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WS08 - PACF d = 1/ D=0 / 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 13:42:59 -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/t12591820240ijde14tgp665ct.htm/, Retrieved Wed, 25 Nov 2009 21:47:06 +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/t12591820240ijde14tgp665ct.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	-0.454769	-4.9609	1e-06
2	0.02449	0.2671	0.394908
3	-0.095358	-1.0402	0.150171
4	-0.013465	-0.1469	0.441735
5	0.158255	1.7264	0.043439
6	-0.169238	-1.8462	0.033676
7	0.049291	0.5377	0.295893
8	0.089658	0.9781	0.165016
9	-0.010132	-0.1105	0.45609
10	-0.068186	-0.7438	0.229226
11	-0.185799	-2.0268	0.022458
12	0.391051	4.2659	2e-05
13	-0.110612	-1.2066	0.114984
14	-0.151454	-1.6522	0.050569
15	0.025002	0.2727	0.392762
16	0.001498	0.0163	0.493493
17	0.020942	0.2285	0.409843
18	0.051635	0.5633	0.287155
19	-0.119154	-1.2998	0.098087
20	0.171735	1.8734	0.031733
21	-0.037981	-0.4143	0.339691
22	-0.106997	-1.1672	0.122731
23	-0.016727	-0.1825	0.427764
24	0.108931	1.1883	0.118542
25	-0.007335	-0.08	0.468178
26	-0.075212	-0.8205	0.206794
27	0.039003	0.4255	0.335629
28	0.024337	0.2655	0.395546
29	-0.042109	-0.4594	0.32341
30	0.026469	0.2887	0.386642
31	-0.055585	-0.6064	0.272716
32	0.104115	1.1358	0.129169
33	-0.038323	-0.4181	0.338331
34	-0.100423	-1.0955	0.137758
35	0.019826	0.2163	0.414571
36	0.127494	1.3908	0.083442
37	-0.027564	-0.3007	0.382088
38	-0.075014	-0.8183	0.207408
39	0.007344	0.0801	0.46814
40	0.028368	0.3095	0.378756
41	0.034744	0.379	0.352678
42	-0.094978	-1.0361	0.151131
43	0.087154	0.9507	0.171831
44	0.0056	0.0611	0.475694
45	0.003715	0.0405	0.483871
46	-0.042586	-0.4646	0.321547
47	-0.110917	-1.21	0.114347
48	0.217038	2.3676	0.009758
49	-0.079709	-0.8695	0.193157
50	-0.021631	-0.236	0.406932
51	-0.027711	-0.3023	0.381478
52	0.030798	0.336	0.368745
53	0.040815	0.4452	0.328477
54	-0.089542	-0.9768	0.165327
55	0.069504	0.7582	0.224917
56	-0.035988	-0.3926	0.347664
57	0.061893	0.6752	0.250437
58	-0.053692	-0.5857	0.279589
59	-0.063106	-0.6884	0.246269
60	0.076864	0.8385	0.201719

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.454769	-4.9609	1e-06
2	-0.229865	-2.5075	0.006753
3	-0.24784	-2.7036	0.003932
4	-0.249483	-2.7215	0.003737
5	0.002417	0.0264	0.489504
6	-0.150061	-1.637	0.052139
7	-0.137595	-1.501	0.068004
8	0.062705	0.684	0.247642
9	0.091422	0.9973	0.160321
10	-0.02944	-0.3212	0.374329
11	-0.277265	-3.0246	0.001525
12	0.222892	2.4315	0.008264
13	0.201463	2.1977	0.014953
14	-0.159768	-1.7429	0.04197
15	-0.078931	-0.861	0.195474
16	0.034966	0.3814	0.351781
17	-0.239403	-2.6116	0.005086
18	-0.017957	-0.1959	0.422516
19	0.019416	0.2118	0.41631
20	-0.00287	-0.0313	0.48754
21	-0.009934	-0.1084	0.456944
22	0.006037	0.0659	0.473802
23	0.040034	0.4367	0.331555
24	-0.026169	-0.2855	0.387889
25	-0.092147	-1.0052	0.158418
26	0.015336	0.1673	0.433712
27	0.045259	0.4937	0.311206
28	-0.020315	-0.2216	0.412497
29	-0.029351	-0.3202	0.374696
30	-0.04824	-0.5262	0.299853
31	-0.034012	-0.371	0.355637
32	0.00768	0.0838	0.466684
33	-0.055163	-0.6018	0.274242
34	-0.072227	-0.7879	0.216159
35	-0.071177	-0.7765	0.219511
36	0.0411	0.4483	0.32736
37	0.101664	1.109	0.134829
38	-0.044338	-0.4837	0.314753
39	-0.084261	-0.9192	0.179931
40	-0.010558	-0.1152	0.454253
41	0.06842	0.7464	0.228458
42	-0.079315	-0.8652	0.194329
43	0.086559	0.9442	0.17348
44	0.051923	0.5664	0.286089
45	-0.04557	-0.4971	0.310012
46	0.083278	0.9085	0.182738
47	-0.064926	-0.7083	0.240086
48	-0.04161	-0.4539	0.32536
49	-0.001738	-0.019	0.492454
50	0.031075	0.339	0.367609
51	-0.005966	-0.0651	0.47411
52	0.00598	0.0652	0.474047
53	-0.015898	-0.1734	0.431305
54	-0.016803	-0.1833	0.427437
55	0.012159	0.1326	0.447353
56	-0.058796	-0.6414	0.261251
57	0.030291	0.3304	0.370824
58	0.009602	0.1047	0.458376
59	0.016706	0.1822	0.427852
60	-0.042234	-0.4607	0.32292

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/25/t12591820240ijde14tgp665ct/1lhcx1259181778.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t12591820240ijde14tgp665ct/1lhcx1259181778.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t12591820240ijde14tgp665ct/261fu1259181778.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/25/t12591820240ijde14tgp665ct/261fu1259181778.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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