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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Mon, 29 Nov 2010 21:10:32 +0000

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/2010/Nov/29/t1291065445zyl6wfqbjrk6amo.htm/, Retrieved Tue, 07 May 2024 00:28:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103130, Retrieved Tue, 07 May 2024 00:28:47 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

108

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

-     [Univariate Data Series] [web traffic] [2010-10-19 15:13:07] [b98453cac15ba1066b407e146608df68]
- RMP   [Variance Reduction Matrix] [Traffic] [2010-11-29 09:57:15] [b98453cac15ba1066b407e146608df68]
- RM      [Standard Deviation-Mean Plot] [Traffic] [2010-11-29 11:05:08] [b98453cac15ba1066b407e146608df68]
- RMP         [ARIMA Forecasting] [Traffic] [2010-11-29 21:10:32] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
- R PD          [ARIMA Forecasting] [Workshop 9 - Arim...] [2010-12-03 14:58:35] [6f0e7a2d1a07390e3505a2db8288f975] 
- R PD          [ARIMA Forecasting] [] [2011-12-06 10:39:07] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- R               [ARIMA Forecasting] [] [2011-12-06 10:40:07] [aba4febe8a2e49e81bdc61a6c01f5c21] 
-   PD            [ARIMA Forecasting] [] [2011-12-20 15:47:34] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- R                 [ARIMA Forecasting] [ARIMA Forecasting CV] [2011-12-20 15:48:10] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RMPD                [Kendall tau Correlation Matrix] [Paper Pearson Cor...] [2011-12-21 09:24:40] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RMPD                [Kendall tau Correlation Matrix] [Paper Kendall Tau...] [2011-12-21 09:28:32] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RMPD                [Multiple Regression] [Paper Multiple Re...] [2011-12-21 09:30:56] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RMPD                [Recursive Partitioning (Regression Trees)] [Paper Recursive p...] [2011-12-21 09:38:44] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RMPD                [(Partial) Autocorrelation Function] [Paper ACF] [2011-12-21 09:45:21] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RMPD                [Spectral Analysis] [Paper spectral an...] [2011-12-21 09:47:42] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RMPD                [Variance Reduction Matrix] [Paper variance re...] [2011-12-21 09:52:02] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RMPD                [Standard Deviation-Mean Plot] [Paper standard de...] [2011-12-21 09:54:23] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RMPD                [ARIMA Backward Selection] [paper arima forec...] [2011-12-21 10:17:35] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RMPD                [ARIMA Backward Selection] [paper arima backw...] [2011-12-21 10:36:30] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RM                    [ARIMA Forecasting] [paper arima forec...] [2011-12-21 10:55:20] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RM D                  [(Partial) Autocorrelation Function] [Paper ACF wisselk...] [2011-12-21 11:30:33] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RM D                  [Decomposition by Loess] [Paper Decompositi...] [2011-12-21 11:37:38] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RM D                  [Decomposition by Loess] [Paper Decompositi...] [2011-12-21 11:44:07] [aba4febe8a2e49e81bdc61a6c01f5c21] 
- RM D                  [Decomposition by Loess] [Paper Decompositi...] [2011-12-21 11:45:20] [aba4febe8a2e49e81bdc61a6c01f5c21] 
-   PD          [ARIMA Forecasting] [WS IX-aantal over...] [2011-12-06 20:52:36] [74be16979710d4c4e7c6647856088456] 
-   PD            [ARIMA Forecasting] [paper voorspellin...] [2011-12-22 11:42:00] [7c680a04865e75aa8ab422cdbfd97ac3] 
- R  D          [ARIMA Forecasting] [forecast] [2011-12-07 12:48:05] [6bdab4f5b22620afa7d9dc512ad4e377] 
- RMP           [ARIMA Backward Selection] [] [2012-11-22 21:08:01] [83c7ccdb194e46f99f0902896e3c3ab1] 
- R P             [ARIMA Backward Selection] [] [2012-11-23 15:12:50] [83c7ccdb194e46f99f0902896e3c3ab1] 

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Dataseries X:

