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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 computationMon, 15 Dec 2008 11:00:13 -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/15/t1229364085vcks5t5yvdwer0k.htm/, Retrieved Wed, 15 May 2024 04:03:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33754, Retrieved Wed, 15 May 2024 04:03:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact245

Tree of Dependent Computations

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]
- RMPD  [Standard Deviation-Mean Plot] [Identification an...] [2008-12-07 14:45:52] [b943bd7078334192ff8343563ee31113]
- RM      [Variance Reduction Matrix] [Identification an...] [2008-12-07 14:47:22] [b943bd7078334192ff8343563ee31113]
- RMP       [(Partial) Autocorrelation Function] [Identification an...] [2008-12-07 14:51:36] [b943bd7078334192ff8343563ee31113]
F   P         [(Partial) Autocorrelation Function] [Identification an...] [2008-12-07 14:54:30] [b943bd7078334192ff8343563ee31113]
-   P           [(Partial) Autocorrelation Function] [Identification an...] [2008-12-07 14:58:01] [b943bd7078334192ff8343563ee31113]
F RMP             [Spectral Analysis] [Identification an...] [2008-12-07 15:02:51] [b943bd7078334192ff8343563ee31113]
F RMP               [(Partial) Autocorrelation Function] [Identification an...] [2008-12-07 15:05:29] [b943bd7078334192ff8343563ee31113]
F RMP                 [ARIMA Backward Selection] [Identification an...] [2008-12-07 15:45:38] [b943bd7078334192ff8343563ee31113]
-   P                   [ARIMA Backward Selection] [ARIMA Backward Mo...] [2008-12-12 14:40:13] [b943bd7078334192ff8343563ee31113]
- RMP                     [ARIMA Forecasting] [ARIMA Forecasting...] [2008-12-15 17:00:29] [b943bd7078334192ff8343563ee31113]
F   P                         [ARIMA Forecasting] [ARIMA Forecasting...] [2008-12-15 18:00:13] [620b6ad5c4696049e39cb73ce029682c] [Current]
Feedback Forum
2008-12-21 18:20:21 [Ciska Tanghe] [reply] 
Voor mijn paper heb ik het ARIMA-model gebruikt. Dit is een ander model dan in de workshop wordt gebruikt. De correcte parameters om de voorspelling te berekenen zijn:
- lambda = -1
- d = 1
- d = 0
- P = 1
- q = 1
- Q = 1

Daaruit volgt de volgende voorspelling:

http://www.freestatistics.org/blog/date/2008/Dec/21/t122986521294jc5mpoifvjge0.htm

Eerst en vooral wordt de grafiek bekeken. De voorspelling wordt voorgesteld door de witte lijn en de werkelijke waarde door de zwarte lijn. Het oranjegekleurde gebied stelt het betrouwbaarheidsinterval voor met zijn boven- en ondergrens. De witte lijn ligt daar volledig binnen. Bij de zwarte lijn valt één coëfficiënt buiten het betrouwbaarheidsinterval, namelijk 94. Het begin van de voorspelling komt zo goed als overeen met de werkelijkheid. Daarna valt op dat de voorspelling een stuk hoger ligt dan de werkelijke waarden.

Op de grafiek ARIMA Extrapolation Forecast wordt ook de voorspelling weergegeven. De stippellijnen stellen het betrouwbaarheidsinterval voor. De bolletjeslijn geeft de voorspelling weer en de volle lijn is de werkelijke situatie. Aan de hand van deze voorspelling wordt de invloed van de financiële crisis op de tijdreeks import uit Amerika weergegeven. Het is duidelijk dat er door de crisis minder geïmporteerd wordt dan voorspeld werd.

