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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimaforecasting.wasp
Title produced by softwareARIMA Forecasting
Date of computationSun, 14 Dec 2008 08:56:40 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/14/t1229270248y8itrq4t20qpcg5.htm/, Retrieved Wed, 15 May 2024 21:54:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33448, Retrieved Wed, 15 May 2024 21:54:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact237

Tree of Dependent Computations

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]
F RMPD  [Cross Correlation Function] [Q7 - zonder trans...] [2008-12-01 20:04:13] [299afd6311e4c20059ea2f05c8dd029d]
F RM D    [Variance Reduction Matrix] [Q8] [2008-12-01 20:20:44] [299afd6311e4c20059ea2f05c8dd029d]
F    D      [Variance Reduction Matrix] [Q8 - 2] [2008-12-01 20:25:07] [299afd6311e4c20059ea2f05c8dd029d]
F RM D        [Standard Deviation-Mean Plot] [Deel 2: Step 1] [2008-12-08 20:09:35] [299afd6311e4c20059ea2f05c8dd029d]
F RM D          [ARIMA Backward Selection] [Deel 2: Step 5] [2008-12-08 20:35:27] [299afd6311e4c20059ea2f05c8dd029d]
F RMP               [ARIMA Forecasting] [Uitvoer vanuit Be...] [2008-12-14 15:56:40] [5e2b1e7aa808f9f0d23fd35605d4968f] [Current]
- RMPD                [ARIMA Forecasting] [Arima Forecasting] [2010-12-28 19:01:32] [74be16979710d4c4e7c6647856088456]
Feedback Forum
2008-12-23 08:12:16 [Jeroen Michel] [reply] 
step 1:
Je hebt de vraag zeer uitgebreid geanalyseerd. Hier is opmerkelijk weinig aan toe te voegen.

Uit de tijdreeks moeten we kunnen stellen of de voorspelling al dan niet tussen de waarden ligt dankzij de betrouwbaarheidsintervallen 95% LB (benedengrens) en 95% UB (bovengrens). Dit is slechts indien de omstandigheden blijven zoals ze waren. We kunnen hier tevens ook bepalen of we met toevalligheid te maken hebben aangezien de P-waarde dit aanduidt. Deze P-waarde gaat van de nullhypothese uit, met andere woorden dat de voorspelde waarden en de werkelijke waarden niet significant verschillend zijn. Indien de P-waarde kleiner is dan 5% kunnen we wel spreken over een significant verschil aangezien deze dan verwaarloosbaar klein is.

step 2:
Ook deze vraag staaf je met de juiste cijfers en verwijzigen naar grafieken en tabellen.

Het betrouwbaarheidsinterval wordt bepaald door de stippellijn welke bij overschrijding bepaalt dat de voorspelde waarde significant verschillend is van de werkelijke waarde. Wanneer de weergegeven bolletjeslijn boven deze stippellijn komt, dan kunnen we spreken van een overschatting, eronder is een onderschatting.

step 3:
Ook bij deze vraag is het voor de lezer makkelijk om de juiste cijfers terug te vinden in de tabel aan de hand van je verwijzingen.

De werkelijke standaardfout wordt bepaald door de kolom PE terwijl de voorspelde standaardfout wordt bepaald door de kolom %SE. Deze voorspelde standaardfout is een voorspelling over hoever we met onze voorspelde waarde naast de eigenlijke waarde liggen.

step 4:
Dit is een uitgebreid antwoord. Zeer goed dat je enkele de lijnen uit de tabel haalt die van belang zijn voor je antwoord. Misschien had je hier nog kunnen verwijzen naar de rest van de tabel?

Hier kunnen we een waarschijnlijkheid P verkennen in de laatste kolommen.

P F(t) > Y(t-1)
De waarschijnlijkheid dat de voorspelde waarde groter is dan de werkelijke waarde van de vorige observatie = (t-1)
P F(t) > Y(t-s)
De waarschijnlijkheid dat de voorspelde waarde groter is dan de werkelijke waarde van de observatie s jaar geleden = (t-s)
P F(t) > Y(48)
De waarschijnlijkheid dat de voorspelde waarde groter is dan de laatst gekende waarde.


step 5:
Dit antwoord is nogal beknopt maar geeft de essentie weer.

