Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_arimabackwardselection.wasp

Title produced by software

ARIMA Backward Selection

Date of computation

Mon, 08 Dec 2008 12:21:54 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t1228764195u5mcdundkccw0me.htm/, Retrieved Sun, 06 Apr 2025 10:01:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30785, Retrieved Sun, 06 Apr 2025 10:01:30 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

280

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD  [Standard Deviation-Mean Plot] [Q5] [2008-11-29 20:10:39] [57fa5e3679c393aa19449b2f1be9928b]
-   P     [Standard Deviation-Mean Plot] [Q5] [2008-11-29 20:18:39] [57fa5e3679c393aa19449b2f1be9928b]
- RM        [Variance Reduction Matrix] [Q6 Variance] [2008-11-29 20:25:29] [57fa5e3679c393aa19449b2f1be9928b]
- RM          [(Partial) Autocorrelation Function] [Q6 ACF] [2008-11-29 20:35:57] [57fa5e3679c393aa19449b2f1be9928b]
-               [(Partial) Autocorrelation Function] [Q6 aangepaste ACF] [2008-11-29 20:44:03] [57fa5e3679c393aa19449b2f1be9928b]
- RM D            [Cross Correlation Function] [Q7] [2008-11-29 20:55:14] [57fa5e3679c393aa19449b2f1be9928b]
F RM D              [Standard Deviation-Mean Plot] [Q8 Mean plot insc...] [2008-11-29 21:03:17] [57fa5e3679c393aa19449b2f1be9928b]
F RM                  [Variance Reduction Matrix] [Q8 VRM Inschrijvi...] [2008-11-29 21:06:11] [57fa5e3679c393aa19449b2f1be9928b]
- RM                    [(Partial) Autocorrelation Function] [Q2 inschrijvingen...] [2008-12-07 14:47:46] [57fa5e3679c393aa19449b2f1be9928b]
-                         [(Partial) Autocorrelation Function] [Q3] [2008-12-07 14:59:20] [57fa5e3679c393aa19449b2f1be9928b]
- RM                        [ARIMA Backward Selection] [Q5 inschrijvingen] [2008-12-07 15:06:11] [57fa5e3679c393aa19449b2f1be9928b]
F   P                           [ARIMA Backward Selection] [Q5 inschrijvingen] [2008-12-08 19:21:54] [270782e2502ae87124d0ebdcd1862d6a] [Current]
-   P                             [ARIMA Backward Selection] [] [2008-12-11 16:10:37] [d134696a922d84037f02d49ded84b0bd] 

Feedback Forum

2008-12-11 16:14:20 [Stijn Van de Velde] [reply] 
Fout. 
Het is de bedoeling om AR, SAR, MA en SMA op het maximum te zetten, zodat we kunnen nagaan of onze bevindingen van stap 4 wel kloppen. 
 
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/11/t1229011869g8y0z8q3hhme770.htm 
 
We zien dat de in principe alle modellen verworpen worden. Je had dus gelijk in stap 4. 
We kunnen er echter over twijfelen om het een AR2 en SMA1 model te noemen. De p-waarde van deze modellen ligt namelijk tussen 1 en 5%, welke dus minder is dan de alpha fout (die meestal 5% bedraagd). Maar dit is voor discussie vatbaar.
2008-12-14 20:26:04 [df2ed12c9b09685cd516719b004050c5] [reply] 
zie uitleg werkloosheiddata

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	12 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 12 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30785&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30785&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	12 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

ARIMA Parameter Estimation and Backward Selection
Iteration	ar1	ma1	sar1	sma1
Estimates ( 1 )	0.7194	-0.5238	0.1747	-1
(p-val)	(0.0023 )	(0.0523 )	(0.2883 )	(0.001 )
Estimates ( 2 )	0.7464	-0.581	0	-1.2169
(p-val)	(0.0017 )	(0.0274 )	(NA )	(0.0243 )
Estimates ( 3 )	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )
Estimates ( 4 )	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )
Estimates ( 5 )	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )
Estimates ( 6 )	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )
Estimates ( 7 )	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & ar1 & ma1 & sar1 & sma1 \tabularnewline
Estimates ( 1 ) & 0.7194 & -0.5238 & 0.1747 & -1 \tabularnewline
(p-val) & (0.0023 ) & (0.0523 ) & (0.2883 ) & (0.001 ) \tabularnewline
Estimates ( 2 ) & 0.7464 & -0.581 & 0 & -1.2169 \tabularnewline
(p-val) & (0.0017 ) & (0.0274 ) & (NA ) & (0.0243 ) \tabularnewline
Estimates ( 3 ) & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 4 ) & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 5 ) & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 6 ) & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30785&T=1

