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_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Tue, 20 Dec 2011 03:44:13 -0500

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/2011/Dec/20/t1324370706h08u8egvalkli0i.htm/, Retrieved Mon, 06 May 2024 05:27:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157799, Retrieved Mon, 06 May 2024 05:27:48 +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

143

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R  D    [(Partial) Autocorrelation Function] [Partial ACF] [2011-12-03 08:54:59] [7ec97e350862fea9ec6e4fa3b5b6058f]
- R P       [(Partial) Autocorrelation Function] [P ACF (d=1)] [2011-12-03 09:06:08] [7ec97e350862fea9ec6e4fa3b5b6058f]
-   P         [(Partial) Autocorrelation Function] [P ACF (d=1)] [2011-12-03 09:07:43] [7ec97e350862fea9ec6e4fa3b5b6058f]
-   P           [(Partial) Autocorrelation Function] [P ACF (d=D=1)] [2011-12-03 09:10:52] [7ec97e350862fea9ec6e4fa3b5b6058f]
- RM                [ARIMA Forecasting] [ARIMA Forecasting] [2011-12-20 08:44:13] [10a6f28c51bb1cb94db47cee32729d66] [Current]

Feedback Forum

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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157799&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157799&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157799&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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value(H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[288])
276	512238	-	-	-	-	-	-	-
277	519164	-	-	-	-	-	-	-
278	517009	-	-	-	-	-	-	-
279	509933	-	-	-	-	-	-	-
280	509127	-	-	-	-	-	-	-
281	500857	-	-	-	-	-	-	-
282	506971	-	-	-	-	-	-	-
283	569323	-	-	-	-	-	-	-
284	579714	-	-	-	-	-	-	-
285	577992	-	-	-	-	-	-	-
286	565464	-	-	-	-	-	-	-
287	547344	-	-	-	-	-	-	-
288	554788	-	-	-	-	-	-	-
289	562325	560061.5043	549060.1061	571019.8475	0.3428	0.8272	1	0.8272
290	560854	554782.0418	537538.1503	571919.3772	0.2437	0.1942	1	0.4997
291	555332	545699.8106	523583.6557	567638.0786	0.1947	0.0879	0.9993	0.2084
292	543599	541236.7283	515079.9534	567142.9772	0.4291	0.1431	0.9924	0.1526
293	536662	532519.3809	502780.0343	561930.008	0.3912	0.2301	0.9826	0.0689
294	542722	535053.9081	502214.2429	567495.023	0.3216	0.4613	0.9551	0.1166
295	593530	592722.7009	557773.3765	627264.3736	0.4817	0.9977	0.9079	0.9843
296	610763	606532.967	569168.4737	643442.336	0.4111	0.7551	0.9228	0.997
297	612613	603451.3075	563627.077	642756.2671	0.3239	0.3577	0.8979	0.9924
298	611324	592562.1793	550293.3958	634235.7709	0.1888	0.1728	0.8988	0.9622
299	594167	577828.8409	533147.2799	621829.0402	0.2334	0.0678	0.9128	0.8476
300	595454	583075.1359	536392.8704	629020.677	0.2987	0.318	0.8862	0.8862
301	590865	586615.55	535822.3226	636542.7618	0.4338	0.3643	0.8299	0.8943
302	589379	579582.9356	524306.2658	633822.9557	0.3617	0.3418	0.7507	0.8149
303	584428	569461.4987	509822.0584	627874.5176	0.3078	0.252	0.6823	0.6888
304	573100	563141.8732	499438.8825	625431.7057	0.377	0.2515	0.7307	0.6037
305	567456	554210.3009	486569.2548	620234.5094	0.3471	0.2875	0.6988	0.4932
306	569028	554919.5659	483765.3572	624288.4918	0.3451	0.3616	0.6348	0.5015
307	620735	610101.246	537091.4354	681399.3432	0.385	0.8706	0.6756	0.9358
308	628884	625636.7752	549879.526	699597.1944	0.4657	0.5517	0.6533	0.9698
309	628232	621865.429	542983.2207	698789.3216	0.4356	0.429	0.5932	0.9563
310	612117	611830.3309	529739.2222	691767.9959	0.4972	0.3438	0.505	0.919
311	595404	598846.7039	513522.6853	681796.604	0.4676	0.3769	0.544	0.8511
312	597141	602964.8402	515013.3165	688412.1496	0.4469	0.5688	0.5684	0.8654

