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WS08 - PACF d = 1/ 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, 25 Nov 2009 13:49:28 -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/Nov/25/t1259182322pbaz3e7bi27jbr9.htm/, Retrieved Wed, 25 Nov 2009 21:52:05 +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/Nov/25/t1259182322pbaz3e7bi27jbr9.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 «

423.4 404.1 500 472.6 496.1 562 434.8 538.2 577.6 518.1 625.2 561.2 523.3 536.1 607.3 637.3 606.9 652.9 617.2 670.4 729.9 677.2 710 844.3 748.2 653.9 742.6 854.2 808.4 1819 1936.5 1966.1 2083.1 1620.1 1527.6 1795 1685.1 1851.8 2164.4 1981.8 1726.5 2144.6 1758.2 1672.9 1837.3 1596.1 1446 1898.4 1964.1 1755.9 2255.3 1881.2 2117.9 1656.5 1544.1 2098.9 2133.3 1963.5 1801.2 2365.4 1936.5 1667.6 1983.5 2058.6 2448.3 1858.1 1625.4 2130.6 2515.7 2230.2 2086.9 2235 2100.2 2288.6 2490 2573.7 2543.8 2004.7 2390 2338.4 2724.5 2292.5 2386 2477.9 2337 2605.1 2560.8 2839.3 2407.2 2085.2 2735.6 2798.7 3053.2 2405 2471.9 2727.3 2790.7 2385.4 3206.6 2705.6 3518.4 1954.9 2584.3 2535.8 2685.9 2866 2236.6 2934.9 2668.6 2371.2 3165.9 2887.2 3112.2 2671.2 2432.6 2812.3 3095.7 2862.9 2607.3 2862.5

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.514912	-5.3263	0
2	0.26654	2.7571	0.003429
3	-0.192242	-1.9886	0.024651
4	-0.078614	-0.8132	0.208957
5	0.151552	1.5677	0.059956
6	-0.16584	-1.7155	0.044577
7	0.077149	0.798	0.213309
8	-0.029416	-0.3043	0.380751
9	0.17017	1.7603	0.040611
10	-0.124527	-1.2881	0.100242
11	0.144375	1.4934	0.069135
12	-0.31498	-3.2582	0.000752
13	0.218514	2.2603	0.012913
14	-0.242314	-2.5065	0.006849
15	0.135601	1.4027	0.081805
16	-0.073744	-0.7628	0.223628
17	-0.010944	-0.1132	0.455041
18	0.218775	2.263	0.012826
19	-0.190979	-1.9755	0.025393
20	0.136454	1.4115	0.0805
21	-0.113685	-1.176	0.121108
22	0.045322	0.4688	0.320076
23	0.061585	0.637	0.26273
24	-0.155999	-1.6137	0.054773
25	0.004493	0.0465	0.481509
26	0.097957	1.0133	0.156608
27	0.028236	0.2921	0.385399
28	0.047061	0.4868	0.313697
29	-0.119444	-1.2355	0.109668
30	0.032747	0.3387	0.367737
31	-0.063591	-0.6578	0.256041
32	0.040178	0.4156	0.339265
33	-0.000164	-0.0017	0.499323
34	-0.084237	-0.8714	0.192755
35	0.155892	1.6126	0.054893
36	-0.090658	-0.9378	0.175236
37	0.061589	0.6371	0.262716
38	-0.051825	-0.5361	0.296508
39	-0.004163	-0.0431	0.482865
40	0.005942	0.0615	0.475554
41	0.067114	0.6942	0.24452
42	-0.10686	-1.1054	0.13574
43	0.098592	1.0198	0.155051
44	0.001262	0.0131	0.494805
45	-0.027395	-0.2834	0.388719
46	0.081603	0.8441	0.200245
47	-0.182114	-1.8838	0.031153
48	0.155018	1.6035	0.055884
49	-0.108443	-1.1217	0.132241
50	0.101714	1.0521	0.147554
51	-0.099541	-1.0297	0.152747
52	0.033695	0.3485	0.36406
53	0.039772	0.4114	0.3408
54	-0.059053	-0.6108	0.271299
55	0.084179	0.8708	0.192919
56	-0.086885	-0.8987	0.185404
57	-0.007439	-0.077	0.469402
58	0.009979	0.1032	0.45899
59	0.002748	0.0284	0.488689
60	0.000896	0.0093	0.496313

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.514912	-5.3263	0
2	0.001912	0.0198	0.492128
3	-0.073857	-0.764	0.223279
4	-0.281599	-2.9129	0.00218
5	0.020651	0.2136	0.415626
6	-0.071455	-0.7391	0.23072
7	-0.155699	-1.6106	0.05511
8	-0.038859	-0.402	0.344258
9	0.240115	2.4838	0.007276
10	-0.020151	-0.2084	0.417641
11	0.088252	0.9129	0.181676
12	-0.194251	-2.0093	0.023509
13	-0.021988	-0.2274	0.410257
14	-0.206007	-2.131	0.017691
15	-0.107316	-1.1101	0.134725
16	-0.162032	-1.6761	0.048322
17	-0.143392	-1.4833	0.070473
18	0.073825	0.7636	0.223379
19	-0.013571	-0.1404	0.444313
20	-0.066403	-0.6869	0.246823
21	0.117249	1.2128	0.113932
22	0.057286	0.5926	0.277361
23	0.175304	1.8134	0.03629
24	-0.141687	-1.4656	0.072842
25	-0.189988	-1.9653	0.025988
26	-0.049845	-0.5156	0.303598
27	0.054129	0.5599	0.288354
28	-0.087842	-0.9086	0.182791
29	-0.184429	-1.9077	0.029552
30	0.025618	0.265	0.395764
31	-0.155796	-1.6116	0.055001
32	-0.063651	-0.6584	0.255845
33	0.132343	1.369	0.086938
34	-0.053966	-0.5582	0.288929
35	0.119176	1.2328	0.110182
36	-0.052278	-0.5408	0.294897
37	-0.065916	-0.6818	0.248408
38	-0.079073	-0.8179	0.207606
39	0.00392	0.0406	0.483864
40	-0.071929	-0.744	0.229241
41	-0.040019	-0.414	0.339867
42	-0.01013	-0.1048	0.458371
43	-0.050288	-0.5202	0.302006
44	0.058226	0.6023	0.274127
45	0.005728	0.0593	0.476431
46	0.033262	0.3441	0.365736
47	0.05411	0.5597	0.288422
48	-0.073103	-0.7562	0.225599
49	-0.078183	-0.8087	0.210233
50	-0.048118	-0.4977	0.309846
51	-0.019136	-0.1979	0.421731
52	-0.052499	-0.5431	0.294109
53	-0.045782	-0.4736	0.318385
54	-0.037768	-0.3907	0.348407
55	0.010993	0.1137	0.454841
56	0.116522	1.2053	0.11537
57	-0.047335	-0.4896	0.312698
58	-0.030958	-0.3202	0.374709
59	-0.011461	-0.1186	0.452925
60	-0.015635	-0.1617	0.435912

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259182322pbaz3e7bi27jbr9/1dxdg1259182166.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259182322pbaz3e7bi27jbr9/1dxdg1259182166.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259182322pbaz3e7bi27jbr9/2khm81259182166.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t1259182322pbaz3e7bi27jbr9/2khm81259182166.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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