[TABLE]
[ROW][C]ARIMA Parameter Estimation and Backward Selection[/C][/ROW]
[ROW][C]Iteration[/C][C]ar1[/C][C]ma1[/C][C]sar1[/C][C]sma1[/C][/ROW]
[ROW][C]Estimates ( 1 )[/C][C]0.7194[/C][C]-0.5238[/C][C]0.1747[/C][C]-1[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0023 )[/C][C](0.0523 )[/C][C](0.2883 )[/C][C](0.001 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.7464[/C][C]-0.581[/C][C]0[/C][C]-1.2169[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0017 )[/C][C](0.0274 )[/C][C](NA )[/C][C](0.0243 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 6 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 7 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30785&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

ARIMA Parameter Estimation and Backward Selection
Iteration	ar1	ma1	sar1	sma1
Estimates ( 1 )	0.7194	-0.5238	0.1747	-1
(p-val)	(0.0023 )	(0.0523 )	(0.2883 )	(0.001 )
Estimates ( 2 )	0.7464	-0.581	0	-1.2169
(p-val)	(0.0017 )	(0.0274 )	(NA )	(0.0243 )
Estimates ( 3 )	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )
Estimates ( 4 )	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )
Estimates ( 5 )	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )
Estimates ( 6 )	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )
Estimates ( 7 )	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )

Estimated ARIMA Residuals
Value
0.0563564424430245
-0.783820409977628
0.818787227129614
-0.516784259958787
0.607519755359095
0.190009988523005
4.03489373548588
-3.06499947073276
1.49576156265039
3.86309216002059
2.84677241366012
-1.04411883434967
-0.359118274760269
-4.02892027042027
0.297197121799522
-0.243674234836553
-1.49067678209133
1.95989254099287
-0.0303046356899331
0.177727070234002
-2.16177193907807
-2.60089085655105
-1.4559293740424
0.632223557876254
2.59878294042536
-2.28797617889283
1.43382431131285
-1.02229715521635
-3.44184162348377
0.971861226544021
-3.14813867906487
2.38372103204257
2.09570728677785
2.16636067655532
-1.05740508942266
3.16172987368864
-2.32486582687228
-1.61828901283311
-0.522783895043787
-1.85037292640478
-0.703143275228537
-0.318945857594845
-3.57841546601133
1.32032076274658
-0.830062383165623
-0.96823900053091
-0.944002906684148
1.30323726653082
1.14575386876810
0.840887818972337
0.776763517648367
0.357648163146274
1.81698127574663
1.36564938847468
0.980313661105642
-0.000215999935086300
1.62562478716134
-1.87863844502181
3.54771040243397
0.676224603334014
0.696109113773888

