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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Mon, 14 Dec 2009 01:41:55 -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/2009/Dec/14/t12607803480uqacm6apx9olia.htm/, Retrieved Fri, 09 May 2025 23:28:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67440, Retrieved Fri, 09 May 2025 23:28:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

245

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
- R PD    [Multiple Regression] [] [2009-11-19 08:06:13] [639dd97b6eeebe46a3c92d62cb04fb95]
- RMPD        [ARIMA Forecasting] [] [2009-12-14 08:41:55] [2795ec65528c1a16d9df20713e7edc71] [Current]
-   PD          [ARIMA Forecasting] [] [2009-12-19 10:06:44] [ea26ab7ea3bba830cfeb08d06278d52c] 
- R PD            [ARIMA Forecasting] [Arima forecast 6 ...] [2009-12-21 17:12:24] [9dbb467a28ad600d808a4e47d5e0774e] 
-   P               [ARIMA Forecasting] [Arima forecast 12...] [2009-12-21 17:19:37] [9dbb467a28ad600d808a4e47d5e0774e] 
-                     [ARIMA Forecasting] [paper] [2010-12-28 17:28:42] [654616a560d52fe6eb611aa3bbf6b3c7] 
-   P               [ARIMA Forecasting] [Arima forecast 24...] [2009-12-21 17:25:53] [9dbb467a28ad600d808a4e47d5e0774e] 
-                     [ARIMA Forecasting] [paper] [2010-12-28 17:32:12] [654616a560d52fe6eb611aa3bbf6b3c7] 
-                   [ARIMA Forecasting] [paper] [2010-12-28 17:26:19] [654616a560d52fe6eb611aa3bbf6b3c7] 
-   PD          [ARIMA Forecasting] [] [2009-12-19 10:31:03] [ea26ab7ea3bba830cfeb08d06278d52c] 
-   PD          [ARIMA Forecasting] [] [2009-12-19 10:32:11] [ea26ab7ea3bba830cfeb08d06278d52c] 

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Dataseries X:

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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

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67440&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67440&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67440&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	'Gwilym Jenkins' @ 72.249.127.135

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[50])
38	517	-	-	-	-	-	-	-
39	508	-	-	-	-	-	-	-
40	493	-	-	-	-	-	-	-
41	490	-	-	-	-	-	-	-
42	469	-	-	-	-	-	-	-
43	478	-	-	-	-	-	-	-
44	528	-	-	-	-	-	-	-
45	534	-	-	-	-	-	-	-
46	518	-	-	-	-	-	-	-
47	506	-	-	-	-	-	-	-
48	502	-	-	-	-	-	-	-
49	516	-	-	-	-	-	-	-
50	528	-	-	-	-	-	-	-
51	533	523.6752	507.0722	540.2782	0.1355	0.3048	0.9679	0.3048
52	536	512.5055	489.1823	535.8287	0.0242	0.0425	0.9494	0.0964
53	537	512.4241	482.3597	542.4885	0.0546	0.0621	0.9281	0.1549
54	524	493.1462	455.271	531.0214	0.0552	0.0116	0.8943	0.0356
55	536	503.5318	459.048	548.0156	0.0763	0.1836	0.8697	0.1405
56	587	554.5084	503.6734	605.3435	0.1051	0.7623	0.8466	0.8466
57	597	561.1401	504.2024	618.0779	0.1085	0.1867	0.8249	0.873
58	581	545.629	483.0758	608.1821	0.1339	0.0537	0.8067	0.7097
59	564	533.9641	466.076	601.8522	0.1929	0.0872	0.7903	0.5684
60	558	530.1931	457.2531	603.133	0.2275	0.1818	0.7757	0.5235

