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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 computationTue, 16 Dec 2008 11:03:19 -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/16/t1229450643dnyw09q71nyt1qv.htm/, Retrieved Wed, 15 May 2024 23:49:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34067, Retrieved Wed, 15 May 2024 23:49:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

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]
F RMP   [Variance Reduction Matrix] [step1.1] [2008-12-08 18:32:25] [922d8ae7bd2fd460a62d9020ccd4931a]
F RMP     [(Partial) Autocorrelation Function] [step2] [2008-12-08 18:51:58] [922d8ae7bd2fd460a62d9020ccd4931a]
F RMP       [Spectral Analysis] [step24] [2008-12-08 19:05:43] [922d8ae7bd2fd460a62d9020ccd4931a]
-   P         [Spectral Analysis] [step242] [2008-12-08 19:08:43] [922d8ae7bd2fd460a62d9020ccd4931a]
F   P           [Spectral Analysis] [step25] [2008-12-08 19:10:33] [922d8ae7bd2fd460a62d9020ccd4931a]
- RMP             [(Partial) Autocorrelation Function] [step4] [2008-12-08 19:25:51] [922d8ae7bd2fd460a62d9020ccd4931a]
F RMP               [ARIMA Backward Selection] [step51] [2008-12-08 19:39:36] [922d8ae7bd2fd460a62d9020ccd4931a]
F   PD                [ARIMA Backward Selection] [step56] [2008-12-09 21:19:40] [922d8ae7bd2fd460a62d9020ccd4931a]
F RMPD                    [ARIMA Forecasting] [ARIMA forecast] [2008-12-16 18:03:19] [a9e6d7cd6e144e8b311d9f96a24c5a25] [Current]
Feedback Forum
2008-12-18 11:05:50 [407693b66d7f2e0b350979005057872d] [reply] 
Dit antwoord is volledig correct.
2008-12-18 12:12:34 [Loïque Verhasselt] [reply] 
Step 1: We krijgen de juiste output van de student. We zien duidelijk dat de voorspelde waarden zicht niet explosief gedragen. AR processen moeten juist stabiel en MA moeten invertibel zijn. We kunnen dus spreken van 'brave' ARMA processen. Zoals de student zegt zien we duidelijk een steeds hoger liggende voorspelde waarde door een stijgende trend. We zien ook dat bijna alle p-waarde van de nulhypothese groter zijn dan 0,05 die wijzen erop dat de voorspelde waarden niet significant verschillen met de werkelijke waarden.
Step2: We zien duidelijk een vorm van seizoenaliteit, zoals de student zegt. Dit komt ook duidelijk voor in de voorspelde waarden. In het 2de deel van de werkelijke waarde in grafiek 1 zien we een licht stijgende trend die de voorspelling overneemt. We zien geen economische trend in de tijdreeks.
Step3: Het was inderdaad hier de bedoeling om de standaard fouten te interpreteren van de 2de tabel. We zien dat we een stijgende standaardfout kunnen vaststellen maar dit is normaal. Hoe verder in de tijd, hoe meer risico maar toch blijft de standaardfout van de voorspelde fout hangen rond de 10% wat zeer goed is. Ook alle voorspelde fouten(SE) zijn groter dan de werkelijke fouten (PE) in absolute waarden. Buiten de laatste en dit zien we ook aan de p-waarden van de laatste omdat deze significante verschillen weergeeft.
Step4: De student geeft de juiste interpretatie van alle waarschijnlijkheden die we vinden in de eerste tabel maar geeft nergens een voorbeeld uit de tijdreeks. We zien dus duidelijk dat er overal niet significante verschillen zijn tussen de voorspelde en de werkelijke waarde omdat de p-waarden van de nulhypothese steeds groter zijn dan 0,05 behalve voor de laatste maand. We zien bij de volgende 3 waarschijnlijkheden steeds een groot percentage wat wil zeggen dat we altijd een stijging kunnen vinden, tegenover de vorige werkelijke maand, tegenover de werkelijke maand vorig jaar en tegenover de laatstgekende werkelijke waarde.
Step 5: We zien duidelijk dat de voorspelde waarde en de werkelijke waarden binnen het betrouwbaarheidsinterval liggen. De voorspelde waarde ligt steeds boven de werkelijke en dit door de stijgende trend in de tijdreeks.
2008-12-22 10:00:56 [Nicolaj Wuyts] [reply] 
Step 1:
De forecast loopt mooi binnen het betrouwbaarheidsinterval en leunt dicht aan bij de werkelijke waarden. Het verloop is dus zoals verwacht.