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
0.0563564424430245 \tabularnewline
-0.783820409977628 \tabularnewline
0.818787227129614 \tabularnewline
-0.516784259958787 \tabularnewline
0.607519755359095 \tabularnewline
0.190009988523005 \tabularnewline
4.03489373548588 \tabularnewline
-3.06499947073276 \tabularnewline
1.49576156265039 \tabularnewline
3.86309216002059 \tabularnewline
2.84677241366012 \tabularnewline
-1.04411883434967 \tabularnewline
-0.359118274760269 \tabularnewline
-4.02892027042027 \tabularnewline
0.297197121799522 \tabularnewline
-0.243674234836553 \tabularnewline
-1.49067678209133 \tabularnewline
1.95989254099287 \tabularnewline
-0.0303046356899331 \tabularnewline
0.177727070234002 \tabularnewline
-2.16177193907807 \tabularnewline
-2.60089085655105 \tabularnewline
-1.4559293740424 \tabularnewline
0.632223557876254 \tabularnewline
2.59878294042536 \tabularnewline
-2.28797617889283 \tabularnewline
1.43382431131285 \tabularnewline
-1.02229715521635 \tabularnewline
-3.44184162348377 \tabularnewline
0.971861226544021 \tabularnewline
-3.14813867906487 \tabularnewline
2.38372103204257 \tabularnewline
2.09570728677785 \tabularnewline
2.16636067655532 \tabularnewline
-1.05740508942266 \tabularnewline
3.16172987368864 \tabularnewline
-2.32486582687228 \tabularnewline
-1.61828901283311 \tabularnewline
-0.522783895043787 \tabularnewline
-1.85037292640478 \tabularnewline
-0.703143275228537 \tabularnewline
-0.318945857594845 \tabularnewline
-3.57841546601133 \tabularnewline
1.32032076274658 \tabularnewline
-0.830062383165623 \tabularnewline
-0.96823900053091 \tabularnewline
-0.944002906684148 \tabularnewline
1.30323726653082 \tabularnewline
1.14575386876810 \tabularnewline
0.840887818972337 \tabularnewline
0.776763517648367 \tabularnewline
0.357648163146274 \tabularnewline
1.81698127574663 \tabularnewline
1.36564938847468 \tabularnewline
0.980313661105642 \tabularnewline
-0.000215999935086300 \tabularnewline
1.62562478716134 \tabularnewline
-1.87863844502181 \tabularnewline
3.54771040243397 \tabularnewline
0.676224603334014 \tabularnewline
0.696109113773888 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30785&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]0.0563564424430245[/C][/ROW]
[ROW][C]-0.783820409977628[/C][/ROW]
[ROW][C]0.818787227129614[/C][/ROW]
[ROW][C]-0.516784259958787[/C][/ROW]
[ROW][C]0.607519755359095[/C][/ROW]
[ROW][C]0.190009988523005[/C][/ROW]
[ROW][C]4.03489373548588[/C][/ROW]
[ROW][C]-3.06499947073276[/C][/ROW]
[ROW][C]1.49576156265039[/C][/ROW]
[ROW][C]3.86309216002059[/C][/ROW]
[ROW][C]2.84677241366012[/C][/ROW]
[ROW][C]-1.04411883434967[/C][/ROW]
[ROW][C]-0.359118274760269[/C][/ROW]
[ROW][C]-4.02892027042027[/C][/ROW]
[ROW][C]0.297197121799522[/C][/ROW]
[ROW][C]-0.243674234836553[/C][/ROW]
[ROW][C]-1.49067678209133[/C][/ROW]
[ROW][C]1.95989254099287[/C][/ROW]
[ROW][C]-0.0303046356899331[/C][/ROW]
[ROW][C]0.177727070234002[/C][/ROW]
[ROW][C]-2.16177193907807[/C][/ROW]
[ROW][C]-2.60089085655105[/C][/ROW]
[ROW][C]-1.4559293740424[/C][/ROW]
[ROW][C]0.632223557876254[/C][/ROW]
[ROW][C]2.59878294042536[/C][/ROW]
[ROW][C]-2.28797617889283[/C][/ROW]
[ROW][C]1.43382431131285[/C][/ROW]
[ROW][C]-1.02229715521635[/C][/ROW]
[ROW][C]-3.44184162348377[/C][/ROW]
[ROW][C]0.971861226544021[/C][/ROW]
[ROW][C]-3.14813867906487[/C][/ROW]
[ROW][C]2.38372103204257[/C][/ROW]
[ROW][C]2.09570728677785[/C][/ROW]
[ROW][C]2.16636067655532[/C][/ROW]
[ROW][C]-1.05740508942266[/C][/ROW]
[ROW][C]3.16172987368864[/C][/ROW]
[ROW][C]-2.32486582687228[/C][/ROW]
[ROW][C]-1.61828901283311[/C][/ROW]
[ROW][C]-0.522783895043787[/C][/ROW]
[ROW][C]-1.85037292640478[/C][/ROW]
[ROW][C]-0.703143275228537[/C][/ROW]
[ROW][C]-0.318945857594845[/C][/ROW]
[ROW][C]-3.57841546601133[/C][/ROW]
[ROW][C]1.32032076274658[/C][/ROW]
[ROW][C]-0.830062383165623[/C][/ROW]
[ROW][C]-0.96823900053091[/C][/ROW]
[ROW][C]-0.944002906684148[/C][/ROW]
[ROW][C]1.30323726653082[/C][/ROW]
[ROW][C]1.14575386876810[/C][/ROW]
[ROW][C]0.840887818972337[/C][/ROW]
[ROW][C]0.776763517648367[/C][/ROW]
[ROW][C]0.357648163146274[/C][/ROW]
[ROW][C]1.81698127574663[/C][/ROW]
[ROW][C]1.36564938847468[/C][/ROW]
[ROW][C]0.980313661105642[/C][/ROW]
[ROW][C]-0.000215999935086300[/C][/ROW]
[ROW][C]1.62562478716134[/C][/ROW]
[ROW][C]-1.87863844502181[/C][/ROW]
[ROW][C]3.54771040243397[/C][/ROW]
[ROW][C]0.676224603334014[/C][/ROW]
[ROW][C]0.696109113773888[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30785&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30785&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated ARIMA Residuals
Value
0.0563564424430245
-0.783820409977628
0.818787227129614
-0.516784259958787
0.607519755359095
0.190009988523005
4.03489373548588
-3.06499947073276
1.49576156265039
3.86309216002059
2.84677241366012
-1.04411883434967
-0.359118274760269
-4.02892027042027
0.297197121799522
-0.243674234836553
-1.49067678209133
1.95989254099287
-0.0303046356899331
0.177727070234002
-2.16177193907807
-2.60089085655105
-1.4559293740424
0.632223557876254
2.59878294042536
-2.28797617889283
1.43382431131285
-1.02229715521635
-3.44184162348377
0.971861226544021
-3.14813867906487
2.38372103204257
2.09570728677785
2.16636067655532
-1.05740508942266
3.16172987368864
-2.32486582687228
-1.61828901283311
-0.522783895043787
-1.85037292640478
-0.703143275228537
-0.318945857594845
-3.57841546601133
1.32032076274658
-0.830062383165623
-0.96823900053091
-0.944002906684148
1.30323726653082
1.14575386876810
0.840887818972337
0.776763517648367
0.357648163146274
1.81698127574663
1.36564938847468
0.980313661105642
-0.000215999935086300
1.62562478716134
-1.87863844502181
3.54771040243397
0.676224603334014
0.696109113773888