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast \tabularnewline
time & Y[t] & F[t] & 95% LB & 95% UB & p-value(H0: Y[t] = F[t]) & P(F[t]>Y[t-1]) & P(F[t]>Y[t-s]) & P(F[t]>Y[288]) \tabularnewline
276 & 512238 & - & - & - & - & - & - & - \tabularnewline
277 & 519164 & - & - & - & - & - & - & - \tabularnewline
278 & 517009 & - & - & - & - & - & - & - \tabularnewline
279 & 509933 & - & - & - & - & - & - & - \tabularnewline
280 & 509127 & - & - & - & - & - & - & - \tabularnewline
281 & 500857 & - & - & - & - & - & - & - \tabularnewline
282 & 506971 & - & - & - & - & - & - & - \tabularnewline
283 & 569323 & - & - & - & - & - & - & - \tabularnewline
284 & 579714 & - & - & - & - & - & - & - \tabularnewline
285 & 577992 & - & - & - & - & - & - & - \tabularnewline
286 & 565464 & - & - & - & - & - & - & - \tabularnewline
287 & 547344 & - & - & - & - & - & - & - \tabularnewline
288 & 554788 & - & - & - & - & - & - & - \tabularnewline
289 & 562325 & 560061.5043 & 549060.1061 & 571019.8475 & 0.3428 & 0.8272 & 1 & 0.8272 \tabularnewline
290 & 560854 & 554782.0418 & 537538.1503 & 571919.3772 & 0.2437 & 0.1942 & 1 & 0.4997 \tabularnewline
291 & 555332 & 545699.8106 & 523583.6557 & 567638.0786 & 0.1947 & 0.0879 & 0.9993 & 0.2084 \tabularnewline
292 & 543599 & 541236.7283 & 515079.9534 & 567142.9772 & 0.4291 & 0.1431 & 0.9924 & 0.1526 \tabularnewline
293 & 536662 & 532519.3809 & 502780.0343 & 561930.008 & 0.3912 & 0.2301 & 0.9826 & 0.0689 \tabularnewline
294 & 542722 & 535053.9081 & 502214.2429 & 567495.023 & 0.3216 & 0.4613 & 0.9551 & 0.1166 \tabularnewline
295 & 593530 & 592722.7009 & 557773.3765 & 627264.3736 & 0.4817 & 0.9977 & 0.9079 & 0.9843 \tabularnewline
296 & 610763 & 606532.967 & 569168.4737 & 643442.336 & 0.4111 & 0.7551 & 0.9228 & 0.997 \tabularnewline
297 & 612613 & 603451.3075 & 563627.077 & 642756.2671 & 0.3239 & 0.3577 & 0.8979 & 0.9924 \tabularnewline
298 & 611324 & 592562.1793 & 550293.3958 & 634235.7709 & 0.1888 & 0.1728 & 0.8988 & 0.9622 \tabularnewline
299 & 594167 & 577828.8409 & 533147.2799 & 621829.0402 & 0.2334 & 0.0678 & 0.9128 & 0.8476 \tabularnewline
300 & 595454 & 583075.1359 & 536392.8704 & 629020.677 & 0.2987 & 0.318 & 0.8862 & 0.8862 \tabularnewline
301 & 590865 & 586615.55 & 535822.3226 & 636542.7618 & 0.4338 & 0.3643 & 0.8299 & 0.8943 \tabularnewline
302 & 589379 & 579582.9356 & 524306.2658 & 633822.9557 & 0.3617 & 0.3418 & 0.7507 & 0.8149 \tabularnewline
303 & 584428 & 569461.4987 & 509822.0584 & 627874.5176 & 0.3078 & 0.252 & 0.6823 & 0.6888 \tabularnewline
304 & 573100 & 563141.8732 & 499438.8825 & 625431.7057 & 0.377 & 0.2515 & 0.7307 & 0.6037 \tabularnewline
305 & 567456 & 554210.3009 & 486569.2548 & 620234.5094 & 0.3471 & 0.2875 & 0.6988 & 0.4932 \tabularnewline
306 & 569028 & 554919.5659 & 483765.3572 & 624288.4918 & 0.3451 & 0.3616 & 0.6348 & 0.5015 \tabularnewline
307 & 620735 & 610101.246 & 537091.4354 & 681399.3432 & 0.385 & 0.8706 & 0.6756 & 0.9358 \tabularnewline
308 & 628884 & 625636.7752 & 549879.526 & 699597.1944 & 0.4657 & 0.5517 & 0.6533 & 0.9698 \tabularnewline
309 & 628232 & 621865.429 & 542983.2207 & 698789.3216 & 0.4356 & 0.429 & 0.5932 & 0.9563 \tabularnewline
310 & 612117 & 611830.3309 & 529739.2222 & 691767.9959 & 0.4972 & 0.3438 & 0.505 & 0.919 \tabularnewline
311 & 595404 & 598846.7039 & 513522.6853 & 681796.604 & 0.4676 & 0.3769 & 0.544 & 0.8511 \tabularnewline
312 & 597141 & 602964.8402 & 515013.3165 & 688412.1496 & 0.4469 & 0.5688 & 0.5684 & 0.8654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157799&T=1