Step 2:
Er is inderdaad duidelijk sprake van seizoenaliteit.

Step 3:
We zien dat de SE% van 5 naar 10% verloopt. Dit wil dus zeggen dat we er op 10% van onze voorspellingen naast zitten. We kunnen dus 90 op 100 waarden correct voorspellen.

Step 4:
De student had hier meer voorbeelden kunnen aanhalen. We zien bij de p-value dat alle waarden boven 0,05 procent liggen. Dit wil zeggen dat er geen significant verschil is tussen de werkelijke en voorspelde waarden.

Step 5:
We kunnen concluderen dat de voorspelling zeer accuraat is. Alle voorspelde waarden leunen zeer dicht aan bij de werkelijke waarden.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2648,9
2669,6
3042,3
2604,2
2732,1
2621,7
2483,7
2479,3
2684,6
2834,7
2566,1
2251,2
2350
2299,8
2542,8
2530,2
2508,1
2616,8
2534,1
2181,8
2578,9
2841,9
2529,9
2103,2
2326,2
2452,6
2782,1
2727,3
2648,2
2760,7
2613
2225,4
2713,9
2923,3
2707
2473,9
2521
2531,8
3068,8
2826,9
2674,2
2966,6
2798,8
2629,6
3124,6
3115,7
3083
2863,9
2728,7
2789,4
3225,7
3148,2
2836,5
3153,5
2656,9
2834,7
3172,5
2998,8
3103,1
2735,6
2818,1
2874,4
3438,5
2949,1
3306,8
3530
3003,8
3206,4
3514,6
3522,6
3525,5
2996,2
3231,1
3030
3541,7
3113,2
3390,8
3424,2
3079,8
3123,4
3317,1
3579,9
3317,9
2668,1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34067&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]7 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=34067&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34067&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 time7 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[72])
602735.6-------
612818.1-------
622874.4-------
633438.5-------
642949.1-------
653306.80000000000-------
663530-------
673003.8-------
683206.4-------
693514.6-------
703522.6-------
713525.5-------
722996.2-------
733231.13142.20692833.26593484.8350.30550.79820.96810.7982
7430303195.86572855.8543576.35860.19640.4280.95110.8481
753541.73763.79333335.47734247.11020.18390.99850.90640.9991
763113.23326.3862924.98183782.87610.180.17760.94740.9219
773390.83550.07943098.8484067.01580.27290.95120.82180.9821
783424.23747.13733248.15744322.770.13580.88750.77020.9947
793079.83298.9492840.72413831.08830.20980.32230.86150.8676
803123.43369.83132883.36963938.36530.19780.84130.71340.9011
813317.13754.1933192.68264414.45850.09720.96940.76150.9878
823579.93811.91233222.74184508.79290.2570.9180.79210.9891
833317.93726.90733133.00664433.38940.12820.65830.71180.9787
842668.13215.25652688.04693845.86840.04450.37490.7520.752