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 0.4 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 1 ;

Parameters (R input):

par1 = FALSE ; par2 = 0.4 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 1 ;

R code (references can be found in the software module):

library(lattice)
if (par1 == 'TRUE') par1 <- TRUE
if (par1 == 'FALSE') par1 <- FALSE
par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial
par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial
par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial
par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial
armaGR <- function(arima.out, names, n){
try1 <- arima.out$coef
try2 <- sqrt(diag(arima.out$var.coef))
try.data.frame  <- data.frame(matrix(NA,ncol=4,nrow=length(names)))
dimnames(try.data.frame) <- list(names,c('coef','std','tstat','pv'))
try.data.frame[,1] <- try1
for(i in 1:length(try2)) try.data.frame[which(rownames(try.data.frame)==names(try2)[i]),2] <- try2[i]
try.data.frame[,3] <- try.data.frame[,1] / try.data.frame[,2]
try.data.frame[,4] <- round((1-pt(abs(try.data.frame[,3]),df=n-(length(try2)+1)))*2,5)
vector <- rep(NA,length(names))
vector[is.na(try.data.frame[,4])] <- 0
maxi <- which.max(try.data.frame[,4])
continue <- max(try.data.frame[,4],na.rm=TRUE) > .05
vector[maxi] <- 0
list(summary=try.data.frame,next.vector=vector,continue=continue)
}
arimaSelect <- function(series, order=c(13,0,0), seasonal=list(order=c(2,0,0),period=12), include.mean=F){
nrc <- order[1]+order[3]+seasonal$order[1]+seasonal$order[3]
coeff <- matrix(NA, nrow=nrc*2, ncol=nrc)
pval <- matrix(NA, nrow=nrc*2, ncol=nrc)
mylist <- rep(list(NULL), nrc)
names  <- NULL
if(order[1] > 0) names <- paste('ar',1:order[1],sep='')
if(order[3] > 0) names <- c( names , paste('ma',1:order[3],sep='') )
if(seasonal$order[1] > 0) names <- c(names, paste('sar',1:seasonal$order[1],sep=''))
if(seasonal$order[3] > 0) names <- c(names, paste('sma',1:seasonal$order[3],sep=''))
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML')
mylist[[1]] <- arima.out
last.arma <- armaGR(arima.out, names, length(series))
mystop <- FALSE
i <- 1
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- 2
aic <- arima.out$aic
while(!mystop){
mylist[[i]] <- arima.out
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML', fixed=last.arma$next.vector)
aic <- c(aic, arima.out$aic)
last.arma <- armaGR(arima.out, names, length(series))
mystop <- !last.arma$continue
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- i+1
}
list(coeff, pval, mylist, aic=aic)
}
arimaSelectplot <- function(arimaSelect.out,noms,choix){
noms <- names(arimaSelect.out[[3]][[1]]$coef)
coeff <- arimaSelect.out[[1]]
k <- min(which(is.na(coeff[,1])))-1
coeff <- coeff[1:k,]
pval  <- arimaSelect.out[[2]][1:k,]
aic   <- arimaSelect.out$aic[1:k]
coeff[coeff==0] <- NA
n <- ncol(coeff)
if(missing(choix)) choix <- k
layout(matrix(c(1,1,1,2,
3,3,3,2,
3,3,3,4,
5,6,7,7),nr=4),
widths=c(10,35,45,15),
heights=c(30,30,15,15))
couleurs <- rainbow(75)[1:50]#(50)
ticks <- pretty(coeff)
par(mar=c(1,1,3,1))
plot(aic,k:1-.5,type='o',pch=21,bg='blue',cex=2,axes=F,lty=2,xpd=NA)
points(aic[choix],k-choix+.5,pch=21,cex=4,bg=2,xpd=NA)
title('aic',line=2)
par(mar=c(3,0,0,0))
plot(0,axes=F,xlab='',ylab='',xlim=range(ticks),ylim=c(.1,1))
rect(xleft  = min(ticks) + (0:49)/50*(max(ticks)-min(ticks)),