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast[/C][/ROW]
[ROW][C]time[/C][C]Y[t][/C][C]F[t][/C][C]95% LB[/C][C]95% UB[/C][C]p-value(H0: Y[t] = F[t])[/C][C]P(F[t]>Y[t-1])[/C][C]P(F[t]>Y[t-s])[/C][C]P(F[t]>Y[288])[/C][/ROW]
[ROW][C]276[/C][C]512238[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]277[/C][C]519164[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]278[/C][C]517009[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]279[/C][C]509933[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]280[/C][C]509127[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]281[/C][C]500857[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]282[/C][C]506971[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]283[/C][C]569323[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]284[/C][C]579714[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]285[/C][C]577992[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]286[/C][C]565464[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]287[/C][C]547344[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]288[/C][C]554788[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]289[/C][C]562325[/C][C]560061.5043[/C][C]549060.1061[/C][C]571019.8475[/C][C]0.3428[/C][C]0.8272[/C][C]1[/C][C]0.8272[/C][/ROW]
[ROW][C]290[/C][C]560854[/C][C]554782.0418[/C][C]537538.1503[/C][C]571919.3772[/C][C]0.2437[/C][C]0.1942[/C][C]1[/C][C]0.4997[/C][/ROW]
[ROW][C]291[/C][C]555332[/C][C]545699.8106[/C][C]523583.6557[/C][C]567638.0786[/C][C]0.1947[/C][C]0.0879[/C][C]0.9993[/C][C]0.2084[/C][/ROW]
[ROW][C]292[/C][C]543599[/C][C]541236.7283[/C][C]515079.9534[/C][C]567142.9772[/C][C]0.4291[/C][C]0.1431[/C][C]0.9924[/C][C]0.1526[/C][/ROW]
[ROW][C]293[/C][C]536662[/C][C]532519.3809[/C][C]502780.0343[/C][C]561930.008[/C][C]0.3912[/C][C]0.2301[/C][C]0.9826[/C][C]0.0689[/C][/ROW]
[ROW][C]294[/C][C]542722[/C][C]535053.9081[/C][C]502214.2429[/C][C]567495.023[/C][C]0.3216[/C][C]0.4613[/C][C]0.9551[/C][C]0.1166[/C][/ROW]
[ROW][C]295[/C][C]593530[/C][C]592722.7009[/C][C]557773.3765[/C][C]627264.3736[/C][C]0.4817[/C][C]0.9977[/C][C]0.9079[/C][C]0.9843[/C][/ROW]
[ROW][C]296[/C][C]610763[/C][C]606532.967[/C][C]569168.4737[/C][C]643442.336[/C][C]0.4111[/C][C]0.7551[/C][C]0.9228[/C][C]0.997[/C][/ROW]
