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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, 24 Nov 2009 07:30:12 -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/24/t12590730308t19t4owjhx9y1x.htm/, Retrieved Tue, 24 Nov 2009 15:30:32 +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/24/t12590730308t19t4owjhx9y1x.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 «

115.47 103.34 102.6 100.69 105.67 123.61 113.08 106.46 123.38 109.87 95.74 123.06 123.39 120.28 115.33 110.4 114.49 132.03 123.16 118.82 128.32 112.24 104.53 132.57 122.52 131.8 124.55 120.96 122.6 145.52 118.57 134.25 136.7 121.37 111.63 134.42 137.65 137.86 119.77 130.69 128.28 147.45 128.42 136.9 143.95 135.64 122.48 136.83 153.04 142.71 123.46 144.37 146.15 147.61 158.51 147.4 165.05 154.64 126.2 157.36 154.15 123.21 113.07 110.45 113.57 122.44 114.93 111.85 126.04 121.34

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	0.596316	4.9891	2e-06
2	0.436256	3.65	0.000251
3	0.525282	4.3948	1.9e-05
4	0.463184	3.8753	0.000119
5	0.36769	3.0763	0.001495
6	0.375729	3.1436	0.001224
7	0.217572	1.8203	0.036491
8	0.273183	2.2856	0.012654
9	0.157751	1.3198	0.095595
10	0.018078	0.1513	0.440106
11	0.13682	1.1447	0.128112
12	0.325976	2.7273	0.004032
13	0.09211	0.7707	0.221754
14	0.008605	0.072	0.471405
15	0.072085	0.6031	0.274194
16	0.10255	0.858	0.196912
17	0.037679	0.3152	0.376758
18	0.064875	0.5428	0.294502
19	0.030799	0.2577	0.398703
20	0.045038	0.3768	0.353727
21	-0.048473	-0.4056	0.343155
22	-0.119893	-1.0031	0.159634
23	-0.041924	-0.3508	0.36341
24	0.066135	0.5533	0.290903
25	-0.0599	-0.5012	0.308917
26	-0.170555	-1.427	0.079017
27	-0.094148	-0.7877	0.216765
28	-0.03586	-0.3	0.382524
29	-0.120849	-1.0111	0.157726
30	-0.101054	-0.8455	0.200362
31	-0.078576	-0.6574	0.256535
32	-0.149229	-1.2485	0.107997
33	-0.171955	-1.4387	0.077349
34	-0.205009	-1.7152	0.045364
35	-0.213933	-1.7899	0.038898
36	-0.108038	-0.9039	0.184571
37	-0.179222	-1.4995	0.069124
38	-0.285478	-2.3885	0.009809
39	-0.190875	-1.597	0.057388
40	-0.168067	-1.4062	0.082052
41	-0.226482	-1.8949	0.031119
42	-0.18408	-1.5401	0.064019
43	-0.162986	-1.3636	0.088526
44	-0.226735	-1.897	0.030977
45	-0.213127	-1.7831	0.039449
46	-0.228208	-1.9093	0.03016
47	-0.220578	-1.8455	0.034598
48	-0.142101	-1.1889	0.119247
49	-0.195515	-1.6358	0.053185
50	-0.247249	-2.0686	0.021138
51	-0.165885	-1.3879	0.084786
52	-0.160119	-1.3397	0.092345
53	-0.176093	-1.4733	0.072576
54	-0.115759	-0.9685	0.168063
55	-0.098945	-0.8278	0.205289
56	-0.081994	-0.686	0.247486
57	-0.028204	-0.236	0.407072
58	-0.021611	-0.1808	0.428519
59	0.021258	0.1779	0.429675
60	0.082296	0.6885	0.246695

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.596316	4.9891	2e-06
2	0.125174	1.0473	0.149287
3	0.351651	2.9421	0.002209
4	0.050384	0.4215	0.337326
5	0.019418	0.1625	0.435706
6	0.059989	0.5019	0.308655
7	-0.235186	-1.9677	0.026532
8	0.196602	1.6449	0.052238
9	-0.295154	-2.4694	0.007987
10	-0.050072	-0.4189	0.338273
11	0.181363	1.5174	0.066836
12	0.368209	3.0807	0.001476
13	-0.204385	-1.71	0.045847
14	-0.167113	-1.3982	0.083239
15	-0.010345	-0.0866	0.465637
16	0.04338	0.3629	0.35887
17	-0.068778	-0.5754	0.283421
18	0.050296	0.4208	0.337593
19	0.048353	0.4045	0.343521
20	-0.108391	-0.9069	0.183795
21	-0.02959	-0.2476	0.402596
22	-0.009917	-0.083	0.467056
23	0.015732	0.1316	0.447828
24	-0.062424	-0.5223	0.301563
25	0.075532	0.6319	0.264741
26	-0.151311	-1.266	0.104862
27	0.078572	0.6574	0.256545
28	0.018814	0.1574	0.437689
29	-0.03222	-0.2696	0.394141
30	-0.052608	-0.4402	0.330592
31	-0.046699	-0.3907	0.348599
32	-0.133262	-1.115	0.134342
33	0.038324	0.3206	0.37472
34	0.004299	0.036	0.485705
35	-0.115622	-0.9674	0.168346
36	0.027052	0.2263	0.410801
37	-0.006108	-0.0511	0.479694
38	0.071694	0.5998	0.275277
39	-0.097601	-0.8166	0.208467
40	0.010961	0.0917	0.463595
41	-0.049645	-0.4154	0.339574
42	-0.052977	-0.4432	0.32948
43	-0.005191	-0.0434	0.48274
44	-0.064373	-0.5386	0.295941
45	-0.005359	-0.0448	0.482183
46	-0.038344	-0.3208	0.374655
47	0.035156	0.2941	0.384762
48	-0.021066	-0.1763	0.430302
49	-0.060977	-0.5102	0.305769
50	0.055569	0.4649	0.321714
51	-0.0259	-0.2167	0.414538
52	-0.037202	-0.3113	0.378265
53	0.018309	0.1532	0.439346
54	0.030743	0.2572	0.398884
55	-0.005544	-0.0464	0.481569
56	0.098567	0.8247	0.20618
57	0.099479	0.8323	0.204034
58	-0.021741	-0.1819	0.428095
59	0.004352	0.0364	0.485529
60	0.037146	0.3108	0.378442

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590730308t19t4owjhx9y1x/16um21259073010.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590730308t19t4owjhx9y1x/16um21259073010.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590730308t19t4owjhx9y1x/23i7g1259073010.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/24/t12590730308t19t4owjhx9y1x/23i7g1259073010.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; 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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