xright = min(ticks) + (1:50)/50*(max(ticks)-min(ticks)),
ytop   = rep(1,50),
ybottom= rep(0,50),col=couleurs,border=NA)
axis(1,ticks)
rect(xleft=min(ticks),xright=max(ticks),ytop=1,ybottom=0)
text(mean(coeff,na.rm=T),.5,'coefficients',cex=2,font=2)
par(mar=c(1,1,3,1))
image(1:n,1:k,t(coeff[k:1,]),axes=F,col=couleurs,zlim=range(ticks))
for(i in 1:n) for(j in 1:k) if(!is.na(coeff[j,i])) {
if(pval[j,i]<.01)                            symb = 'green'
else if( (pval[j,i]<.05) & (pval[j,i]>=.01)) symb = 'orange'
else if( (pval[j,i]<.1)  & (pval[j,i]>=.05)) symb = 'red'
else                                         symb = 'black'
polygon(c(i+.5   ,i+.2   ,i+.5   ,i+.5),
c(k-j+0.5,k-j+0.5,k-j+0.8,k-j+0.5),
col=symb)
if(j==choix)  {
rect(xleft=i-.5,
xright=i+.5,
ybottom=k-j+1.5,
ytop=k-j+.5,
lwd=4)
text(i,
k-j+1,
round(coeff[j,i],2),
cex=1.2,
font=2)
}
else{
rect(xleft=i-.5,xright=i+.5,ybottom=k-j+1.5,ytop=k-j+.5)
text(i,k-j+1,round(coeff[j,i],2),cex=1.2,font=1)
}
}
axis(3,1:n,noms)
par(mar=c(0.5,0,0,0.5))
plot(0,axes=F,xlab='',ylab='',type='n',xlim=c(0,8),ylim=c(-.2,.8))
cols <- c('green','orange','red','black')
niv  <- c('0','0.01','0.05','0.1')
for(i in 0:3){
polygon(c(1+2*i   ,1+2*i   ,1+2*i-.5   ,1+2*i),
c(.4      ,.7      , .4        , .4),
col=cols[i+1])
text(2*i,0.5,niv[i+1],cex=1.5)
}
text(8,.5,1,cex=1.5)
text(4,0,'p-value',cex=2)
box()
residus <- arimaSelect.out[[3]][[choix]]$res
par(mar=c(1,2,4,1))
acf(residus,main='')
title('acf',line=.5)
par(mar=c(1,2,4,1))
pacf(residus,main='')
title('pacf',line=.5)
par(mar=c(2,2,4,1))
qqnorm(residus,main='')
title('qq-norm',line=.5)
qqline(residus)
residus
}
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
(selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5)))
bitmap(file='test1.png')
resid <- arimaSelectplot(selection)
dev.off()
resid
bitmap(file='test2.png')
acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test3.png')
pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
dev.off()
bitmap(file='test4.png')
cpgram(resid, main='Residual Cumulative Periodogram')
dev.off()
bitmap(file='test5.png')
hist(resid, main='Residual Histogram', xlab='values of Residuals')
dev.off()
bitmap(file='test6.png')
densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test7.png')
qqnorm(resid, main='Residual Normal Q-Q Plot')
qqline(resid)
dev.off()
ncols <- length(selection[[1]][1,])
nrows <- length(selection[[2]][,1])-1
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Iteration', header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,names(selection[[3]][[1]]$coef)[i],header=TRUE)
}
a<-table.row.end(a)
for (j in 1:nrows) {
a<-table.row.start(a)
mydum <- 'Estimates ('
mydum <- paste(mydum,j)
mydum <- paste(mydum,')')
a<-table.element(a,mydum, header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,round(selection[[1]][j,i],4))
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'(p-val)', header=TRUE)
for (i in 1:ncols) {
mydum <- '('
mydum <- paste(mydum,round(selection[[2]][j,i],4),sep='')
mydum <- paste(mydum,')')
a<-table.element(a,mydum)
}
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,'Estimated ARIMA Residuals', 1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Value', 1,TRUE)
a<-table.row.end(a)
for (i in (par4*par5+par3):length(resid)) {
a<-table.row.start(a)
a<-table.element(a,resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code