In de tabel 'Univariate ARIMA Extrapolation Forecast' wordt de voorspelling van de tijdreeks in getallen uitgedrukt. In de kolom Y(t) worden de werkelijke waarden weergegeven en in de kolom F(t) de voorspelde waarden. De volgende twee kolommen geven het betrouwbaarheidsinterval weer. De eerste kolom daarvan geeft de lower bound en de tweede kolom de upper bound. Het is duidelijk dat alle werkelijke waarden meestal binnen het betrouwbaarheidsinterval liggen. Slechts één keer is dit niet het geval, namelijk bij de coëfficiënt 94. In de vijfde kolom wordt de p-value weergegeven. Als deze kleiner is dan 5% is de werkelijke waarde significant verschillend van de voorspelde waarde. Bij coëfficiënt 94 komt de laagste p-value voor, namelijk 13.61%. De kans dat er een vergissing gebeurd bij het verwerpen van de nulhypothese is gelijk aan 13.61%. Daaruit volgt dat de voorspelde waarde en de werkelijke waarde niet significant verschillend zijn van elkaar. Een afwijking is aan het toeval te wijken. In de zesde kolom wordt de waarschijnlijkheid weergegeven dat de voorspelde waarde van één jaar groter is dan de werkelijke waarde bij het vorige jaar. Een voorbeeld: de waarschijnlijkheid dat de voorspelde waarde van de 94ste coëfficiënt (2304) groter is dan de werkelijke waarde van de 93ste coëfficiënt is (1731) is gelijk aan 87.7%. Dit percentage betekent dat de kans op stijging ten opzichte van de vorige werkelijke waarde gelijk is aan 87.7%. In de zevende kolom wordt de waarschijnlijkheid weergegeven dat de voorspelde waarde van een bepaalde maand groter is dan de werkelijke waarde in diezelfde maand één jaar eerder. Aangezien s in dit geval gelijk is aan 12, is het vorige voorbeeld hier ook geldig. Tenslotte geeft de negende kolom de kans op stijgen van de voorspelde waarde ten opzichte van de laatst gekende waarde weer . Een voorbeeld: de kans dat de voorspelling gestegen is ten opzichte van de waarde 85ste coëfficiënt (2121.8) is gelijk aan 30.4%.

De tweede kolom van de tabel 'Univariate ARIMA Extrapolation Forecast Performance' geeft het percentage weer van de standaardfout. Hoe meer in de toekomst voorspeld wordt, hoe groter de waarde van de standaardfout. De derde kolom geeft het percentage van de werkelijke voorspellingsfout weer. Bij alle coëfficiënten is de werkelijke voorspellingsfout kleiner dan de standaardfout, behalve bij coëfficiënt 94. Daar is de werkelijke voorspellingsfout (23.52%) groter dan de standaardfout (21.42%).

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1593
1477.9
1733.7
1569.7
1843.7
1950.3
1657.5
1772.1
1568.3
1809.8
1646.7
1808.5
1763.9
1625.5
1538.8
1342.4
1645.1
1619.9
1338.1
1505.5
1529.1
1511.9
1656.7
1694.4
1662.3
1588.7
1483.3
1585.6
1658.9
1584.4
1470.6
1618.7
1407.6
1473.9
1515.3
1485.4
1496.1
1493.5
1298.4
1375.3
1507.9
1455.3
1363.3
1392.8
1348.8
1880.3
1669.2
1543.6
1701.2
1516.5
1466.8
1484.1
1577.2
1684.5
1414.7
1674.5
1598.7
1739.1
1674.6
1671.8
1802
1526.8
1580.9
1634.8
1610.3
1712
1678.8
1708.1
1680.6
2056
1624
2021.4
1861.1
1750.8
1767.5
1710.3
2151.5
2047.9
1915.4
1984.7
1896.5
2170.8
2139.9
2330.5
2121.8
2226.8
1857.9
2155.9
2341.7
2290.2
2006.5
2111.9
1731.3
1762.2
1863.2
1943.5
1975.2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33754&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33754&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33754&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132






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[85])
731861.1-------
741750.8-------
751767.5-------
761710.3-------
772151.5-------
782047.9-------
791915.4-------
801984.7-------
811896.5-------
822170.8-------
832139.9-------
842330.5-------
852121.8-------
862226.82094.43241870.20392318.66090.12360.40550.99870.4055
871857.92085.93671853.95012317.92330.0270.1170.99640.3809
882155.92014.91471767.48772262.34170.1320.89320.99210.1986
892341.72230.64811948.59642512.69990.22010.69830.70880.7753
902290.22236.50011940.91052532.08960.36090.24270.89450.7765
912006.52051.74161738.79252364.69080.38850.06770.80340.3304
922111.92176.68551844.41472508.95630.35120.84230.87130.6269
931731.32088.12511741.45272434.79750.02180.44650.86070.4245
941762.22312.94961950.59082675.30840.00140.99920.7790.8494
951863.22211.27231833.98982588.55480.03530.99020.64460.679
961943.52311.9541921.19072702.71730.03230.98780.46290.8299
971975.22274.53471869.43262679.63680.07380.94540.770.77