[ROW][C]297[/C][C]612613[/C][C]603451.3075[/C][C]563627.077[/C][C]642756.2671[/C][C]0.3239[/C][C]0.3577[/C][C]0.8979[/C][C]0.9924[/C][/ROW]
[ROW][C]298[/C][C]611324[/C][C]592562.1793[/C][C]550293.3958[/C][C]634235.7709[/C][C]0.1888[/C][C]0.1728[/C][C]0.8988[/C][C]0.9622[/C][/ROW]
[ROW][C]299[/C][C]594167[/C][C]577828.8409[/C][C]533147.2799[/C][C]621829.0402[/C][C]0.2334[/C][C]0.0678[/C][C]0.9128[/C][C]0.8476[/C][/ROW]
[ROW][C]300[/C][C]595454[/C][C]583075.1359[/C][C]536392.8704[/C][C]629020.677[/C][C]0.2987[/C][C]0.318[/C][C]0.8862[/C][C]0.8862[/C][/ROW]
[ROW][C]301[/C][C]590865[/C][C]586615.55[/C][C]535822.3226[/C][C]636542.7618[/C][C]0.4338[/C][C]0.3643[/C][C]0.8299[/C][C]0.8943[/C][/ROW]
[ROW][C]302[/C][C]589379[/C][C]579582.9356[/C][C]524306.2658[/C][C]633822.9557[/C][C]0.3617[/C][C]0.3418[/C][C]0.7507[/C][C]0.8149[/C][/ROW]
[ROW][C]303[/C][C]584428[/C][C]569461.4987[/C][C]509822.0584[/C][C]627874.5176[/C][C]0.3078[/C][C]0.252[/C][C]0.6823[/C][C]0.6888[/C][/ROW]
[ROW][C]304[/C][C]573100[/C][C]563141.8732[/C][C]499438.8825[/C][C]625431.7057[/C][C]0.377[/C][C]0.2515[/C][C]0.7307[/C][C]0.6037[/C][/ROW]
[ROW][C]305[/C][C]567456[/C][C]554210.3009[/C][C]486569.2548[/C][C]620234.5094[/C][C]0.3471[/C][C]0.2875[/C][C]0.6988[/C][C]0.4932[/C][/ROW]
[ROW][C]306[/C][C]569028[/C][C]554919.5659[/C][C]483765.3572[/C][C]624288.4918[/C][C]0.3451[/C][C]0.3616[/C][C]0.6348[/C][C]0.5015[/C][/ROW]
[ROW][C]307[/C][C]620735[/C][C]610101.246[/C][C]537091.4354[/C][C]681399.3432[/C][C]0.385[/C][C]0.8706[/C][C]0.6756[/C][C]0.9358[/C][/ROW]
[ROW][C]308[/C][C]628884[/C][C]625636.7752[/C][C]549879.526[/C][C]699597.1944[/C][C]0.4657[/C][C]0.5517[/C][C]0.6533[/C][C]0.9698[/C][/ROW]
[ROW][C]309[/C][C]628232[/C][C]621865.429[/C][C]542983.2207[/C][C]698789.3216[/C][C]0.4356[/C][C]0.429[/C][C]0.5932[/C][C]0.9563[/C][/ROW]
[ROW][C]310[/C][C]612117[/C][C]611830.3309[/C][C]529739.2222[/C][C]691767.9959[/C][C]0.4972[/C][C]0.3438[/C][C]0.505[/C][C]0.919[/C][/ROW]
[ROW][C]311[/C][C]595404[/C][C]598846.7039[/C][C]513522.6853[/C][C]681796.604[/C][C]0.4676[/C][C]0.3769[/C][C]0.544[/C][C]0.8511[/C][/ROW]
[ROW][C]312[/C][C]597141[/C][C]602964.8402[/C][C]515013.3165[/C][C]688412.1496[/C][C]0.4469[/C][C]0.5688[/C][C]0.5684[/C][C]0.8654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157799&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157799&T=1