\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[72]) \tabularnewline
60 & 2735.6 & - & - & - & - & - & - & - \tabularnewline
61 & 2818.1 & - & - & - & - & - & - & - \tabularnewline
62 & 2874.4 & - & - & - & - & - & - & - \tabularnewline
63 & 3438.5 & - & - & - & - & - & - & - \tabularnewline
64 & 2949.1 & - & - & - & - & - & - & - \tabularnewline
65 & 3306.80000000000 & - & - & - & - & - & - & - \tabularnewline
66 & 3530 & - & - & - & - & - & - & - \tabularnewline
67 & 3003.8 & - & - & - & - & - & - & - \tabularnewline
68 & 3206.4 & - & - & - & - & - & - & - \tabularnewline
69 & 3514.6 & - & - & - & - & - & - & - \tabularnewline
70 & 3522.6 & - & - & - & - & - & - & - \tabularnewline
71 & 3525.5 & - & - & - & - & - & - & - \tabularnewline
72 & 2996.2 & - & - & - & - & - & - & - \tabularnewline
73 & 3231.1 & 3142.2069 & 2833.2659 & 3484.835 & 0.3055 & 0.7982 & 0.9681 & 0.7982 \tabularnewline
74 & 3030 & 3195.8657 & 2855.854 & 3576.3586 & 0.1964 & 0.428 & 0.9511 & 0.8481 \tabularnewline
75 & 3541.7 & 3763.7933 & 3335.4773 & 4247.1102 & 0.1839 & 0.9985 & 0.9064 & 0.9991 \tabularnewline
76 & 3113.2 & 3326.386 & 2924.9818 & 3782.8761 & 0.18 & 0.1776 & 0.9474 & 0.9219 \tabularnewline
77 & 3390.8 & 3550.0794 & 3098.848 & 4067.0158 & 0.2729 & 0.9512 & 0.8218 & 0.9821 \tabularnewline
78 & 3424.2 & 3747.1373 & 3248.1574 & 4322.77 & 0.1358 & 0.8875 & 0.7702 & 0.9947 \tabularnewline
79 & 3079.8 & 3298.949 & 2840.7241 & 3831.0883 & 0.2098 & 0.3223 & 0.8615 & 0.8676 \tabularnewline
80 & 3123.4 & 3369.8313 & 2883.3696 & 3938.3653 & 0.1978 & 0.8413 & 0.7134 & 0.9011 \tabularnewline
81 & 3317.1 & 3754.193 & 3192.6826 & 4414.4585 & 0.0972 & 0.9694 & 0.7615 & 0.9878 \tabularnewline
82 & 3579.9 & 3811.9123 & 3222.7418 & 4508.7929 & 0.257 & 0.918 & 0.7921 & 0.9891 \tabularnewline
83 & 3317.9 & 3726.9073 & 3133.0066 & 4433.3894 & 0.1282 & 0.6583 & 0.7118 & 0.9787 \tabularnewline
84 & 2668.1 & 3215.2565 & 2688.0469 & 3845.8684 & 0.0445 & 0.3749 & 0.752 & 0.752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34067&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[72])[/C][/ROW]
[ROW][C]60[/C][C]2735.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]2818.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]62[/C][C]2874.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]63[/C][C]3438.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]64[/C][C]2949.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]65[/C][C]3306.80000000000[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]66[/C][C]3530[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]67[/C][C]3003.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]68[/C][C]3206.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]69[/C][C]3514.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]70[/C][C]3522.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]71[/C][C]3525.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]72[/C][C]2996.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]73[/C][C]3231.1[/C][C]3142.2069[/C][C]2833.2659[/C][C]3484.835[/C][C]0.3055[/C][C]0.7982[/C][C]0.9681[/C][C]0.7982[/C][/ROW]
