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Paper - autocorrelation function

*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: Sun, 21 Dec 2008 08:54:30 -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/21/t1229874920am5zhr40u12y0zm.htm/, Retrieved Sun, 21 Dec 2008 16:55:22 +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/21/t1229874920am5zhr40u12y0zm.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 «

2490 3266 3475 3127 2955 3870 2852 3142 3029 3180 2560 2733 2452 2553 2777 2520 2318 2873 2311 2395 2099 2268 2316 2181 2175 2627 2578 3090 2634 3225 2938 3174 3350 2588 2061 2691 2061 2918 2223 2651 2379 3146 2883 2768 3258 2839 2470 5072 1463 1600 2203 2013 2169 2640 2411 2528 2292 1988 1774 2279

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	0.185147	1.4341	0.078361
2	0.226797	1.7568	0.04203
3	0.247831	1.9197	0.029828
4	0.063748	0.4938	0.31163
5	-0.025631	-0.1985	0.421647
6	0.101915	0.7894	0.216484
7	-0.136646	-1.0585	0.147045
8	-0.015661	-0.1213	0.451926
9	-0.105892	-0.8202	0.207664
10	0.005903	0.0457	0.48184
11	-0.258939	-2.0057	0.0247
12	0.012847	0.0995	0.460532
13	-0.108624	-0.8414	0.201732
14	-0.028781	-0.2229	0.412171
15	0.063342	0.4906	0.312733
16	-0.012023	-0.0931	0.463056
17	-0.12505	-0.9686	0.168308
18	-0.005163	-0.04	0.484116
19	-0.173653	-1.3451	0.091826
20	-0.01816	-0.1407	0.444302
21	-0.111926	-0.867	0.194706
22	-0.015227	-0.1179	0.453251
23	-0.048884	-0.3787	0.353141
24	0.034859	0.27	0.394036
25	0.006714	0.052	0.479347
26	0.008072	0.0625	0.475178
27	-0.010386	-0.0804	0.468074
28	0.053807	0.4168	0.33916
29	-0.035353	-0.2738	0.392573
30	0.115171	0.8921	0.187948
31	-0.06678	-0.5173	0.303434
32	0.004225	0.0327	0.487
33	0.045937	0.3558	0.36161
34	0.04857	0.3762	0.35404
35	0.031942	0.2474	0.402714
36	0.138709	1.0744	0.143465
37	0.059189	0.4585	0.324134
38	0.147928	1.1458	0.128205
39	0.118314	0.9165	0.181549
40	0.084177	0.652	0.258435
41	-0.011264	-0.0873	0.465381
42	0.137998	1.0689	0.144692
43	-0.053668	-0.4157	0.339553
44	-0.059228	-0.4588	0.324027
45	0.004264	0.033	0.48688
46	-0.049726	-0.3852	0.350736
47	-0.17265	-1.3373	0.093079
48	-0.096929	-0.7508	0.227852
49	-0.107609	-0.8335	0.203925
50	-0.098614	-0.7639	0.223972
51	-0.078846	-0.6107	0.271839
52	-0.076976	-0.5963	0.276625
53	-0.092891	-0.7195	0.237304
54	-0.072086	-0.5584	0.289332
55	-0.067442	-0.5224	0.301656
56	-0.065982	-0.5111	0.30558
57	-0.039072	-0.3027	0.381601
58	-0.00473	-0.0366	0.485448
59	0.003085	0.0239	0.490508
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.185147	1.4341	0.078361
2	0.199351	1.5442	0.063903
3	0.191194	1.481	0.071922
4	-0.042227	-0.3271	0.372369
5	-0.127752	-0.9896	0.163181
6	0.076914	0.5958	0.276784
7	-0.14843	-1.1497	0.127408
8	0.025544	0.1979	0.421911
9	-0.099618	-0.7716	0.22168
10	0.102934	0.7973	0.214203
11	-0.262831	-2.0359	0.023092
12	0.112	0.8676	0.194549
13	-0.059229	-0.4588	0.324023
14	0.081726	0.633	0.264555
15	0.093683	0.7257	0.235433
16	-0.099859	-0.7735	0.221131
17	-0.0856	-0.6631	0.254916
18	-0.137404	-1.0643	0.145722
19	-0.05191	-0.4021	0.344522
20	0.019369	0.15	0.440623
21	-0.012213	-0.0946	0.462473
22	0.008582	0.0665	0.47361
23	0.003724	0.0288	0.488541
24	0.027462	0.2127	0.416133
25	0.01342	0.1039	0.458778
26	-0.006889	-0.0534	0.478812
27	-0.028903	-0.2239	0.411804
28	-0.024547	-0.1901	0.424919
29	-0.041477	-0.3213	0.374558
30	0.033445	0.2591	0.398235
31	-0.074611	-0.5779	0.282735
32	-0.00402	-0.0311	0.487631
33	0.086972	0.6737	0.251551
34	0.077138	0.5975	0.276207
35	0.037392	0.2896	0.386548
36	0.071054	0.5504	0.292051
37	0.021453	0.1662	0.434289
38	0.045179	0.35	0.3638
39	0.046459	0.3599	0.360103
40	-0.061923	-0.4797	0.31661
41	-0.02343	-0.1815	0.428299
42	0.081863	0.6341	0.264209
43	-0.063416	-0.4912	0.312533
44	-0.04853	-0.3759	0.354154
45	0.037087	0.2873	0.387447
46	0.043079	0.3337	0.369888
47	-0.081766	-0.6334	0.264453
48	-0.144432	-1.1188	0.13385
49	0.049791	0.3857	0.35055
50	-0.031454	-0.2436	0.404171
51	0.010097	0.0782	0.468959
52	-0.112368	-0.8704	0.193776
53	0.031435	0.2435	0.404226
54	-0.101263	-0.7844	0.217951
55	0.013666	0.1059	0.458025
56	0.009226	0.0715	0.471634
57	0.010414	0.0807	0.467987
58	0.024445	0.1893	0.42523
59	-0.021999	-0.1704	0.432632
60	NA	NA	NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229874920am5zhr40u12y0zm/1q1w91229874868.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229874920am5zhr40u12y0zm/1q1w91229874868.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229874920am5zhr40u12y0zm/29zy81229874868.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/21/t1229874920am5zhr40u12y0zm/29zy81229874868.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 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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