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Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103130&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]2 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=103130&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103130&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	2 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[340])
328	15300578	-	-	-	-	-	-	-
329	10623864.0000000	-	-	-	-	-	-	-
330	6880178	-	-	-	-	-	-	-
331	29947357	-	-	-	-	-	-	-
332	18611399.0	-	-	-	-	-	-	-
333	42432604	-	-	-	-	-	-	-
334	20208278.0000000	-	-	-	-	-	-	-
335	14004392	-	-	-	-	-	-	-
336	25737765	-	-	-	-	-	-	-
337	16735738	-	-	-	-	-	-	-
338	22450825.0000000	-	-	-	-	-	-	-
339	6880840	-	-	-	-	-	-	-
340	8510379	-	-	-	-	-	-	-
341	8182481	11693131.9586	3131846.3587	43657740.3039	0.4148	0.5774	0.5261	0.5774
342	10948683	12426978.1668	2950745.1494	52335860.4491	0.4711	0.5826	0.6073	0.5763
343	4805277	13541200.9968	3020952.6413	60697450.8402	0.3583	0.5429	0.2476	0.5828
344	2589229	13522341.8863	2884189.0524	63398663.1143	0.3337	0.634	0.4207	0.5781
345	5658407	13663368.8126	2796433.548	66759193.1315	0.3838	0.6587	0.1441	0.5754
346	12862611	11542122.072	2288347.2294	58216943.7446	0.4779	0.5976	0.358	0.5507
347	5666188	11495463.8215	2190752.6643	60319766.1815	0.4075	0.4781	0.4599	0.5477
348	6875556	11956246.5342	2090244.871	68389992.5647	0.43	0.5865	0.3161	0.5476
349	7098766	12207337.8022	2000415.8398	74494059.309	0.4361	0.5666	0.4433	0.5463
350	36083309	12420143.3157	1927810.9088	80018200.5834	0.2463	0.5613	0.3856	0.5451
351	10200330	12532090.0245	1852677.653	84770969.2664	0.4748	0.2614	0.5609	0.5434
352	7784976	12534264.3316	1769956.1648	88763657.234	0.4514	0.5239	0.5412	0.5412

