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Autocorrelation VSA

*Unverified author*

R Software Module: rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 14 Dec 2008 10:43:20 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/14/t1229276804wdbkhksqtdvxoax.htm/, Retrieved Sun, 14 Dec 2008 18:46:45 +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/2008/Dec/14/t1229276804wdbkhksqtdvxoax.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

358.59 362.96 362.42 364.97 364.04 361.06 358.48 352.96 359.59 360.39 357.40 362.93 364.55 365.73 364.70 364.65 359.43 362.14 356.97 354.82 353.17 357.06 356.18 355.01 355.65 357.31 357.07 357.91 358.48 358.97 351.77 352.16 359.08 360.35 359.53 359.30 358.41 359.68 355.31 357.08 349.71 354.13 345.49 341.69 344.25 340.17 342.47 344.43 333.23 339.72 342.61 346.36 339.09 339.73 341.12 335.94 333.46 335.66 341.12 342.21 342.62 346.06 344.43 346.65 343.74 335.67 342.75 341.77 345.84 346.52 350.79 345.44 345.87 338.48 337.21 340.81 339.86 342.86 343.33 341.73 351.38 351.13 345.99 347.55 346.02 345.29 347.03 348.01 345.48 349.40 351.05 349.70 350.86 354.45 355.30 357.48 355.24 351.79 355.22 351.02 350.28 350.17 348.16 340.30 343.75 344.71 344.13 342.14 345.04 346.02 346.43 347.07 339.33 339.10 337.19 339.58 327.85 326.81 321.73 320.45 327.69 323.95 320.47 322.13 316.34 314.78 308.90 308.62 314.41 306.88 310.60 321.60 321.50 325.68 324.35 320.01 326.88 332.39 331.48 332.62 324.79 327.12 328.91 328.37 324.83 325.90 326.18 328.94 333.78 328.06 325.87 325.41 318.86 319.13 310.16 311.73 306.54 311.16 311.98 306.72 308.05 300.76 301.90 293.09 292.76 294.58 289.90 296.69 297.21 293.31 296.25 298.60 296.87 301.02 304.73 301.92 295.72 293.18 298.35 297.99 299.85 299.85 304.45 299.45 298.14 298.78 297.02 301.33 294.96 296.69 300.73 301.96 297.38 293.87 285.96 285.41 283.70 284.76 277.11 274.73 274.73 274.73 274.73 274.69 275.42 264.15 276.24 268.88 277.97 280.49 281.09 276.16 272.58 270.94 284.31 283.94 284.18 282.83 283.84 282.71 279.29 280.70 274.47 273.44 275.49 279.46 280.19 288.21 284.80 281.41 283.39 287.97 290.77 290.60 289.67 289.84 298.55 296.07 297.14 295.34 296.25 294.30 296.15 296.49 298.05 301.03 300.52 301.50 296.93 289.84 291.44 286.88 286.74 288.93 292.19 295.39 295.86 293.36 292.86 292.73 296.73 285.02 285.24 288.62 283.36 285.84 291.48 291.41 287.77 284.97 286.05 278.19 281.21 277.92 280.08 269.24 268.48 268.83 269.54 262.37 265.12 265.34 263.32 267.18 260.75 261.78 257.27 255.63 251.39 259.49 261.18 261.65 262.01 265.23 268.10 262.27 263.59 257.85 265.69 271.15 266.69 265.77 262.32 270.48 273.03 269.13 280.65 282.75 281.44 281.99 282.86 287.21 283.11 280.66 282.39 280.83 284.71 279.99 283.50 284.88 288.60 284.80 287.20 286.22 286.54 279.58 283.08 288.88 280.18 284.16 290.57 286.82 273.00 278.69 264.54 271.92 283.60 269.25 263.58 264.16 268.85 269.67 249.41 268.99 268.65 260.16 256.55 251.47 234.93 232.96 215.49 213.68 236.07 235.41 214.77 225.85 224.64 238.26 232.44 222.50 225.28 220.49 216.86 234.70 230.06 238.27 238.56 242.70 249.14 234.89 227.78 234.04 230.70 230.17 218.23 232.20 220.76 215.60 217.69 204.35 191.44 203.84 211.86 210.57 219.57 219.98 226.01 207.04 212.52 217.92 210.45 218.53 223.32 218.76 217.63