As an alternative you can also use a QR Code:

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

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value(H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[288])
276	512238	-	-	-	-	-	-	-
277	519164	-	-	-	-	-	-	-
278	517009	-	-	-	-	-	-	-
279	509933	-	-	-	-	-	-	-
280	509127	-	-	-	-	-	-	-
281	500857	-	-	-	-	-	-	-
282	506971	-	-	-	-	-	-	-
283	569323	-	-	-	-	-	-	-
284	579714	-	-	-	-	-	-	-
285	577992	-	-	-	-	-	-	-
286	565464	-	-	-	-	-	-	-
287	547344	-	-	-	-	-	-	-
288	554788	-	-	-	-	-	-	-
289	562325	560061.5043	549060.1061	571019.8475	0.3428	0.8272	1	0.8272
290	560854	554782.0418	537538.1503	571919.3772	0.2437	0.1942	1	0.4997
291	555332	545699.8106	523583.6557	567638.0786	0.1947	0.0879	0.9993	0.2084
292	543599	541236.7283	515079.9534	567142.9772	0.4291	0.1431	0.9924	0.1526
293	536662	532519.3809	502780.0343	561930.008	0.3912	0.2301	0.9826	0.0689
294	542722	535053.9081	502214.2429	567495.023	0.3216	0.4613	0.9551	0.1166
295	593530	592722.7009	557773.3765	627264.3736	0.4817	0.9977	0.9079	0.9843
296	610763	606532.967	569168.4737	643442.336	0.4111	0.7551	0.9228	0.997
297	612613	603451.3075	563627.077	642756.2671	0.3239	0.3577	0.8979	0.9924
298	611324	592562.1793	550293.3958	634235.7709	0.1888	0.1728	0.8988	0.9622
299	594167	577828.8409	533147.2799	621829.0402	0.2334	0.0678	0.9128	0.8476
300	595454	583075.1359	536392.8704	629020.677	0.2987	0.318	0.8862	0.8862
301	590865	586615.55	535822.3226	636542.7618	0.4338	0.3643	0.8299	0.8943
302	589379	579582.9356	524306.2658	633822.9557	0.3617	0.3418	0.7507	0.8149
303	584428	569461.4987	509822.0584	627874.5176	0.3078	0.252	0.6823	0.6888
304	573100	563141.8732	499438.8825	625431.7057	0.377	0.2515	0.7307	0.6037
305	567456	554210.3009	486569.2548	620234.5094	0.3471	0.2875	0.6988	0.4932
306	569028	554919.5659	483765.3572	624288.4918	0.3451	0.3616	0.6348	0.5015
307	620735	610101.246	537091.4354	681399.3432	0.385	0.8706	0.6756	0.9358
308	628884	625636.7752	549879.526	699597.1944	0.4657	0.5517	0.6533	0.9698
309	628232	621865.429	542983.2207	698789.3216	0.4356	0.429	0.5932	0.9563
310	612117	611830.3309	529739.2222	691767.9959	0.4972	0.3438	0.505	0.919
311	595404	598846.7039	513522.6853	681796.604	0.4676	0.3769	0.544	0.8511
312	597141	602964.8402	515013.3165	688412.1496	0.4469	0.5688	0.5684	0.8654

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
289	0.01	0.004	0	5123412.7512	0	0
290	0.0158	0.0109	0.0075	36868676.8518	20996044.8015	4582.1441
291	0.0205	0.0177	0.0109	92779072.1633	44923720.5888	6702.516
292	0.0244	0.0044	0.0093	5580327.6877	35087872.3635	5923.5017
293	0.0282	0.0078	0.009	17161293.3418	31502556.5592	5612.7138
294	0.0309	0.0143	0.0099	58799633.8668	36052069.4438	6004.3376
295	0.0297	0.0014	0.0086	651731.8281	30994878.3558	5567.3044
296	0.031	0.007	0.0084	17893179.2094	29357165.9625	5418.2254
297	0.0332	0.0152	0.0092	83936609.8488	35421548.6165	5951.6005
298	0.0359	0.0317	0.0114	352005915.4818	67079985.3031	8190.2372
299	0.0389	0.0283	0.013	266935443.5574	85248663.3262	9233.0203
300	0.0402	0.0212	0.0136	153236276.8873	90914297.7896	9534.8989
301	0.0434	0.0072	0.0132	18057825.1284	85309953.7388	9236.3388
302	0.0477	0.0169	0.0134	95962877.912	86070876.894	9277.4391
303	0.0523	0.0263	0.0143	223996160.8237	95265895.8226	9760.425
304	0.0564	0.0177	0.0145	99164289.7253	95509545.4415	9772.8985
305	0.0608	0.0239	0.015	175448545.7409	100211839.5768	10010.5864
306	0.0638	0.0254	0.0156	199047911.88	105702732.4825	10281.1834
307	0.0596	0.0174	0.0157	113076724.7072	106090837.3365	10300.0406
308	0.0603	0.0052	0.0152	10544468.9657	101313518.9179	10065.4617
309	0.0631	0.0102	0.015	40533226.9186	98419219.2989	9920.6461
310	0.0667	5e-04	0.0143	82179.1997	93949353.8399	9692.7475
311	0.0707	-0.0057	0.0139	11852210.3747	90379912.8196	9506.8351
312	0.0723	-0.0097	0.0137	33917115.1638	88027296.2506	9382.2863