\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[340]) \tabularnewline
328 & 15300578 & - & - & - & - & - & - & - \tabularnewline
329 & 10623864.0000000 & - & - & - & - & - & - & - \tabularnewline
330 & 6880178 & - & - & - & - & - & - & - \tabularnewline
331 & 29947357 & - & - & - & - & - & - & - \tabularnewline
332 & 18611399.0 & - & - & - & - & - & - & - \tabularnewline
333 & 42432604 & - & - & - & - & - & - & - \tabularnewline
334 & 20208278.0000000 & - & - & - & - & - & - & - \tabularnewline
335 & 14004392 & - & - & - & - & - & - & - \tabularnewline
336 & 25737765 & - & - & - & - & - & - & - \tabularnewline
337 & 16735738 & - & - & - & - & - & - & - \tabularnewline
338 & 22450825.0000000 & - & - & - & - & - & - & - \tabularnewline
339 & 6880840 & - & - & - & - & - & - & - \tabularnewline
340 & 8510379 & - & - & - & - & - & - & - \tabularnewline
341 & 8182481 & 11693131.9586 & 3131846.3587 & 43657740.3039 & 0.4148 & 0.5774 & 0.5261 & 0.5774 \tabularnewline
342 & 10948683 & 12426978.1668 & 2950745.1494 & 52335860.4491 & 0.4711 & 0.5826 & 0.6073 & 0.5763 \tabularnewline
343 & 4805277 & 13541200.9968 & 3020952.6413 & 60697450.8402 & 0.3583 & 0.5429 & 0.2476 & 0.5828 \tabularnewline
344 & 2589229 & 13522341.8863 & 2884189.0524 & 63398663.1143 & 0.3337 & 0.634 & 0.4207 & 0.5781 \tabularnewline
345 & 5658407 & 13663368.8126 & 2796433.548 & 66759193.1315 & 0.3838 & 0.6587 & 0.1441 & 0.5754 \tabularnewline
346 & 12862611 & 11542122.072 & 2288347.2294 & 58216943.7446 & 0.4779 & 0.5976 & 0.358 & 0.5507 \tabularnewline
347 & 5666188 & 11495463.8215 & 2190752.6643 & 60319766.1815 & 0.4075 & 0.4781 & 0.4599 & 0.5477 \tabularnewline
348 & 6875556 & 11956246.5342 & 2090244.871 & 68389992.5647 & 0.43 & 0.5865 & 0.3161 & 0.5476 \tabularnewline
349 & 7098766 & 12207337.8022 & 2000415.8398 & 74494059.309 & 0.4361 & 0.5666 & 0.4433 & 0.5463 \tabularnewline
350 & 36083309 & 12420143.3157 & 1927810.9088 & 80018200.5834 & 0.2463 & 0.5613 & 0.3856 & 0.5451 \tabularnewline
351 & 10200330 & 12532090.0245 & 1852677.653 & 84770969.2664 & 0.4748 & 0.2614 & 0.5609 & 0.5434 \tabularnewline
352 & 7784976 & 12534264.3316 & 1769956.1648 & 88763657.234 & 0.4514 & 0.5239 & 0.5412 & 0.5412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103130&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[340])[/C][/ROW]
[ROW][C]328[/C][C]15300578[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]329[/C][C]10623864.0000000[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]330[/C][C]6880178[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]331[/C][C]29947357[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]332[/C][C]18611399.0[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]333[/C][C]42432604[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]334[/C][C]20208278.0000000[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]335[/C][C]14004392[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]336[/C][C]25737765[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]337[/C][C]16735738[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]338[/C][C]22450825.0000000[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]339[/C][C]6880840[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]340[/C][C]8510379[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]341[/C][C]8182481[/C][C]11693131.9586[/C][C]3131846.3587[/C][C]43657740.3039[/C][C]0.4148[/C][C]0.5774[/C][C]0.5261[/C][C]0.5774[/C][/ROW]
