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WS10 - PACF Y d = 0/ D=1 / lambda = 1

*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, 09 Dec 2009 07:54:53 -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/09/t1260370527bpuchtorpzkpyox.htm/, Retrieved Wed, 09 Dec 2009 15:55:30 +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/09/t1260370527bpuchtorpzkpyox.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 «

286.1 307 358.1 341.8 378.8 375.2 295.6 362.7 409.6 336.8 389.1 389.3 355.9 542 648.4 452 582.4 506.5 555.5 530.4 609.4 543.9 616.2 634.6 541.7 549.8 627.6 797.4 689.8 1576.6 1572.1 1626.4 1972.4 1509.6 1584.9 1880 1324 1777.7 2172.4 1780.3 2134.9 1838.4 1557 1755.2 1702 1577.5 1485.9 2179.1 1740.9 1724.5 2328.1 1774.1 2224.2 1536.3 1521.2 2051.8 2483.1 1929.8 1808.6 2584.9 1997.9 1639.9 2379.1 1715 2750.9 1865.4 1647.4 2180.4 2593 2057.2 2635.8 2315.4 1863.6 2038 2235.8 2222.1 2636.9 2076.8 1935.5 2086.3 2470.9 1854.6 2041.3 2170.8 1905.5 2130.2 2791.2 2539.7 2661.3 1764.9 2176.9 2458.5 2179 2242.5 2089.6 2661.6 2112 2367.3 2543 2603.9 3146.7 1789.2 2114.8 2236.3 2288.1 2173.2 1877.7 2807.4 2357.4 2107.7 2856.8 2510.8 2875 2229.7 2055.1 2545.4 2775.1 2252.2 2091.7 2433

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	0.845929	9.2667	0
2	0.820418	8.9872	0
3	0.824154	9.0282	0
4	0.776976	8.5113	0
5	0.768294	8.4162	0
6	0.729656	7.993	0
7	0.708749	7.764	0
8	0.69593	7.6235	0
9	0.673242	7.375	0
10	0.613252	6.7178	0
11	0.588708	6.449	0
12	0.636683	6.9745	0
13	0.527491	5.7784	0
14	0.49839	5.4596	0
15	0.499709	5.474	0
16	0.473365	5.1854	0
17	0.464043	5.0833	1e-06
18	0.43614	4.7777	3e-06
19	0.400824	4.3908	1.2e-05
20	0.379122	4.1531	3.1e-05
21	0.351862	3.8545	9.4e-05
22	0.291892	3.1975	0.000886
23	0.271292	2.9719	0.001789
24	0.296289	3.2457	0.000759
25	0.213393	2.3376	0.010532
26	0.184164	2.0174	0.022942
27	0.178104	1.951	0.026692
28	0.136638	1.4968	0.068536
29	0.119673	1.311	0.096188
30	0.114942	1.2591	0.105213
31	0.084728	0.9282	0.177596
32	0.074704	0.8183	0.207392
33	0.068276	0.7479	0.227983
34	0.025384	0.2781	0.390721
35	0.041163	0.4509	0.326429
36	0.068152	0.7466	0.228391
37	0.004176	0.0457	0.481795
38	0.007525	0.0824	0.467219
39	0.01593	0.1745	0.430882
40	0.001805	0.0198	0.492127
41	-0.002262	-0.0248	0.490137
42	-0.026049	-0.2853	0.387934
43	-0.027542	-0.3017	0.3817
44	-0.051605	-0.5653	0.28646
45	-0.055356	-0.6064	0.2727
46	-0.083382	-0.9134	0.181431
47	-0.098087	-1.0745	0.14238
48	-0.055813	-0.6114	0.271045
49	-0.119851	-1.3129	0.09586
50	-0.128888	-1.4119	0.080284
51	-0.116634	-1.2777	0.101917
52	-0.136265	-1.4927	0.06907
53	-0.132777	-1.4545	0.07421
54	-0.155918	-1.708	0.045111
55	-0.159989	-1.7526	0.041113
56	-0.166259	-1.8213	0.035528
57	-0.156792	-1.7176	0.044227
58	-0.190133	-2.0828	0.019696
59	-0.196064	-2.1478	0.016871
60	-0.164739	-1.8046	0.036821

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.845929	9.2667	0
2	0.368568	4.0375	4.8e-05
3	0.301698	3.3049	0.000626
4	0.013502	0.1479	0.441331
5	0.0893	0.9782	0.164964
6	-0.065413	-0.7166	0.237518
7	0.017641	0.1932	0.423546
8	0.022602	0.2476	0.402435
9	0.030131	0.3301	0.370963
10	-0.185927	-2.0367	0.021939
11	-0.051185	-0.5607	0.288021
12	0.309703	3.3926	0.000469
13	-0.329736	-3.6121	0.000222
14	-0.09131	-1.0002	0.159601
15	0.064896	0.7109	0.239263
16	0.141843	1.5538	0.061431
17	-0.029971	-0.3283	0.371623
18	0.046139	0.5054	0.307091
19	-0.080973	-0.887	0.188423
20	-0.125128	-1.3707	0.086512
21	-0.0529	-0.5795	0.281671
22	-0.027936	-0.306	0.380057
23	-0.015577	-0.1706	0.4324
24	0.035174	0.3853	0.350345
25	-0.07445	-0.8156	0.208183
26	-0.056474	-0.6186	0.268661
27	0.013629	0.1493	0.440784
28	-0.04828	-0.5289	0.298931
29	-0.012258	-0.1343	0.446704
30	0.165693	1.8151	0.036005
31	0.0543	0.5948	0.276541
32	-0.045525	-0.4987	0.309453
33	0.014045	0.1539	0.438991
34	-0.014367	-0.1574	0.437603
35	0.078853	0.8638	0.194712
36	0.04672	0.5118	0.304867
37	-0.081273	-0.8903	0.187544
38	0.004382	0.048	0.480896
39	0.020092	0.2201	0.413087
40	0.058383	0.6396	0.261841
41	-0.039331	-0.4308	0.333676
42	-0.194684	-2.1327	0.017495
43	0.067866	0.7434	0.229336
44	-0.095841	-1.0499	0.14794
45	0.052213	0.572	0.284208
46	0.034298	0.3757	0.353896
47	-0.164291	-1.7997	0.037209
48	0.076357	0.8364	0.202283
49	-0.028042	-0.3072	0.379618
50	-0.043438	-0.4758	0.317528
51	-0.024689	-0.2705	0.393638
52	0.023378	0.2561	0.399159
53	0.017108	0.1874	0.425828
54	-0.038366	-0.4203	0.337518
55	-0.048808	-0.5347	0.296936
56	0.000954	0.0105	0.495838
57	0.025894	0.2837	0.388582
58	-0.054665	-0.5988	0.275207
59	0.047238	0.5175	0.302891
60	-0.064675	-0.7085	0.240012

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260370527bpuchtorpzkpyox/12c261260370491.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260370527bpuchtorpzkpyox/12c261260370491.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260370527bpuchtorpzkpyox/2euet1260370491.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260370527bpuchtorpzkpyox/2euet1260370491.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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