[ROW][C]74[/C][C]3030[/C][C]3195.8657[/C][C]2855.854[/C][C]3576.3586[/C][C]0.1964[/C][C]0.428[/C][C]0.9511[/C][C]0.8481[/C][/ROW]
[ROW][C]75[/C][C]3541.7[/C][C]3763.7933[/C][C]3335.4773[/C][C]4247.1102[/C][C]0.1839[/C][C]0.9985[/C][C]0.9064[/C][C]0.9991[/C][/ROW]
[ROW][C]76[/C][C]3113.2[/C][C]3326.386[/C][C]2924.9818[/C][C]3782.8761[/C][C]0.18[/C][C]0.1776[/C][C]0.9474[/C][C]0.9219[/C][/ROW]
[ROW][C]77[/C][C]3390.8[/C][C]3550.0794[/C][C]3098.848[/C][C]4067.0158[/C][C]0.2729[/C][C]0.9512[/C][C]0.8218[/C][C]0.9821[/C][/ROW]
[ROW][C]78[/C][C]3424.2[/C][C]3747.1373[/C][C]3248.1574[/C][C]4322.77[/C][C]0.1358[/C][C]0.8875[/C][C]0.7702[/C][C]0.9947[/C][/ROW]
[ROW][C]79[/C][C]3079.8[/C][C]3298.949[/C][C]2840.7241[/C][C]3831.0883[/C][C]0.2098[/C][C]0.3223[/C][C]0.8615[/C][C]0.8676[/C][/ROW]
[ROW][C]80[/C][C]3123.4[/C][C]3369.8313[/C][C]2883.3696[/C][C]3938.3653[/C][C]0.1978[/C][C]0.8413[/C][C]0.7134[/C][C]0.9011[/C][/ROW]
[ROW][C]81[/C][C]3317.1[/C][C]3754.193[/C][C]3192.6826[/C][C]4414.4585[/C][C]0.0972[/C][C]0.9694[/C][C]0.7615[/C][C]0.9878[/C][/ROW]
[ROW][C]82[/C][C]3579.9[/C][C]3811.9123[/C][C]3222.7418[/C][C]4508.7929[/C][C]0.257[/C][C]0.918[/C][C]0.7921[/C][C]0.9891[/C][/ROW]
[ROW][C]83[/C][C]3317.9[/C][C]3726.9073[/C][C]3133.0066[/C][C]4433.3894[/C][C]0.1282[/C][C]0.6583[/C][C]0.7118[/C][C]0.9787[/C][/ROW]
[ROW][C]84[/C][C]2668.1[/C][C]3215.2565[/C][C]2688.0469[/C][C]3845.8684[/C][C]0.0445[/C][C]0.3749[/C][C]0.752[/C][C]0.752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34067&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34067&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[72])
602735.6-------
612818.1-------
622874.4-------
633438.5-------
642949.1-------
653306.80000000000-------
663530-------
673003.8-------
683206.4-------
693514.6-------
703522.6-------
713525.5-------
722996.2-------
733231.13142.20692833.26593484.8350.30550.79820.96810.7982
7430303195.86572855.8543576.35860.19640.4280.95110.8481
753541.73763.79333335.47734247.11020.18390.99850.90640.9991
763113.23326.3862924.98183782.87610.180.17760.94740.9219
773390.83550.07943098.8484067.01580.27290.95120.82180.9821
783424.23747.13733248.15744322.770.13580.88750.77020.9947
793079.83298.9492840.72413831.08830.20980.32230.86150.8676
803123.43369.83132883.36963938.36530.19780.84130.71340.9011
813317.13754.1933192.68264414.45850.09720.96940.76150.9878
823579.93811.91233222.74184508.79290.2570.9180.79210.9891
833317.93726.90733133.00664433.38940.12820.65830.71180.9787
842668.13215.25652688.04693845.86840.04450.37490.7520.752