\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[85]) \tabularnewline
73 & 1861.1 & - & - & - & - & - & - & - \tabularnewline
74 & 1750.8 & - & - & - & - & - & - & - \tabularnewline
75 & 1767.5 & - & - & - & - & - & - & - \tabularnewline
76 & 1710.3 & - & - & - & - & - & - & - \tabularnewline
77 & 2151.5 & - & - & - & - & - & - & - \tabularnewline
78 & 2047.9 & - & - & - & - & - & - & - \tabularnewline
79 & 1915.4 & - & - & - & - & - & - & - \tabularnewline
80 & 1984.7 & - & - & - & - & - & - & - \tabularnewline
81 & 1896.5 & - & - & - & - & - & - & - \tabularnewline
82 & 2170.8 & - & - & - & - & - & - & - \tabularnewline
83 & 2139.9 & - & - & - & - & - & - & - \tabularnewline
84 & 2330.5 & - & - & - & - & - & - & - \tabularnewline
85 & 2121.8 & - & - & - & - & - & - & - \tabularnewline
86 & 2226.8 & 2094.4324 & 1870.2039 & 2318.6609 & 0.1236 & 0.4055 & 0.9987 & 0.4055 \tabularnewline
87 & 1857.9 & 2085.9367 & 1853.9501 & 2317.9233 & 0.027 & 0.117 & 0.9964 & 0.3809 \tabularnewline
88 & 2155.9 & 2014.9147 & 1767.4877 & 2262.3417 & 0.132 & 0.8932 & 0.9921 & 0.1986 \tabularnewline
89 & 2341.7 & 2230.6481 & 1948.5964 & 2512.6999 & 0.2201 & 0.6983 & 0.7088 & 0.7753 \tabularnewline
90 & 2290.2 & 2236.5001 & 1940.9105 & 2532.0896 & 0.3609 & 0.2427 & 0.8945 & 0.7765 \tabularnewline
91 & 2006.5 & 2051.7416 & 1738.7925 & 2364.6908 & 0.3885 & 0.0677 & 0.8034 & 0.3304 \tabularnewline
92 & 2111.9 & 2176.6855 & 1844.4147 & 2508.9563 & 0.3512 & 0.8423 & 0.8713 & 0.6269 \tabularnewline
93 & 1731.3 & 2088.1251 & 1741.4527 & 2434.7975 & 0.0218 & 0.4465 & 0.8607 & 0.4245 \tabularnewline
94 & 1762.2 & 2312.9496 & 1950.5908 & 2675.3084 & 0.0014 & 0.9992 & 0.779 & 0.8494 \tabularnewline
95 & 1863.2 & 2211.2723 & 1833.9898 & 2588.5548 & 0.0353 & 0.9902 & 0.6446 & 0.679 \tabularnewline
96 & 1943.5 & 2311.954 & 1921.1907 & 2702.7173 & 0.0323 & 0.9878 & 0.4629 & 0.8299 \tabularnewline
97 & 1975.2 & 2274.5347 & 1869.4326 & 2679.6368 & 0.0738 & 0.9454 & 0.77 & 0.77 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33754&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[85])[/C][/ROW]
[ROW][C]73[/C][C]1861.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]74[/C][C]1750.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]75[/C][C]1767.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]76[/C][C]1710.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]77[/C][C]2151.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]78[/C][C]2047.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]79[/C][C]1915.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]80[/C][C]1984.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]81[/C][C]1896.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]82[/C][C]2170.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]83[/C][C]2139.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]84[/C][C]2330.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]85[/C][C]2121.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]86[/C][C]2226.8[/C][C]2094.4324[/C][C]1870.2039[/C][C]2318.6609[/C][C]0.1236[/C][C]0.4055[/C][C]0.9987[/C][C]0.4055[/C][/ROW]