Vallen bepaalde voorspelde waarden buiten het betrouwbaarheidsinterval? Voorspelde waarden vergelijken met de werkelijke waarden!
2009-01-07 15:21:19 [Simon Meeusen] [reply] 
1: De cijfers zijn correct gebruikt, de vraag is uitgebreid verantwoord. Hier kan ik geen verdere commentaar bijvoegen.
2: Juiste toepassing van het betrouwbaarheidsinterval.
3: Goede uitvoering en verantwoording van de standaardfout.
4: Uitgebreid, maar toch to the point.
5: Goed uitgevoerde berekeningen.

Algemeen: De student geeft uitgebreid weer hoe ze te werk gaat en welke technieken ze gebruikt! Soms worden wel iets te lange en soms ingewikkelde zinnen gebruikt.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
14291.1
14205.3
15859.4
15258.9
15498.6
15106.5
15023.6
12083
15761.3
16943
15070.3
13659.6
14768.9
14725.1
15998.1
15370.6
14956.9
15469.7
15101.8
11703.7
16283.6
16726.5
14968.9
14861
14583.3
15305.8
17903.9
16379.4
15420.3
17870.5
15912.8
13866.5
17823.2
17872
17420.4
16704.4
15991.2
16583.6
19123.5
17838.7
17209.4
18586.5
16258.1
15141.6
19202.1
17746.5
19090.1
18040.3
17515.5
17751.8
21072.4
17170
19439.5
19795.4
17574.9
16165.4
19464.6
19932.1
19961.2
17343.4
18924.2
18574.1
21350.6
18594.6
19823.1
20844.4
19640.2
17735.4
19813.6
22160
20664.3
17877.4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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=33448&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=33448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33448&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[60])
4818040.3-------
4917515.5-------
5017751.8-------
5121072.4-------
5217170-------
5319439.5-------
5419795.4-------
5517574.9-------
5616165.4-------
5719464.6-------
5819932.1-------
5919961.2-------
6017343.4-------
6118924.218917.14417631.798720202.48930.49570.99180.98370.9918
6218574.118484.625217198.910619770.33970.44580.25140.8680.959
6321350.620988.818719635.838422341.79890.30010.99980.45181
6418594.618988.261717401.63520574.88840.31340.00180.98770.9789
6519823.119380.187417790.559720969.81510.29250.83360.47090.994
6620844.420443.564218762.429622124.69870.32010.76530.77510.9998
6719640.218768.647216994.727520542.56690.16780.01090.90640.9423
6817735.416635.778314847.021318424.53520.11415e-040.69690.2191
6919813.620324.933218456.132722193.73370.29590.99670.81660.9991
702216020756.745118837.709922675.78040.07590.83230.80020.9998
7120664.320353.457618408.182322298.73280.37710.03440.65370.9988
7217877.418546.317816539.675920552.95960.25680.01930.880.88