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
730.05560.02830.00247901.9842658.498725.6612
740.0607-0.05190.004327511.44072292.620147.8813
750.0655-0.0590.004949325.41414110.451264.1128
760.07-0.06410.005345448.25383787.354561.5415
770.0743-0.04490.003725369.93922114.161645.98
780.0784-0.08620.0072104288.47748690.706593.224
790.0823-0.06640.005548026.29364002.191163.2629
800.0861-0.07310.006160728.36365060.69771.1386
810.0897-0.11640.0097191050.268415920.8557126.1779
820.0933-0.06090.005153829.71734485.809866.9762
830.0967-0.10970.0091167287.011513940.5843118.0703
840.1001-0.17020.0142299380.277824948.3565157.9505

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
73 & 0.0556 & 0.0283 & 0.0024 & 7901.9842 & 658.4987 & 25.6612 \tabularnewline
74 & 0.0607 & -0.0519 & 0.0043 & 27511.4407 & 2292.6201 & 47.8813 \tabularnewline
75 & 0.0655 & -0.059 & 0.0049 & 49325.4141 & 4110.4512 & 64.1128 \tabularnewline
76 & 0.07 & -0.0641 & 0.0053 & 45448.2538 & 3787.3545 & 61.5415 \tabularnewline
77 & 0.0743 & -0.0449 & 0.0037 & 25369.9392 & 2114.1616 & 45.98 \tabularnewline
78 & 0.0784 & -0.0862 & 0.0072 & 104288.4774 & 8690.7065 & 93.224 \tabularnewline
79 & 0.0823 & -0.0664 & 0.0055 & 48026.2936 & 4002.1911 & 63.2629 \tabularnewline
80 & 0.0861 & -0.0731 & 0.0061 & 60728.3636 & 5060.697 & 71.1386 \tabularnewline
81 & 0.0897 & -0.1164 & 0.0097 & 191050.2684 & 15920.8557 & 126.1779 \tabularnewline
82 & 0.0933 & -0.0609 & 0.0051 & 53829.7173 & 4485.8098 & 66.9762 \tabularnewline
83 & 0.0967 & -0.1097 & 0.0091 & 167287.0115 & 13940.5843 & 118.0703 \tabularnewline
84 & 0.1001 & -0.1702 & 0.0142 & 299380.2778 & 24948.3565 & 157.9505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34067&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]73[/C][C]0.0556[/C][C]0.0283[/C][C]0.0024[/C][C]7901.9842[/C][C]658.4987[/C][C]25.6612[/C][/ROW]
[ROW][C]74[/C][C]0.0607[/C][C]-0.0519[/C][C]0.0043[/C][C]27511.4407[/C][C]2292.6201[/C][C]47.8813[/C][/ROW]
[ROW][C]75[/C][C]0.0655[/C][C]-0.059[/C][C]0.0049[/C][C]49325.4141[/C][C]4110.4512[/C][C]64.1128[/C][/ROW]
[ROW][C]76[/C][C]0.07[/C][C]-0.0641[/C][C]0.0053[/C][C]45448.2538[/C][C]3787.3545[/C][C]61.5415[/C][/ROW]
[ROW][C]77[/C][C]0.0743[/C][C]-0.0449[/C][C]0.0037[/C][C]25369.9392[/C][C]2114.1616[/C][C]45.98[/C][/ROW]
[ROW][C]78[/C][C]0.0784[/C][C]-0.0862[/C][C]0.0072[/C][C]104288.4774[/C][C]8690.7065[/C][C]93.224[/C][/ROW]
[ROW][C]79[/C][C]0.0823[/C][C]-0.0664[/C][C]0.0055[/C][C]48026.2936[/C][C]4002.1911[/C][C]63.2629[/C][/ROW]
[ROW][C]80[/C][C]0.0861[/C][C]-0.0731[/C][C]0.0061[/C][C]60728.3636[/C][C]5060.697[/C][C]71.1386[/C][/ROW]
[ROW][C]81[/C][C]0.0897[/C][C]-0.1164[/C][C]0.0097[/C][C]191050.2684[/C][C]15920.8557[/C][C]126.1779[/C][/ROW]
[ROW][C]82[/C][C]0.0933[/C][C]-0.0609[/C][C]0.0051[/C][C]53829.7173[/C][C]4485.8098[/C][C]66.9762[/C][/ROW]
[ROW][C]83[/C][C]0.0967[/C][C]-0.1097[/C][C]0.0091[/C][C]167287.0115[/C][C]13940.5843[/C][C]118.0703[/C][/ROW]
[ROW][C]84[/C][C]0.1001[/C][C]-0.1702[/C][C]0.0142[/C][C]299380.2778[/C][C]24948.3565[/C][C]157.9505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34067&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34067&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
730.05560.02830.00247901.9842658.498725.6612
740.0607-0.05190.004327511.44072292.620147.8813
750.0655-0.0590.004949325.41414110.451264.1128
760.07-0.06410.005345448.25383787.354561.5415
770.0743-0.04490.003725369.93922114.161645.98
780.0784-0.08620.0072104288.47748690.706593.224
790.0823-0.06640.005548026.29364002.191163.2629
800.0861-0.07310.006160728.36365060.69771.1386
810.0897-0.11640.0097191050.268415920.8557126.1779
820.0933-0.06090.005153829.71734485.809866.9762
830.0967-0.10970.0091167287.011513940.5843118.0703
840.1001-0.17020.0142299380.277824948.3565157.9505


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,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')