478214
14	-0.051383	-0.356	0.361704
15	0.295149	2.0449	0.023187
16	-0.091059	-0.6309	0.265557
17	-0.131881	-0.9137	0.18272
18	-0.07344	-0.5088	0.306609
19	-0.208539	-1.4448	0.077505
20	-0.07589	-0.5258	0.300731
21	0.102799	0.7122	0.23989
22	-0.053046	-0.3675	0.357425
23	0.012183	0.0844	0.466541
24	-0.229079	-1.5871	0.059527
25	0.054539	0.3779	0.353601
26	0.025294	0.1752	0.430812
27	-0.026448	-0.1832	0.427693
28	0.191052	1.3236	0.095945
29	0.209402	1.4508	0.076673
30	-0.054725	-0.3791	0.353125
31	-0.156047	-1.0811	0.142522
32	0.052197	0.3616	0.359607
33	-0.160238	-1.1102	0.136231
34	-0.081881	-0.5673	0.286581
35	0.024863	0.1723	0.43198
36	-0.125439	-0.8691	0.194567
37	0.072582	0.5029	0.30868
38	-0.090636	-0.6279	0.266508
39	0.025443	0.1763	0.43041
40	0.018054	0.1251	0.450489
41	0.094883	0.6574	0.257043
42	0.152457	1.0563	0.14807
43	-0.134482	-0.9317	0.178072
44	-0.144479	-1.001	0.160928
45	0.014746	0.1022	0.459527
46	-0.072212	-0.5003	0.309575
47	-0.073612	-0.51	0.306194
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
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/2010/Dec/16/t1292511209rn7sq08f8kq94p1/1pf021292511344.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292511209rn7sq08f8kq94p1/1pf021292511344.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292511209rn7sq08f8kq94p1/2pf021292511344.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292511209rn7sq08f8kq94p1/2pf021292511344.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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