\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[60]) \tabularnewline
48 & 18040.3 & - & - & - & - & - & - & - \tabularnewline
49 & 17515.5 & - & - & - & - & - & - & - \tabularnewline
50 & 17751.8 & - & - & - & - & - & - & - \tabularnewline
51 & 21072.4 & - & - & - & - & - & - & - \tabularnewline
52 & 17170 & - & - & - & - & - & - & - \tabularnewline
53 & 19439.5 & - & - & - & - & - & - & - \tabularnewline
54 & 19795.4 & - & - & - & - & - & - & - \tabularnewline
55 & 17574.9 & - & - & - & - & - & - & - \tabularnewline
56 & 16165.4 & - & - & - & - & - & - & - \tabularnewline
57 & 19464.6 & - & - & - & - & - & - & - \tabularnewline
58 & 19932.1 & - & - & - & - & - & - & - \tabularnewline
59 & 19961.2 & - & - & - & - & - & - & - \tabularnewline
60 & 17343.4 & - & - & - & - & - & - & - \tabularnewline
61 & 18924.2 & 18917.144 & 17631.7987 & 20202.4893 & 0.4957 & 0.9918 & 0.9837 & 0.9918 \tabularnewline
62 & 18574.1 & 18484.6252 & 17198.9106 & 19770.3397 & 0.4458 & 0.2514 & 0.868 & 0.959 \tabularnewline
63 & 21350.6 & 20988.8187 & 19635.8384 & 22341.7989 & 0.3001 & 0.9998 & 0.4518 & 1 \tabularnewline
64 & 18594.6 & 18988.2617 & 17401.635 & 20574.8884 & 0.3134 & 0.0018 & 0.9877 & 0.9789 \tabularnewline
65 & 19823.1 & 19380.1874 & 17790.5597 & 20969.8151 & 0.2925 & 0.8336 & 0.4709 & 0.994 \tabularnewline
66 & 20844.4 & 20443.5642 & 18762.4296 & 22124.6987 & 0.3201 & 0.7653 & 0.7751 & 0.9998 \tabularnewline
67 & 19640.2 & 18768.6472 & 16994.7275 & 20542.5669 & 0.1678 & 0.0109 & 0.9064 & 0.9423 \tabularnewline
68 & 17735.4 & 16635.7783 & 14847.0213 & 18424.5352 & 0.1141 & 5e-04 & 0.6969 & 0.2191 \tabularnewline
69 & 19813.6 & 20324.9332 & 18456.1327 & 22193.7337 & 0.2959 & 0.9967 & 0.8166 & 0.9991 \tabularnewline
70 & 22160 & 20756.7451 & 18837.7099 & 22675.7804 & 0.0759 & 0.8323 & 0.8002 & 0.9998 \tabularnewline
71 & 20664.3 & 20353.4576 & 18408.1823 & 22298.7328 & 0.3771 & 0.0344 & 0.6537 & 0.9988 \tabularnewline
72 & 17877.4 & 18546.3178 & 16539.6759 & 20552.9596 & 0.2568 & 0.0193 & 0.88 & 0.88 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33448&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[60])[/C][/ROW]
[ROW][C]48[/C][C]18040.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]17515.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]17751.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]21072.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]17170[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]19439.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]19795.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]17574.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]16165.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]19464.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]19932.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]19961.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]17343.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]18924.2[/C][C]18917.144[/C][C]17631.7987[/C][C]20202.4893[/C][C]0.4957[/C][C]0.9918[/C][C]0.9837[/C][C]0.9918[/C][/ROW]