\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[50]) \tabularnewline
38 & 517 & - & - & - & - & - & - & - \tabularnewline
39 & 508 & - & - & - & - & - & - & - \tabularnewline
40 & 493 & - & - & - & - & - & - & - \tabularnewline
41 & 490 & - & - & - & - & - & - & - \tabularnewline
42 & 469 & - & - & - & - & - & - & - \tabularnewline
43 & 478 & - & - & - & - & - & - & - \tabularnewline
44 & 528 & - & - & - & - & - & - & - \tabularnewline
45 & 534 & - & - & - & - & - & - & - \tabularnewline
46 & 518 & - & - & - & - & - & - & - \tabularnewline
47 & 506 & - & - & - & - & - & - & - \tabularnewline
48 & 502 & - & - & - & - & - & - & - \tabularnewline
49 & 516 & - & - & - & - & - & - & - \tabularnewline
50 & 528 & - & - & - & - & - & - & - \tabularnewline
51 & 533 & 523.6752 & 507.0722 & 540.2782 & 0.1355 & 0.3048 & 0.9679 & 0.3048 \tabularnewline
52 & 536 & 512.5055 & 489.1823 & 535.8287 & 0.0242 & 0.0425 & 0.9494 & 0.0964 \tabularnewline
53 & 537 & 512.4241 & 482.3597 & 542.4885 & 0.0546 & 0.0621 & 0.9281 & 0.1549 \tabularnewline
54 & 524 & 493.1462 & 455.271 & 531.0214 & 0.0552 & 0.0116 & 0.8943 & 0.0356 \tabularnewline
55 & 536 & 503.5318 & 459.048 & 548.0156 & 0.0763 & 0.1836 & 0.8697 & 0.1405 \tabularnewline
56 & 587 & 554.5084 & 503.6734 & 605.3435 & 0.1051 & 0.7623 & 0.8466 & 0.8466 \tabularnewline
57 & 597 & 561.1401 & 504.2024 & 618.0779 & 0.1085 & 0.1867 & 0.8249 & 0.873 \tabularnewline
58 & 581 & 545.629 & 483.0758 & 608.1821 & 0.1339 & 0.0537 & 0.8067 & 0.7097 \tabularnewline
59 & 564 & 533.9641 & 466.076 & 601.8522 & 0.1929 & 0.0872 & 0.7903 & 0.5684 \tabularnewline
60 & 558 & 530.1931 & 457.2531 & 603.133 & 0.2275 & 0.1818 & 0.7757 & 0.5235 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67440&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[50])[/C][/ROW]
[ROW][C]38[/C][C]517[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]508[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]493[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]490[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]469[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]478[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]528[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]534[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]518[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]506[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]502[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]516[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]528[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]533[/C][C]523.6752[/C][C]507.0722[/C][C]540.2782[/C][C]0.1355[/C][C]0.3048[/C][C]0.9679[/C][C]0.3048[/C][/ROW]
[ROW][C]52[/C][C]536[/C][C]512.5055[/C][C]489.1823[/C][C]535.8287[/C][C]0.0242[/C][C]0.0425[/C][C]0.9494[/C][C]0.0964[/C][/ROW]
[ROW][C]53[/C][C]537[/C][C]512.4241[/C][C]482.3597[/C][C]542.4885[/C][C]0.0546[/C][C]0.0621[/C][C]0.9281[/C][C]0.1549[/C][/ROW]
[ROW][C]54[/C][C]524[/C][C]493.1462[/C][C]455.271[/C][C]531.0214[/C][C]0.0552[/C][C]0.0116[/C][C]0.8943[/C][C]0.0356[/C][/ROW]
[ROW][C]55[/C][C]536[/C][C]503.5318[/C][C]459.048[/C][C]548.0156[/C][C]0.0763[/C][C]0.1836[/C][C]0.8697[/C][C]0.1405[/C][/ROW]
[ROW][C]56[/C][C]587[/C][C]554.5084[/C][C]503.6734[/C][C]605.3435[/C][C]0.1051[/C][C]0.7623[/C][C]0.8466[/C][C]0.8466[/C][/ROW]
[ROW][C]57[/C][C]597[/C][C]561.1401[/C][C]504.2024[/C][C]618.0779[/C][C]0.1085[/C][C]0.1867[/C][C]0.8249[/C][C]0.873[/C][/ROW]
[ROW][C]58[/C][C]581[/C][C]545.629[/C][C]483.0758[/C][C]608.1821[/C][C]0.1339[/C][C]0.0537[/C][C]0.8067[/C][C]0.7097[/C][/ROW]
[ROW][C]59[/C][C]564[/C][C]533.9641[/C][C]466.076[/C][C]601.8522[/C][C]0.1929[/C][C]0.0872[/C][C]0.7903[/C][C]0.5684[/C][/ROW]
[ROW][C]60[/C][C]558[/C][C]530.1931[/C][C]457.2531[/C][C]603.133[/C][C]0.2275[/C][C]0.1818[/C][C]0.7757[/C][C]0.5235[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67440&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67440&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[50])
38	517	-	-	-	-	-	-	-
39	508	-	-	-	-	-	-	-
40	493	-	-	-	-	-	-	-
41	490	-	-	-	-	-	-	-
42	469	-	-	-	-	-	-	-
43	478	-	-	-	-	-	-	-
44	528	-	-	-	-	-	-	-
45	534	-	-	-	-	-	-	-
46	518	-	-	-	-	-	-	-
47	506	-	-	-	-	-	-	-
48	502	-	-	-	-	-	-	-
49	516	-	-	-	-	-	-	-
50	528	-	-	-	-	-	-	-
51	533	523.6752	507.0722	540.2782	0.1355	0.3048	0.9679	0.3048
52	536	512.5055	489.1823	535.8287	0.0242	0.0425	0.9494	0.0964
53	537	512.4241	482.3597	542.4885	0.0546	0.0621	0.9281	0.1549
54	524	493.1462	455.271	531.0214	0.0552	0.0116	0.8943	0.0356
55	536	503.5318	459.048	548.0156	0.0763	0.1836	0.8697	0.1405
56	587	554.5084	503.6734	605.3435	0.1051	0.7623	0.8466	0.8466
57	597	561.1401	504.2024	618.0779	0.1085	0.1867	0.8249	0.873
58	581	545.629	483.0758	608.1821	0.1339	0.0537	0.8067	0.7097
59	564	533.9641	466.076	601.8522	0.1929	0.0872	0.7903	0.5684
60	558	530.1931	457.2531	603.133	0.2275	0.1818	0.7757	0.5235

