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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, 21 Dec 2010 15:54:36 +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/21/t1292946733bo7nwxtxik32o32.htm/, Retrieved Tue, 21 Dec 2010 16:52:16 +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/2010/Dec/21/t1292946733bo7nwxtxik32o32.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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.177151	1.2145	0.115315
2	0.060138	0.4123	0.341002
3	-0.192048	-1.3166	0.097176
4	-0.205836	-1.4111	0.082394
5	0.003082	0.0211	0.491615
6	0.236405	1.6207	0.055885
7	0.158102	1.0839	0.141971
8	0.172703	1.184	0.121184
9	0.180895	1.2402	0.110537
10	-0.074365	-0.5098	0.30628
11	-0.255204	-1.7496	0.043358
12	-0.28286	-1.9392	0.029247
13	-0.076669	-0.5256	0.300813
14	0.126755	0.869	0.194635
15	0.224129	1.5366	0.065554
16	0.010165	0.0697	0.472368
17	-0.121614	-0.8337	0.204321
18	-0.12261	-0.8406	0.202421
19	-0.270078	-1.8516	0.035188
20	-0.029663	-0.2034	0.419865
21	-0.149126	-1.0224	0.155923
22	0.00623	0.0427	0.483055
23	0.149212	1.0229	0.155785
24	-0.078052	-0.5351	0.297553
25	-0.107666	-0.7381	0.232055
26	-0.197465	-1.3538	0.091145
27	-0.117795	-0.8076	0.211706
28	0.019458	0.1334	0.447226
29	0.167798	1.1504	0.127907
30	-0.045259	-0.3103	0.37886
31	0.004701	0.0322	0.487214
32	-0.026631	-0.1826	0.427959
33	0.010477	0.0718	0.471521
34	0.007788	0.0534	0.478824
35	0.080048	0.5488	0.292876
36	-0.020873	-0.1431	0.443413
37	0.025439	0.1744	0.431149
38	0.066551	0.4563	0.325155
39	-0.017654	-0.121	0.45209
40	-0.029825	-0.2045	0.419434
41	-0.023488	-0.161	0.436382
42	-0.004435	-0.0304	0.487938
43	0.009488	0.065	0.474206
44	0.039136	0.2683	0.394819
45	0.010176	0.0698	0.47234
46	0.003189	0.0219	0.491324
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.177151	1.2145	0.115315
2	0.029688	0.2035	0.4198
3	-0.214561	-1.471	0.073984
4	-0.14904	-1.0218	0.156061
5	0.094816	0.65	0.259421
6	0.235671	1.6157	0.056429
7	0.0161	0.1104	0.456292
8	0.090925	0.6234	0.268034
9	0.259003	1.7756	0.041134
10	-0.047797	-0.3277	0.372304
11	-0.300334	-2.059	0.022531
12	-0.228832	-1.5688	0.061703
13	0.069256	0.4748	0.318566
14	0.040595	0.2783	0.391
15	-0.085294	-0.5847	0.280757
16	-0.135956	-0.9321	0.178032
17	0.042372	0.2905	0.386361
18	0.143241	0.982	0.165562
19	-0.268768	-1.8426	0.035852
20	0.015477	0.1061	0.457976
21	-0.044373	-0.3042	0.381156
22	-0.056122	-0.3848	0.351078
23	-0.004029	-0.0276	0.489042
24	-0.287781	-1.9729	0.027201
25	0.035884	0.246	0.403374
26	0.043816	0.3004	0.382604
27	0.01627	0.1115	0.455832
28	-0.018462	-0.1266	0.44991
29	0.097401	0.6677	0.25378
30	-0.034198	-0.2345	0.407827
31	-0.043517	-0.2983	0.38338
32	-0.009353	-0.0641	0.474572
33	0.04858	0.333	0.370291
34	0.055303	0.3791	0.353147
35	0.015703	0.1077	0.457364
36	-0.116913	-0.8015	0.213433
37	-0.083268	-0.5709	0.285408
38	-0.045752	-0.3137	0.377584
39	0.120895	0.8288	0.2057
40	-0.129115	-0.8852	0.190287
41	-0.166882	-1.1441	0.12919
42	0.028206	0.1934	0.423751
43	-0.095956	-0.6578	0.256925
44	0.020895	0.1432	0.443353
45	-0.050278	-0.3447	0.365932
46	0.054834	0.3759	0.354333
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292946733bo7nwxtxik32o32/1g9wb1292946873.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292946733bo7nwxtxik32o32/1g9wb1292946873.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292946733bo7nwxtxik32o32/2g9wb1292946873.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292946733bo7nwxtxik32o32/2g9wb1292946873.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 48 ; 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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