[ROW][C]342[/C][C]10948683[/C][C]12426978.1668[/C][C]2950745.1494[/C][C]52335860.4491[/C][C]0.4711[/C][C]0.5826[/C][C]0.6073[/C][C]0.5763[/C][/ROW]
[ROW][C]343[/C][C]4805277[/C][C]13541200.9968[/C][C]3020952.6413[/C][C]60697450.8402[/C][C]0.3583[/C][C]0.5429[/C][C]0.2476[/C][C]0.5828[/C][/ROW]
[ROW][C]344[/C][C]2589229[/C][C]13522341.8863[/C][C]2884189.0524[/C][C]63398663.1143[/C][C]0.3337[/C][C]0.634[/C][C]0.4207[/C][C]0.5781[/C][/ROW]
[ROW][C]345[/C][C]5658407[/C][C]13663368.8126[/C][C]2796433.548[/C][C]66759193.1315[/C][C]0.3838[/C][C]0.6587[/C][C]0.1441[/C][C]0.5754[/C][/ROW]
[ROW][C]346[/C][C]12862611[/C][C]11542122.072[/C][C]2288347.2294[/C][C]58216943.7446[/C][C]0.4779[/C][C]0.5976[/C][C]0.358[/C][C]0.5507[/C][/ROW]
[ROW][C]347[/C][C]5666188[/C][C]11495463.8215[/C][C]2190752.6643[/C][C]60319766.1815[/C][C]0.4075[/C][C]0.4781[/C][C]0.4599[/C][C]0.5477[/C][/ROW]
[ROW][C]348[/C][C]6875556[/C][C]11956246.5342[/C][C]2090244.871[/C][C]68389992.5647[/C][C]0.43[/C][C]0.5865[/C][C]0.3161[/C][C]0.5476[/C][/ROW]
[ROW][C]349[/C][C]7098766[/C][C]12207337.8022[/C][C]2000415.8398[/C][C]74494059.309[/C][C]0.4361[/C][C]0.5666[/C][C]0.4433[/C][C]0.5463[/C][/ROW]
[ROW][C]350[/C][C]36083309[/C][C]12420143.3157[/C][C]1927810.9088[/C][C]80018200.5834[/C][C]0.2463[/C][C]0.5613[/C][C]0.3856[/C][C]0.5451[/C][/ROW]
[ROW][C]351[/C][C]10200330[/C][C]12532090.0245[/C][C]1852677.653[/C][C]84770969.2664[/C][C]0.4748[/C][C]0.2614[/C][C]0.5609[/C][C]0.5434[/C][/ROW]
[ROW][C]352[/C][C]7784976[/C][C]12534264.3316[/C][C]1769956.1648[/C][C]88763657.234[/C][C]0.4514[/C][C]0.5239[/C][C]0.5412[/C][C]0.5412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103130&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103130&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[340])
328	15300578	-	-	-	-	-	-	-
329	10623864.0000000	-	-	-	-	-	-	-
330	6880178	-	-	-	-	-	-	-
331	29947357	-	-	-	-	-	-	-
332	18611399.0	-	-	-	-	-	-	-
333	42432604	-	-	-	-	-	-	-
334	20208278.0000000	-	-	-	-	-	-	-
335	14004392	-	-	-	-	-	-	-
336	25737765	-	-	-	-	-	-	-
337	16735738	-	-	-	-	-	-	-
338	22450825.0000000	-	-	-	-	-	-	-
339	6880840	-	-	-	-	-	-	-
340	8510379	-	-	-	-	-	-	-
341	8182481	11693131.9586	3131846.3587	43657740.3039	0.4148	0.5774	0.5261	0.5774
342	10948683	12426978.1668	2950745.1494	52335860.4491	0.4711	0.5826	0.6073	0.5763
343	4805277	13541200.9968	3020952.6413	60697450.8402	0.3583	0.5429	0.2476	0.5828
344	2589229	13522341.8863	2884189.0524	63398663.1143	0.3337	0.634	0.4207	0.5781
345	5658407	13663368.8126	2796433.548	66759193.1315	0.3838	0.6587	0.1441	0.5754
346	12862611	11542122.072	2288347.2294	58216943.7446	0.4779	0.5976	0.358	0.5507
347	5666188	11495463.8215	2190752.6643	60319766.1815	0.4075	0.4781	0.4599	0.5477
348	6875556	11956246.5342	2090244.871	68389992.5647	0.43	0.5865	0.3161	0.5476
349	7098766	12207337.8022	2000415.8398	74494059.309	0.4361	0.5666	0.4433	0.5463
350	36083309	12420143.3157	1927810.9088	80018200.5834	0.2463	0.5613	0.3856	0.5451
351	10200330	12532090.0245	1852677.653	84770969.2664	0.4748	0.2614	0.5609	0.5434
352	7784976	12534264.3316	1769956.1648	88763657.234	0.4514	0.5239	0.5412	0.5412