[ROW][C]87[/C][C]1857.9[/C][C]2085.9367[/C][C]1853.9501[/C][C]2317.9233[/C][C]0.027[/C][C]0.117[/C][C]0.9964[/C][C]0.3809[/C][/ROW]
[ROW][C]88[/C][C]2155.9[/C][C]2014.9147[/C][C]1767.4877[/C][C]2262.3417[/C][C]0.132[/C][C]0.8932[/C][C]0.9921[/C][C]0.1986[/C][/ROW]
[ROW][C]89[/C][C]2341.7[/C][C]2230.6481[/C][C]1948.5964[/C][C]2512.6999[/C][C]0.2201[/C][C]0.6983[/C][C]0.7088[/C][C]0.7753[/C][/ROW]
[ROW][C]90[/C][C]2290.2[/C][C]2236.5001[/C][C]1940.9105[/C][C]2532.0896[/C][C]0.3609[/C][C]0.2427[/C][C]0.8945[/C][C]0.7765[/C][/ROW]
[ROW][C]91[/C][C]2006.5[/C][C]2051.7416[/C][C]1738.7925[/C][C]2364.6908[/C][C]0.3885[/C][C]0.0677[/C][C]0.8034[/C][C]0.3304[/C][/ROW]
[ROW][C]92[/C][C]2111.9[/C][C]2176.6855[/C][C]1844.4147[/C][C]2508.9563[/C][C]0.3512[/C][C]0.8423[/C][C]0.8713[/C][C]0.6269[/C][/ROW]
[ROW][C]93[/C][C]1731.3[/C][C]2088.1251[/C][C]1741.4527[/C][C]2434.7975[/C][C]0.0218[/C][C]0.4465[/C][C]0.8607[/C][C]0.4245[/C][/ROW]
[ROW][C]94[/C][C]1762.2[/C][C]2312.9496[/C][C]1950.5908[/C][C]2675.3084[/C][C]0.0014[/C][C]0.9992[/C][C]0.779[/C][C]0.8494[/C][/ROW]
[ROW][C]95[/C][C]1863.2[/C][C]2211.2723[/C][C]1833.9898[/C][C]2588.5548[/C][C]0.0353[/C][C]0.9902[/C][C]0.6446[/C][C]0.679[/C][/ROW]
[ROW][C]96[/C][C]1943.5[/C][C]2311.954[/C][C]1921.1907[/C][C]2702.7173[/C][C]0.0323[/C][C]0.9878[/C][C]0.4629[/C][C]0.8299[/C][/ROW]
[ROW][C]97[/C][C]1975.2[/C][C]2274.5347[/C][C]1869.4326[/C][C]2679.6368[/C][C]0.0738[/C][C]0.9454[/C][C]0.77[/C][C]0.77[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33754&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33754&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[85])
731861.1-------
741750.8-------
751767.5-------
761710.3-------
772151.5-------
782047.9-------
791915.4-------
801984.7-------
811896.5-------
822170.8-------
832139.9-------
842330.5-------
852121.8-------
862226.82094.43241870.20392318.66090.12360.40550.99870.4055
871857.92085.93671853.95012317.92330.0270.1170.99640.3809
882155.92014.91471767.48772262.34170.1320.89320.99210.1986
892341.72230.64811948.59642512.69990.22010.69830.70880.7753
902290.22236.50011940.91052532.08960.36090.24270.89450.7765
912006.52051.74161738.79252364.69080.38850.06770.80340.3304
922111.92176.68551844.41472508.95630.35120.84230.87130.6269
931731.32088.12511741.45272434.79750.02180.44650.86070.4245
941762.22312.94961950.59082675.30840.00140.99920.7790.8494
951863.22211.27231833.98982588.55480.03530.99020.64460.679
961943.52311.9541921.19072702.71730.03230.98780.46290.8299
971975.22274.53471869.43262679.63680.07380.94540.770.77