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
289 & 0.01 & 0.004 & 0 & 5123412.7512 & 0 & 0 \tabularnewline
290 & 0.0158 & 0.0109 & 0.0075 & 36868676.8518 & 20996044.8015 & 4582.1441 \tabularnewline
291 & 0.0205 & 0.0177 & 0.0109 & 92779072.1633 & 44923720.5888 & 6702.516 \tabularnewline
292 & 0.0244 & 0.0044 & 0.0093 & 5580327.6877 & 35087872.3635 & 5923.5017 \tabularnewline
293 & 0.0282 & 0.0078 & 0.009 & 17161293.3418 & 31502556.5592 & 5612.7138 \tabularnewline
294 & 0.0309 & 0.0143 & 0.0099 & 58799633.8668 & 36052069.4438 & 6004.3376 \tabularnewline
295 & 0.0297 & 0.0014 & 0.0086 & 651731.8281 & 30994878.3558 & 5567.3044 \tabularnewline
296 & 0.031 & 0.007 & 0.0084 & 17893179.2094 & 29357165.9625 & 5418.2254 \tabularnewline
297 & 0.0332 & 0.0152 & 0.0092 & 83936609.8488 & 35421548.6165 & 5951.6005 \tabularnewline
298 & 0.0359 & 0.0317 & 0.0114 & 352005915.4818 & 67079985.3031 & 8190.2372 \tabularnewline
299 & 0.0389 & 0.0283 & 0.013 & 266935443.5574 & 85248663.3262 & 9233.0203 \tabularnewline
300 & 0.0402 & 0.0212 & 0.0136 & 153236276.8873 & 90914297.7896 & 9534.8989 \tabularnewline
301 & 0.0434 & 0.0072 & 0.0132 & 18057825.1284 & 85309953.7388 & 9236.3388 \tabularnewline
302 & 0.0477 & 0.0169 & 0.0134 & 95962877.912 & 86070876.894 & 9277.4391 \tabularnewline
303 & 0.0523 & 0.0263 & 0.0143 & 223996160.8237 & 95265895.8226 & 9760.425 \tabularnewline
304 & 0.0564 & 0.0177 & 0.0145 & 99164289.7253 & 95509545.4415 & 9772.8985 \tabularnewline
305 & 0.0608 & 0.0239 & 0.015 & 175448545.7409 & 100211839.5768 & 10010.5864 \tabularnewline
306 & 0.0638 & 0.0254 & 0.0156 & 199047911.88 & 105702732.4825 & 10281.1834 \tabularnewline
307 & 0.0596 & 0.0174 & 0.0157 & 113076724.7072 & 106090837.3365 & 10300.0406 \tabularnewline
308 & 0.0603 & 0.0052 & 0.0152 & 10544468.9657 & 101313518.9179 & 10065.4617 \tabularnewline
309 & 0.0631 & 0.0102 & 0.015 & 40533226.9186 & 98419219.2989 & 9920.6461 \tabularnewline
310 & 0.0667 & 5e-04 & 0.0143 & 82179.1997 & 93949353.8399 & 9692.7475 \tabularnewline
311 & 0.0707 & -0.0057 & 0.0139 & 11852210.3747 & 90379912.8196 & 9506.8351 \tabularnewline
312 & 0.0723 & -0.0097 & 0.0137 & 33917115.1638 & 88027296.2506 & 9382.2863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157799&T=2