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	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	19.8494	0
1	-0.223938	-4.445	0.999994
2	-0.068793	-1.3655	0.913562
3	0.075265	1.494	0.067993
4	-0.039439	-0.7828	0.782903
5	0.013532	0.2686	0.394184
6	-0.026224	-0.5205	0.698504
7	-0.068468	-1.3591	0.912547
8	0.08618	1.7106	0.043969
9	-0.02138	-0.4244	0.664243
10	0.063547	1.2614	0.103959
11	0.035351	0.7017	0.241643
12	-0.025071	-0.4976	0.690491
13	0.033907	0.673	0.25066
14	-0.01024	-0.2033	0.580483
15	-0.133581	-2.6515	0.995832
16	0.011651	0.2313	0.408611
17	0.086187	1.7108	0.043956
18	-0.087681	-1.7404	0.958717
19	-0.019329	-0.3837	0.649286
20	0.01207	0.2396	0.405391
21	-0.070743	-1.4042	0.919477
22	0.039406	0.7822	0.217287
23	-0.023519	-0.4668	0.679565
24	-0.004279	-0.0849	0.533818
25	-0.009514	-0.1888	0.574846
26	0.015006	0.2979	0.382986
27	-0.007272	-0.1443	0.557346
28	-0.021017	-0.4172	0.661614
29	0.038294	0.7601	0.223821
30	0.020974	0.4163	0.338698
31	-0.094635	-1.8784	0.969471
32	0.022439	0.4454	0.32814
33	-0.027794	-0.5517	0.709264
34	-0.015797	-0.3136	0.62299
35	-0.052626	-1.0446	0.851577
36	0.009452	0.1876	0.425641
37	0.080752	1.6029	0.054881
38	-0.027226	-0.5404	0.705391
39	-0.013093	-0.2599	0.60246
40	-0.004396	-0.0873	0.534745
41	-0.015254	-0.3028	0.618893
42	0.041166	0.8171	0.207178
43	-0.056217	-1.1159	0.867421
44	-0.073653	-1.462	0.927727
45	0.046465	0.9223	0.178465
46	0.038503	0.7643	0.222585
47	-0.04678	-0.9286	0.823158
48	0.016301	0.3236	0.373216
49	0.036221	0.719	0.236291
50	-0.077642	-1.5412	0.937959
51	0.039498	0.784	0.216752
52	-0.067091	-1.3317	0.908138
53	0.081297	1.6137	0.053697
54	0.002778	0.0551	0.478025
55	-0.06029	-1.1967	0.883932
56	0.009542	0.1894	0.424939
57	-0.001928	-0.0383	0.515255
58	-0.012257	-0.2433	0.59605
59	0.057213	1.1357	0.128396

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.223938	-4.445	0.999994
1	-0.12522	-2.4856	0.993326
2	0.031968	0.6345	0.263045
3	-0.023208	-0.4607	0.677351
4	0.010082	0.2001	0.420747
5	-0.030909	-0.6135	0.73006
6	-0.082683	-1.6412	0.949223
7	0.046697	0.9269	0.17727
8	0.001427	0.0283	0.488707
9	0.083275	1.653	0.049567
10	0.062911	1.2487	0.106249
11	0.014922	0.2962	0.383616
12	0.028681	0.5693	0.284739
13	0.001447	0.0287	0.488552
14	-0.129797	-2.5764	0.994827
15	-0.061739	-1.2255	0.889436
16	0.07303	1.4496	0.073983
17	-0.048224	-0.9572	0.83048
18	-0.051077	-1.0138	0.844361
19	-0.031459	-0.6245	0.733654
20	-0.103754	-2.0595	0.979947
21	-0.022301	-0.4427	0.670874
22	-0.015884	-0.3153	0.623643
23	0.007642	0.1517	0.439755
24	-0.015518	-0.308	0.620884
25	0.03362	0.6673	0.252472
26	-0.012162	-0.2414	0.595316
27	-0.021197	-0.4208	0.662919
28	0.050693	1.0062	0.157463
29	0.026412	0.5243	0.300192
30	-0.064806	-1.2864	0.900464
31	0.007317	0.1452	0.442298
32	-0.054794	-1.0876	0.861286
33	-0.055368	-1.099	0.863786
34	-0.085754	-1.7022	0.955244
35	-0.042526	-0.8441	0.80044
36	0.055963	1.1108	0.133657
37	0.009949	0.1975	0.421779
38	-0.022609	-0.4488	0.673081
39	-0.048941	-0.9715	0.834043
40	-0.018899	-0.3751	0.646121
41	0.029582	0.5872	0.278705
42	-0.028298	-0.5617	0.712682
43	-0.060088	-1.1927	0.88315
44	0.007302	0.1449	0.442416
45	0.022787	0.4523	0.325647
46	-0.041096	-0.8157	0.792424
47	-0.005749	-0.1141	0.545398
48	0.015152	0.3008	0.381881
49	-0.096598	-1.9174	0.972046
50	0.000882	0.0175	0.493021
51	-0.067894	-1.3477	0.910729
52	0.061409	1.2189	0.111799
53	-0.002295	-0.0455	0.518152
54	-0.046108	-0.9152	0.819682
55	-0.049014	-0.9729	0.834399
56	-0.011727	-0.2328	0.591969
57	-0.018517	-0.3676	0.643299
58	0.004361	0.0866	0.465532
59	0.015452	0.3067	0.379613

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229276804wdbkhksqtdvxoax/12qfs1229276593.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229276804wdbkhksqtdvxoax/12qfs1229276593.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229276804wdbkhksqtdvxoax/2po1f1229276593.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229276804wdbkhksqtdvxoax/2po1f1229276593.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 2.0 ; par3 = 1 ; par4 = 0 ; par5 = 1 ;

Parameters (R input):

par1 = 60 ; par2 = 2.0 ; par3 = 1 ; par4 = 0 ; par5 = 1 ;

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 (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='lags',ylab='ACF')

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 1:par1) {

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(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-1,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(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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