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
860.05460.06320.005317521.17731460.098138.2112
870.0567-0.10930.009152000.73594333.394765.8285
880.06270.070.005819876.85491656.404640.699
890.06450.04980.004112332.51811027.709832.0579
900.06740.0240.0022883.6831240.306915.5018
910.0778-0.02210.00182046.8048170.567113.0601
920.0779-0.02980.00254197.1665349.763918.702
930.0847-0.17090.0142127324.174410610.3479103.0065
940.0799-0.23810.0198303325.148125277.0957158.9877
950.087-0.15740.0131121154.330710096.1942100.4798
960.0862-0.15940.0133135758.357211313.1964106.3635
970.0909-0.13160.01189601.25897466.771686.4105

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
86 & 0.0546 & 0.0632 & 0.0053 & 17521.1773 & 1460.0981 & 38.2112 \tabularnewline
87 & 0.0567 & -0.1093 & 0.0091 & 52000.7359 & 4333.3947 & 65.8285 \tabularnewline
88 & 0.0627 & 0.07 & 0.0058 & 19876.8549 & 1656.4046 & 40.699 \tabularnewline
89 & 0.0645 & 0.0498 & 0.0041 & 12332.5181 & 1027.7098 & 32.0579 \tabularnewline
90 & 0.0674 & 0.024 & 0.002 & 2883.6831 & 240.3069 & 15.5018 \tabularnewline
91 & 0.0778 & -0.0221 & 0.0018 & 2046.8048 & 170.5671 & 13.0601 \tabularnewline
92 & 0.0779 & -0.0298 & 0.0025 & 4197.1665 & 349.7639 & 18.702 \tabularnewline
93 & 0.0847 & -0.1709 & 0.0142 & 127324.1744 & 10610.3479 & 103.0065 \tabularnewline
94 & 0.0799 & -0.2381 & 0.0198 & 303325.1481 & 25277.0957 & 158.9877 \tabularnewline
95 & 0.087 & -0.1574 & 0.0131 & 121154.3307 & 10096.1942 & 100.4798 \tabularnewline
96 & 0.0862 & -0.1594 & 0.0133 & 135758.3572 & 11313.1964 & 106.3635 \tabularnewline
97 & 0.0909 & -0.1316 & 0.011 & 89601.2589 & 7466.7716 & 86.4105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33754&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]86[/C][C]0.0546[/C][C]0.0632[/C][C]0.0053[/C][C]17521.1773[/C][C]1460.0981[/C][C]38.2112[/C][/ROW]
[ROW][C]87[/C][C]0.0567[/C][C]-0.1093[/C][C]0.0091[/C][C]52000.7359[/C][C]4333.3947[/C][C]65.8285[/C][/ROW]
[ROW][C]88[/C][C]0.0627[/C][C]0.07[/C][C]0.0058[/C][C]19876.8549[/C][C]1656.4046[/C][C]40.699[/C][/ROW]
[ROW][C]89[/C][C]0.0645[/C][C]0.0498[/C][C]0.0041[/C][C]12332.5181[/C][C]1027.7098[/C][C]32.0579[/C][/ROW]
[ROW][C]90[/C][C]0.0674[/C][C]0.024[/C][C]0.002[/C][C]2883.6831[/C][C]240.3069[/C][C]15.5018[/C][/ROW]
[ROW][C]91[/C][C]0.0778[/C][C]-0.0221[/C][C]0.0018[/C][C]2046.8048[/C][C]170.5671[/C][C]13.0601[/C][/ROW]
[ROW][C]92[/C][C]0.0779[/C][C]-0.0298[/C][C]0.0025[/C][C]4197.1665[/C][C]349.7639[/C][C]18.702[/C][/ROW]
[ROW][C]93[/C][C]0.0847[/C][C]-0.1709[/C][C]0.0142[/C][C]127324.1744[/C][C]10610.3479[/C][C]103.0065[/C][/ROW]
[ROW][C]94[/C][C]0.0799[/C][C]-0.2381[/C][C]0.0198[/C][C]303325.1481[/C][C]25277.0957[/C][C]158.9877[/C][/ROW]
[ROW][C]95[/C][C]0.087[/C][C]-0.1574[/C][C]0.0131[/C][C]121154.3307[/C][C]10096.1942[/C][C]100.4798[/C][/ROW]
[ROW][C]96[/C][C]0.0862[/C][C]-0.1594[/C][C]0.0133[/C][C]135758.3572[/C][C]11313.1964[/C][C]106.3635[/C][/ROW]
[ROW][C]97[/C][C]0.0909[/C][C]-0.1316[/C][C]0.011[/C][C]89601.2589[/C][C]7466.7716[/C][C]86.4105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33754&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33754&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
860.05460.06320.005317521.17731460.098138.2112
870.0567-0.10930.009152000.73594333.394765.8285
880.06270.070.005819876.85491656.404640.699
890.06450.04980.004112332.51811027.709832.0579
900.06740.0240.0022883.6831240.306915.5018
910.0778-0.02210.00182046.8048170.567113.0601
920.0779-0.02980.00254197.1665349.763918.702
930.0847-0.17090.0142127324.174410610.3479103.0065
940.0799-0.23810.0198303325.148125277.0957158.9877
950.087-0.15740.0131121154.330710096.1942100.4798
960.0862-0.15940.0133135758.357211313.1964106.3635
970.0909-0.13160.01189601.25897466.771686.4105


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; 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,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')