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
51	0.0162	0.0178	0	86.9515	0	0
52	0.0232	0.0458	0.0318	551.9906	319.471	17.8738
53	0.0299	0.048	0.0372	603.9759	414.306	20.3545
54	0.0392	0.0626	0.0435	951.9586	548.7192	23.4248
55	0.0451	0.0645	0.0477	1054.1833	649.812	25.4914
56	0.0468	0.0586	0.0495	1055.7019	717.4603	26.7854
57	0.0518	0.0639	0.0516	1285.929	798.6701	28.2608
58	0.0585	0.0648	0.0532	1251.111	855.2252	29.2442
59	0.0649	0.0563	0.0536	902.1577	860.4399	29.3333
60	0.0702	0.0524	0.0535	773.2257	851.7185	29.1842

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
51 & 0.0162 & 0.0178 & 0 & 86.9515 & 0 & 0 \tabularnewline
52 & 0.0232 & 0.0458 & 0.0318 & 551.9906 & 319.471 & 17.8738 \tabularnewline
53 & 0.0299 & 0.048 & 0.0372 & 603.9759 & 414.306 & 20.3545 \tabularnewline
54 & 0.0392 & 0.0626 & 0.0435 & 951.9586 & 548.7192 & 23.4248 \tabularnewline
55 & 0.0451 & 0.0645 & 0.0477 & 1054.1833 & 649.812 & 25.4914 \tabularnewline
56 & 0.0468 & 0.0586 & 0.0495 & 1055.7019 & 717.4603 & 26.7854 \tabularnewline
57 & 0.0518 & 0.0639 & 0.0516 & 1285.929 & 798.6701 & 28.2608 \tabularnewline
58 & 0.0585 & 0.0648 & 0.0532 & 1251.111 & 855.2252 & 29.2442 \tabularnewline
59 & 0.0649 & 0.0563 & 0.0536 & 902.1577 & 860.4399 & 29.3333 \tabularnewline
60 & 0.0702 & 0.0524 & 0.0535 & 773.2257 & 851.7185 & 29.1842 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67440&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]51[/C][C]0.0162[/C][C]0.0178[/C][C]0[/C][C]86.9515[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]52[/C][C]0.0232[/C][C]0.0458[/C][C]0.0318[/C][C]551.9906[/C][C]319.471[/C][C]17.8738[/C][/ROW]
[ROW][C]53[/C][C]0.0299[/C][C]0.048[/C][C]0.0372[/C][C]603.9759[/C][C]414.306[/C][C]20.3545[/C][/ROW]
[ROW][C]54[/C][C]0.0392[/C][C]0.0626[/C][C]0.0435[/C][C]951.9586[/C][C]548.7192[/C][C]23.4248[/C][/ROW]
[ROW][C]55[/C][C]0.0451[/C][C]0.0645[/C][C]0.0477[/C][C]1054.1833[/C][C]649.812[/C][C]25.4914[/C][/ROW]
[ROW][C]56[/C][C]0.0468[/C][C]0.0586[/C][C]0.0495[/C][C]1055.7019[/C][C]717.4603[/C][C]26.7854[/C][/ROW]
[ROW][C]57[/C][C]0.0518[/C][C]0.0639[/C][C]0.0516[/C][C]1285.929[/C][C]798.6701[/C][C]28.2608[/C][/ROW]
[ROW][C]58[/C][C]0.0585[/C][C]0.0648[/C][C]0.0532[/C][C]1251.111[/C][C]855.2252[/C][C]29.2442[/C][/ROW]
[ROW][C]59[/C][C]0.0649[/C][C]0.0563[/C][C]0.0536[/C][C]902.1577[/C][C]860.4399[/C][C]29.3333[/C][/ROW]
[ROW][C]60[/C][C]0.0702[/C][C]0.0524[/C][C]0.0535[/C][C]773.2257[/C][C]851.7185[/C][C]29.1842[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67440&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67440&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
51	0.0162	0.0178	0	86.9515	0	0
52	0.0232	0.0458	0.0318	551.9906	319.471	17.8738
53	0.0299	0.048	0.0372	603.9759	414.306	20.3545
54	0.0392	0.0626	0.0435	951.9586	548.7192	23.4248
55	0.0451	0.0645	0.0477	1054.1833	649.812	25.4914
56	0.0468	0.0586	0.0495	1055.7019	717.4603	26.7854
57	0.0518	0.0639	0.0516	1285.929	798.6701	28.2608
58	0.0585	0.0648	0.0532	1251.111	855.2252	29.2442
59	0.0649	0.0563	0.0536	902.1577	860.4399	29.3333
60	0.0702	0.0524	0.0535	773.2257	851.7185	29.1842

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 10 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 10 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; 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