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
341	1.3947	-0.3002	0	12324670153042.0	0	0
342	1.6385	-0.119	0.2096	2185356600244.08	7255013376643.06	2693513.2034
343	1.7767	-0.6451	0.3548	76316368078589.5	30275464943958.5	5502314.5079
344	1.8819	-0.8085	0.4682	119532957384958	52589838054208.5	7251885.138
345	1.9827	-0.5859	0.4917	64079413621018.8	54887753167570.6	7408626.9421
346	2.0632	0.1144	0.4289	1743691009010.13	46030409474477.2	6784571.4289
347	2.167	-0.5071	0.44	33980456602633.4	44308987635642.4	6656499.6534
348	2.4082	-0.4249	0.4381	25813416304293.6	41997041219223.8	6480512.4195
349	2.6033	-0.4185	0.436	26097505857838.2	40230426179069.8	6342745.9494
350	2.7768	1.9052	0.5829	559945410200786	92201924581241.4	9602183.3237
351	2.941	-0.1861	0.5468	5437104811913.68	84314213693120.7	9182277.1518
352	3.1029	-0.3789	0.5328	22555739656402.6	79167674190060.9	8897621.8278

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
341 & 1.3947 & -0.3002 & 0 & 12324670153042.0 & 0 & 0 \tabularnewline
342 & 1.6385 & -0.119 & 0.2096 & 2185356600244.08 & 7255013376643.06 & 2693513.2034 \tabularnewline
343 & 1.7767 & -0.6451 & 0.3548 & 76316368078589.5 & 30275464943958.5 & 5502314.5079 \tabularnewline
344 & 1.8819 & -0.8085 & 0.4682 & 119532957384958 & 52589838054208.5 & 7251885.138 \tabularnewline
345 & 1.9827 & -0.5859 & 0.4917 & 64079413621018.8 & 54887753167570.6 & 7408626.9421 \tabularnewline
346 & 2.0632 & 0.1144 & 0.4289 & 1743691009010.13 & 46030409474477.2 & 6784571.4289 \tabularnewline
347 & 2.167 & -0.5071 & 0.44 & 33980456602633.4 & 44308987635642.4 & 6656499.6534 \tabularnewline
348 & 2.4082 & -0.4249 & 0.4381 & 25813416304293.6 & 41997041219223.8 & 6480512.4195 \tabularnewline
349 & 2.6033 & -0.4185 & 0.436 & 26097505857838.2 & 40230426179069.8 & 6342745.9494 \tabularnewline
350 & 2.7768 & 1.9052 & 0.5829 & 559945410200786 & 92201924581241.4 & 9602183.3237 \tabularnewline
351 & 2.941 & -0.1861 & 0.5468 & 5437104811913.68 & 84314213693120.7 & 9182277.1518 \tabularnewline
352 & 3.1029 & -0.3789 & 0.5328 & 22555739656402.6 & 79167674190060.9 & 8897621.8278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103130&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]341[/C][C]1.3947[/C][C]-0.3002[/C][C]0[/C][C]12324670153042.0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]342[/C][C]1.6385[/C][C]-0.119[/C][C]0.2096[/C][C]2185356600244.08[/C][C]7255013376643.06[/C][C]2693513.2034[/C][/ROW]
[ROW][C]343[/C][C]1.7767[/C][C]-0.6451[/C][C]0.3548[/C][C]76316368078589.5[/C][C]30275464943958.5[/C][C]5502314.5079[/C][/ROW]
[ROW][C]344[/C][C]1.8819[/C][C]-0.8085[/C][C]0.4682[/C][C]119532957384958[/C][C]52589838054208.5[/C][C]7251885.138[/C][/ROW]
[ROW][C]345[/C][C]1.9827[/C][C]-0.5859[/C][C]0.4917[/C][C]64079413621018.8[/C][C]54887753167570.6[/C][C]7408626.9421[/C][/ROW]
[ROW][C]346[/C][C]2.0632[/C][C]0.1144[/C][C]0.4289[/C][C]1743691009010.13[/C][C]46030409474477.2[/C][C]6784571.4289[/C][/ROW]
[ROW][C]347[/C][C]2.167[/C][C]-0.5071[/C][C]0.44[/C][C]33980456602633.4[/C][C]44308987635642.4[/C][C]6656499.6534[/C][/ROW]
[ROW][C]348[/C][C]2.4082[/C][C]-0.4249[/C][C]0.4381[/C][C]25813416304293.6[/C][C]41997041219223.8[/C][C]6480512.4195[/C][/ROW]
[ROW][C]349[/C][C]2.6033[/C][C]-0.4185[/C][C]0.436[/C][C]26097505857838.2[/C][C]40230426179069.8[/C][C]6342745.9494[/C][/ROW]
[ROW][C]350[/C][C]2.7768[/C][C]1.9052[/C][C]0.5829[/C][C]559945410200786[/C][C]92201924581241.4[/C][C]9602183.3237[/C][/ROW]
[ROW][C]351[/C][C]2.941[/C][C]-0.1861[/C][C]0.5468[/C][C]5437104811913.68[/C][C]84314213693120.7[/C][C]9182277.1518[/C][/ROW]
[ROW][C]352[/C][C]3.1029[/C][C]-0.3789[/C][C]0.5328[/C][C]22555739656402.6[/C][C]79167674190060.9[/C][C]8897621.8278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103130&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103130&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
341	1.3947	-0.3002	0	12324670153042.0	0	0
342	1.6385	-0.119	0.2096	2185356600244.08	7255013376643.06	2693513.2034
343	1.7767	-0.6451	0.3548	76316368078589.5	30275464943958.5	5502314.5079
344	1.8819	-0.8085	0.4682	119532957384958	52589838054208.5	7251885.138
345	1.9827	-0.5859	0.4917	64079413621018.8	54887753167570.6	7408626.9421
346	2.0632	0.1144	0.4289	1743691009010.13	46030409474477.2	6784571.4289
347	2.167	-0.5071	0.44	33980456602633.4	44308987635642.4	6656499.6534
348	2.4082	-0.4249	0.4381	25813416304293.6	41997041219223.8	6480512.4195
349	2.6033	-0.4185	0.436	26097505857838.2	40230426179069.8	6342745.9494
350	2.7768	1.9052	0.5829	559945410200786	92201924581241.4	9602183.3237
351	2.941	-0.1861	0.5468	5437104811913.68	84314213693120.7	9182277.1518
352	3.1029	-0.3789	0.5328	22555739656402.6	79167674190060.9	8897621.8278

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; 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 <- 6 #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