[ROW][C]62[/C][C]18574.1[/C][C]18484.6252[/C][C]17198.9106[/C][C]19770.3397[/C][C]0.4458[/C][C]0.2514[/C][C]0.868[/C][C]0.959[/C][/ROW]
[ROW][C]63[/C][C]21350.6[/C][C]20988.8187[/C][C]19635.8384[/C][C]22341.7989[/C][C]0.3001[/C][C]0.9998[/C][C]0.4518[/C][C]1[/C][/ROW]
[ROW][C]64[/C][C]18594.6[/C][C]18988.2617[/C][C]17401.635[/C][C]20574.8884[/C][C]0.3134[/C][C]0.0018[/C][C]0.9877[/C][C]0.9789[/C][/ROW]
[ROW][C]65[/C][C]19823.1[/C][C]19380.1874[/C][C]17790.5597[/C][C]20969.8151[/C][C]0.2925[/C][C]0.8336[/C][C]0.4709[/C][C]0.994[/C][/ROW]
[ROW][C]66[/C][C]20844.4[/C][C]20443.5642[/C][C]18762.4296[/C][C]22124.6987[/C][C]0.3201[/C][C]0.7653[/C][C]0.7751[/C][C]0.9998[/C][/ROW]
[ROW][C]67[/C][C]19640.2[/C][C]18768.6472[/C][C]16994.7275[/C][C]20542.5669[/C][C]0.1678[/C][C]0.0109[/C][C]0.9064[/C][C]0.9423[/C][/ROW]
[ROW][C]68[/C][C]17735.4[/C][C]16635.7783[/C][C]14847.0213[/C][C]18424.5352[/C][C]0.1141[/C][C]5e-04[/C][C]0.6969[/C][C]0.2191[/C][/ROW]
[ROW][C]69[/C][C]19813.6[/C][C]20324.9332[/C][C]18456.1327[/C][C]22193.7337[/C][C]0.2959[/C][C]0.9967[/C][C]0.8166[/C][C]0.9991[/C][/ROW]
[ROW][C]70[/C][C]22160[/C][C]20756.7451[/C][C]18837.7099[/C][C]22675.7804[/C][C]0.0759[/C][C]0.8323[/C][C]0.8002[/C][C]0.9998[/C][/ROW]
[ROW][C]71[/C][C]20664.3[/C][C]20353.4576[/C][C]18408.1823[/C][C]22298.7328[/C][C]0.3771[/C][C]0.0344[/C][C]0.6537[/C][C]0.9988[/C][/ROW]
[ROW][C]72[/C][C]17877.4[/C][C]18546.3178[/C][C]16539.6759[/C][C]20552.9596[/C][C]0.2568[/C][C]0.0193[/C][C]0.88[/C][C]0.88[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33448&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[60])
4818040.3-------
4917515.5-------
5017751.8-------
5121072.4-------
5217170-------
5319439.5-------
5419795.4-------
5517574.9-------
5616165.4-------
5719464.6-------
5819932.1-------
5919961.2-------
6017343.4-------
6118924.218917.14417631.798720202.48930.49570.99180.98370.9918
6218574.118484.625217198.910619770.33970.44580.25140.8680.959
6321350.620988.818719635.838422341.79890.30010.99980.45181
6418594.618988.261717401.63520574.88840.31340.00180.98770.9789
6519823.119380.187417790.559720969.81510.29250.83360.47090.994
6620844.420443.564218762.429622124.69870.32010.76530.77510.9998
6719640.218768.647216994.727520542.56690.16780.01090.90640.9423
6817735.416635.778314847.021318424.53520.11415e-040.69690.2191
6919813.620324.933218456.132722193.73370.29590.99670.81660.9991
702216020756.745118837.709922675.78040.07590.83230.80020.9998
7120664.320353.457618408.182322298.73280.37710.03440.65370.9988
7217877.418546.317816539.675920552.95960.25680.01930.880.88