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast Performance[/C][/ROW]
[ROW][C]time[/C][C]% S.E.[/C][C]PE[/C][C]MAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][/ROW]
[ROW][C]289[/C][C]0.01[/C][C]0.004[/C][C]0[/C][C]5123412.7512[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]290[/C][C]0.0158[/C][C]0.0109[/C][C]0.0075[/C][C]36868676.8518[/C][C]20996044.8015[/C][C]4582.1441[/C][/ROW]
[ROW][C]291[/C][C]0.0205[/C][C]0.0177[/C][C]0.0109[/C][C]92779072.1633[/C][C]44923720.5888[/C][C]6702.516[/C][/ROW]
[ROW][C]292[/C][C]0.0244[/C][C]0.0044[/C][C]0.0093[/C][C]5580327.6877[/C][C]35087872.3635[/C][C]5923.5017[/C][/ROW]
[ROW][C]293[/C][C]0.0282[/C][C]0.0078[/C][C]0.009[/C][C]17161293.3418[/C][C]31502556.5592[/C][C]5612.7138[/C][/ROW]
[ROW][C]294[/C][C]0.0309[/C][C]0.0143[/C][C]0.0099[/C][C]58799633.8668[/C][C]36052069.4438[/C][C]6004.3376[/C][/ROW]
[ROW][C]295[/C][C]0.0297[/C][C]0.0014[/C][C]0.0086[/C][C]651731.8281[/C][C]30994878.3558[/C][C]5567.3044[/C][/ROW]
[ROW][C]296[/C][C]0.031[/C][C]0.007[/C][C]0.0084[/C][C]17893179.2094[/C][C]29357165.9625[/C][C]5418.2254[/C][/ROW]
[ROW][C]297[/C][C]0.0332[/C][C]0.0152[/C][C]0.0092[/C][C]83936609.8488[/C][C]35421548.6165[/C][C]5951.6005[/C][/ROW]
[ROW][C]298[/C][C]0.0359[/C][C]0.0317[/C][C]0.0114[/C][C]352005915.4818[/C][C]67079985.3031[/C][C]8190.2372[/C][/ROW]
[ROW][C]299[/C][C]0.0389[/C][C]0.0283[/C][C]0.013[/C][C]266935443.5574[/C][C]85248663.3262[/C][C]9233.0203[/C][/ROW]
[ROW][C]300[/C][C]0.0402[/C][C]0.0212[/C][C]0.0136[/C][C]153236276.8873[/C][C]90914297.7896[/C][C]9534.8989[/C][/ROW]
[ROW][C]301[/C][C]0.0434[/C][C]0.0072[/C][C]0.0132[/C][C]18057825.1284[/C][C]85309953.7388[/C][C]9236.3388[/C][/ROW]
[ROW][C]302[/C][C]0.0477[/C][C]0.0169[/C][C]0.0134[/C][C]95962877.912[/C][C]86070876.894[/C][C]9277.4391[/C][/ROW]
[ROW][C]303[/C][C]0.0523[/C][C]0.0263[/C][C]0.0143[/C][C]223996160.8237[/C][C]95265895.8226[/C][C]9760.425[/C][/ROW]
[ROW][C]304[/C][C]0.0564[/C][C]0.0177[/C][C]0.0145[/C][C]99164289.7253[/C][C]95509545.4415[/C][C]9772.8985[/C][/ROW]
[ROW][C]305[/C][C]0.0608[/C][C]0.0239[/C][C]0.015[/C][C]175448545.7409[/C][C]100211839.5768[/C][C]10010.5864[/C][/ROW]
[ROW][C]306[/C][C]0.0638[/C][C]0.0254[/C][C]0.0156[/C][C]199047911.88[/C][C]105702732.4825[/C][C]10281.1834[/C][/ROW]
[ROW][C]307[/C][C]0.0596[/C][C]0.0174[/C][C]0.0157[/C][C]113076724.7072[/C][C]106090837.3365[/C][C]10300.0406[/C][/ROW]
[ROW][C]308[/C][C]0.0603[/C][C]0.0052[/C][C]0.0152[/C][C]10544468.9657[/C][C]101313518.9179[/C][C]10065.4617[/C][/ROW]
[ROW][C]309[/C][C]0.0631[/C][C]0.0102[/C][C]0.015[/C][C]40533226.9186[/C][C]98419219.2989[/C][C]9920.6461[/C][/ROW]
[ROW][C]310[/C][C]0.0667[/C][C]5e-04[/C][C]0.0143[/C][C]82179.1997[/C][C]93949353.8399[/C][C]9692.7475[/C][/ROW]
[ROW][C]311[/C][C]0.0707[/C][C]-0.0057[/C][C]0.0139[/C][C]11852210.3747[/C][C]90379912.8196[/C][C]9506.8351[/C][/ROW]
[ROW][C]312[/C][C]0.0723[/C][C]-0.0097[/C][C]0.0137[/C][C]33917115.1638[/C][C]88027296.2506[/C][C]9382.2863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157799&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157799&T=2

As an alternative you can also use a QR Code:

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

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
289	0.01	0.004	0	5123412.7512	0	0
290	0.0158	0.0109	0.0075	36868676.8518	20996044.8015	4582.1441
291	0.0205	0.0177	0.0109	92779072.1633	44923720.5888	6702.516
292	0.0244	0.0044	0.0093	5580327.6877	35087872.3635	5923.5017
293	0.0282	0.0078	0.009	17161293.3418	31502556.5592	5612.7138
294	0.0309	0.0143	0.0099	58799633.8668	36052069.4438	6004.3376
295	0.0297	0.0014	0.0086	651731.8281	30994878.3558	5567.3044
296	0.031	0.007	0.0084	17893179.2094	29357165.9625	5418.2254
297	0.0332	0.0152	0.0092	83936609.8488	35421548.6165	5951.6005
298	0.0359	0.0317	0.0114	352005915.4818	67079985.3031	8190.2372
299	0.0389	0.0283	0.013	266935443.5574	85248663.3262	9233.0203
300	0.0402	0.0212	0.0136	153236276.8873	90914297.7896	9534.8989
301	0.0434	0.0072	0.0132	18057825.1284	85309953.7388	9236.3388
302	0.0477	0.0169	0.0134	95962877.912	86070876.894	9277.4391
303	0.0523	0.0263	0.0143	223996160.8237	95265895.8226	9760.425
304	0.0564	0.0177	0.0145	99164289.7253	95509545.4415	9772.8985
305	0.0608	0.0239	0.015	175448545.7409	100211839.5768	10010.5864
306	0.0638	0.0254	0.0156	199047911.88	105702732.4825	10281.1834
307	0.0596	0.0174	0.0157	113076724.7072	106090837.3365	10300.0406
308	0.0603	0.0052	0.0152	10544468.9657	101313518.9179	10065.4617
309	0.0631	0.0102	0.015	40533226.9186	98419219.2989	9920.6461
310	0.0667	5e-04	0.0143	82179.1997	93949353.8399	9692.7475
311	0.0707	-0.0057	0.0139	11852210.3747	90379912.8196	9506.8351
312	0.0723	-0.0097	0.0137	33917115.1638	88027296.2506	9382.2863

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = 24 ; par2 = 1.2 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

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

par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
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) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,par1))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
if (par2 == 0) {
x <- exp(x)
forecast$pred <- exp(forecast$pred)
lb <- exp(lb)
ub <- exp(ub)
}
if (par2 != 0) {
x <- x^(1/par2)
forecast$pred <- forecast$pred^(1/par2)
lb <- lb^(1/par2)
ub <- ub^(1/par2)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file='test1.png')
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type='n',xlim=c(first,lx))
usr <- par('usr')
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
abline(h= (-3:3)*2 , col ='gray', lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
box()
par(opar)
dev.off()
prob.dec <- array(NA, dim=fx)
prob.sdec <- array(NA, dim=fx)
prob.ldec <- array(NA, dim=fx)
prob.pval <- array(NA, dim=fx)
perf.pe <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.mse1 <- array(0, dim=fx)
perf.rmse <- array(0, dim=fx)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
}
perf.mape[1] = abs(perf.pe[1])
perf.mse[1] = abs(perf.se[1])
for (i in 2:fx) {
perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
perf.mape1[i] = perf.mape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
}
perf.rmse = sqrt(perf.mse1)
bitmap(file='test2.png')
plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
dum <- forecast$pred
dum[1:par1] <- x[(nx+1):lx]
lines(dum, lty=1)
lines(ub,lty=3)
lines(lb,lty=3)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'Y[t]',1,header=TRUE)
a<-table.element(a,'F[t]',1,header=TRUE)
a<-table.element(a,'95% LB',1,header=TRUE)
a<-table.element(a,'95% UB',1,header=TRUE)
a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
mylab <- paste('P(F[t]>Y[',nx,sep='')
mylab <- paste(mylab,'])',sep='')
a<-table.element(a,mylab,1,header=TRUE)
a<-table.row.end(a)
for (i in (nx-par5):nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.row.end(a)
}
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(x[nx+i],4))
a<-table.element(a,round(forecast$pred[i],4))
a<-table.element(a,round(lb[i],4))
a<-table.element(a,round(ub[i],4))
a<-table.element(a,round((1-prob.pval[i]),4))
a<-table.element(a,round((1-prob.dec[i]),4))
a<-table.element(a,round((1-prob.sdec[i]),4))
a<-table.element(a,round((1-prob.ldec[i]),4))
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,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'% S.E.',1,header=TRUE)
a<-table.element(a,'PE',1,header=TRUE)
a<-table.element(a,'MAPE',1,header=TRUE)
a<-table.element(a,'Sq.E',1,header=TRUE)
a<-table.element(a,'MSE',1,header=TRUE)
a<-table.element(a,'RMSE',1,header=TRUE)
a<-table.row.end(a)
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(perc.se[i],4))
a<-table.element(a,round(perf.pe[i],4))
a<-table.element(a,round(perf.mape1[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse1[i],4))
a<-table.element(a,round(perf.rmse[i],4))
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