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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: Mon, 27 Dec 2010 23:34:43 +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/28/t1293492762fr8bbzjb8x8w0eo.htm/, Retrieved Tue, 28 Dec 2010 00:32:44 +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/28/t1293492762fr8bbzjb8x8w0eo.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 «

224 215 196 159 187 208 131 93 210 228 176 195 188 188 190 188 176 225 93 79 235 247 195 197 211 156 209 180 185 303 129 85 249 231 212 240 234 217 287 221 208 241 156 96 320 242 227 200 215 238 279 208 262 259 167 123 302 246 235

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.111499	0.8564	0.197609
2	-0.241636	-1.856	0.034222
3	0.159692	1.2266	0.112419
4	0.098174	0.7541	0.226897
5	5.5e-05	4e-04	0.499832
6	0.215143	1.6525	0.051868
7	-0.026978	-0.2072	0.418276
8	0.108304	0.8319	0.204411
9	0.144278	1.1082	0.136132
10	-0.262625	-2.0173	0.024113
11	0.057337	0.4404	0.330624
12	0.684797	5.26	1e-06
13	0.001551	0.0119	0.495267
14	-0.229836	-1.7654	0.041335
15	0.140298	1.0777	0.142788
16	0.023678	0.1819	0.428154
17	-0.016251	-0.1248	0.450542
18	0.062935	0.4834	0.315297
19	-0.156611	-1.203	0.1169
20	0.008088	0.0621	0.475337
21	0.049075	0.377	0.353781
22	-0.252269	-1.9377	0.028724
23	0.03213	0.2468	0.402962
24	0.38882	2.9866	0.002052
25	-0.095487	-0.7335	0.233093
26	-0.301284	-2.3142	0.012078
27	0.009501	0.073	0.471034
28	-0.016577	-0.1273	0.449557
29	-0.005216	-0.0401	0.484087
30	-0.057383	-0.4408	0.330497
31	-0.186961	-1.4361	0.078131
32	-0.077935	-0.5986	0.275856
33	-0.064921	-0.4987	0.309935
34	-0.208496	-1.6015	0.057305
35	-0.003499	-0.0269	0.489324
36	0.196747	1.5112	0.068032
37	-0.059612	-0.4579	0.324356
38	-0.191466	-1.4707	0.073346
39	-0.046445	-0.3568	0.361274
40	-0.023711	-0.1821	0.428054
41	-0.033163	-0.2547	0.399909
42	-0.07507	-0.5766	0.283194
43	-0.085069	-0.6534	0.258011
44	-0.01421	-0.1091	0.456728
45	-0.040865	-0.3139	0.377355
46	-0.112512	-0.8642	0.195484
47	-0.017562	-0.1349	0.446576
48	0.069954	0.5373	0.296532

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.111499	0.8564	0.197609
2	-0.257267	-1.9761	0.026412
3	0.240999	1.8512	0.034577
4	-0.036048	-0.2769	0.391415
5	0.105499	0.8104	0.210498
6	0.20601	1.5824	0.059453
7	-0.121664	-0.9345	0.176923
8	0.299397	2.2997	0.01251
9	-0.089146	-0.6847	0.248094
10	-0.231301	-1.7767	0.04039
11	0.23657	1.8171	0.037139
12	0.528259	4.0576	7.4e-05
13	-0.174209	-1.3381	0.092995
14	-0.011923	-0.0916	0.46367
15	-0.005972	-0.0459	0.481783
16	-0.084153	-0.6464	0.260265
17	-0.002009	-0.0154	0.493869
18	-0.241132	-1.8522	0.034503
19	-0.100063	-0.7686	0.222599
20	-0.154987	-1.1905	0.119314
21	-0.107753	-0.8277	0.205597
22	0.108001	0.8296	0.205062
23	-0.03037	-0.2333	0.408177
24	-0.072233	-0.5548	0.290553
25	0.069793	0.5361	0.296955
26	-0.228712	-1.7568	0.042073
27	-0.027693	-0.2127	0.416141
28	0.014623	0.1123	0.455476
29	-0.022087	-0.1697	0.432932
30	-0.028937	-0.2223	0.412437
31	0.043682	0.3355	0.369207
32	-0.091418	-0.7022	0.242659
33	-0.017657	-0.1356	0.446291
34	0.06321	0.4855	0.31455
35	-0.109626	-0.8421	0.201579
36	0.035117	0.2697	0.394151
37	0.041325	0.3174	0.376023
38	0.187843	1.4428	0.077176
39	-0.013657	-0.1049	0.458406
40	-0.05304	-0.4074	0.342593
41	-0.018286	-0.1405	0.44439
42	0.020975	0.1611	0.436279
43	0.061996	0.4762	0.317846
44	0.076867	0.5904	0.27858
45	0.030406	0.2336	0.408069
46	-0.081596	-0.6268	0.266619
47	0.022639	0.1739	0.431273
48	-0.083957	-0.6449	0.260751

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293492762fr8bbzjb8x8w0eo/13u3z1293492881.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293492762fr8bbzjb8x8w0eo/13u3z1293492881.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293492762fr8bbzjb8x8w0eo/2jo9r1293492881.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293492762fr8bbzjb8x8w0eo/2jo9r1293492881.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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