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
610.03474e-04049.78774.1492.0369
620.03550.00484e-048005.742667.145225.8292
630.03290.01720.0014130885.723810907.1437104.4373
640.0426-0.02070.0017154969.569112914.1308113.6404
650.04180.02290.0019196171.601816347.6335127.8579
660.0420.01960.0016160669.352113389.1127115.7113
670.04820.04640.0039759604.236863300.3531251.5956
680.05490.06610.00551209167.948100763.9957317.4335
690.0469-0.02520.0021261461.605721788.4671147.6092
700.04720.06760.00561969124.1884164093.6824405.0848
710.04880.01530.001396623.00418051.91789.7325
720.0552-0.03610.003447450.981837287.5818193.0999

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
61 & 0.0347 & 4e-04 & 0 & 49.7877 & 4.149 & 2.0369 \tabularnewline
62 & 0.0355 & 0.0048 & 4e-04 & 8005.742 & 667.1452 & 25.8292 \tabularnewline
63 & 0.0329 & 0.0172 & 0.0014 & 130885.7238 & 10907.1437 & 104.4373 \tabularnewline
64 & 0.0426 & -0.0207 & 0.0017 & 154969.5691 & 12914.1308 & 113.6404 \tabularnewline
65 & 0.0418 & 0.0229 & 0.0019 & 196171.6018 & 16347.6335 & 127.8579 \tabularnewline
66 & 0.042 & 0.0196 & 0.0016 & 160669.3521 & 13389.1127 & 115.7113 \tabularnewline
67 & 0.0482 & 0.0464 & 0.0039 & 759604.2368 & 63300.3531 & 251.5956 \tabularnewline
68 & 0.0549 & 0.0661 & 0.0055 & 1209167.948 & 100763.9957 & 317.4335 \tabularnewline
69 & 0.0469 & -0.0252 & 0.0021 & 261461.6057 & 21788.4671 & 147.6092 \tabularnewline
70 & 0.0472 & 0.0676 & 0.0056 & 1969124.1884 & 164093.6824 & 405.0848 \tabularnewline
71 & 0.0488 & 0.0153 & 0.0013 & 96623.0041 & 8051.917 & 89.7325 \tabularnewline
72 & 0.0552 & -0.0361 & 0.003 & 447450.9818 & 37287.5818 & 193.0999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33448&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]61[/C][C]0.0347[/C][C]4e-04[/C][C]0[/C][C]49.7877[/C][C]4.149[/C][C]2.0369[/C][/ROW]
[ROW][C]62[/C][C]0.0355[/C][C]0.0048[/C][C]4e-04[/C][C]8005.742[/C][C]667.1452[/C][C]25.8292[/C][/ROW]
[ROW][C]63[/C][C]0.0329[/C][C]0.0172[/C][C]0.0014[/C][C]130885.7238[/C][C]10907.1437[/C][C]104.4373[/C][/ROW]
[ROW][C]64[/C][C]0.0426[/C][C]-0.0207[/C][C]0.0017[/C][C]154969.5691[/C][C]12914.1308[/C][C]113.6404[/C][/ROW]
[ROW][C]65[/C][C]0.0418[/C][C]0.0229[/C][C]0.0019[/C][C]196171.6018[/C][C]16347.6335[/C][C]127.8579[/C][/ROW]
[ROW][C]66[/C][C]0.042[/C][C]0.0196[/C][C]0.0016[/C][C]160669.3521[/C][C]13389.1127[/C][C]115.7113[/C][/ROW]
[ROW][C]67[/C][C]0.0482[/C][C]0.0464[/C][C]0.0039[/C][C]759604.2368[/C][C]63300.3531[/C][C]251.5956[/C][/ROW]
[ROW][C]68[/C][C]0.0549[/C][C]0.0661[/C][C]0.0055[/C][C]1209167.948[/C][C]100763.9957[/C][C]317.4335[/C][/ROW]
[ROW][C]69[/C][C]0.0469[/C][C]-0.0252[/C][C]0.0021[/C][C]261461.6057[/C][C]21788.4671[/C][C]147.6092[/C][/ROW]
[ROW][C]70[/C][C]0.0472[/C][C]0.0676[/C][C]0.0056[/C][C]1969124.1884[/C][C]164093.6824[/C][C]405.0848[/C][/ROW]
[ROW][C]71[/C][C]0.0488[/C][C]0.0153[/C][C]0.0013[/C][C]96623.0041[/C][C]8051.917[/C][C]89.7325[/C][/ROW]
[ROW][C]72[/C][C]0.0552[/C][C]-0.0361[/C][C]0.003[/C][C]447450.9818[/C][C]37287.5818[/C][C]193.0999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33448&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33448&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
610.03474e-04049.78774.1492.0369
620.03550.00484e-048005.742667.145225.8292
630.03290.01720.0014130885.723810907.1437104.4373
640.0426-0.02070.0017154969.569112914.1308113.6404
650.04180.02290.0019196171.601816347.6335127.8579
660.0420.01960.0016160669.352113389.1127115.7113
670.04820.04640.0039759604.236863300.3531251.5956
680.05490.06610.00551209167.948100763.9957317.4335
690.0469-0.02520.0021261461.605721788.4671147.6092
700.04720.06760.00561969124.1884164093.6824405.0848
710.04880.01530.001396623.00418051.91789.7325
720.0552-0.03610.003447450.981837287.5818193.0999


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; 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,fx))
(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.se <- array(0, dim=fx)
perf.mse <- 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$pred[i]
perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
perf.mse[i] = perf.mse[i] + perf.se[i]
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 = perf.mape / fx
perf.mse = perf.mse / fx
perf.rmse = sqrt(perf.mse)
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[1:12] <- 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.mape[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse[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')