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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, 09 Dec 2008 13:21:38 -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/09/t1228854191jgda63mltszyun9.htm/, Retrieved Sat, 18 May 2024 06:16:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31780, Retrieved Sat, 18 May 2024 06:16:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact247

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] [Run sequence plot...] [2008-12-02 22:19:27] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMPD  [Standard Deviation-Mean Plot] [SD mean plot] [2008-12-06 11:49:39] [ed2ba3b6182103c15c0ab511ae4e6284]
F RMP     [(Partial) Autocorrelation Function] [ACF d=1 en D=1 la...] [2008-12-06 13:30:27] [ed2ba3b6182103c15c0ab511ae4e6284]
- RM        [ARIMA Backward Selection] [ARIMA model met q...] [2008-12-06 17:04:18] [4242609301e759e844b9196c1994e4ef]
-   P         [ARIMA Backward Selection] [ARima backward se...] [2008-12-08 11:53:47] [ed2ba3b6182103c15c0ab511ae4e6284]
F RMP             [ARIMA Forecasting] [ARIMA forecasting] [2008-12-09 20:21:38] [a8228479d4547a92e2d3f176a5299609] [Current]
F                   [ARIMA Forecasting] [Arima forecasting...] [2008-12-15 09:55:01] [4ad596f10399a71ad29b7d76e6ab90ac]
F                   [ARIMA Forecasting] [ARIMA forecasting] [2008-12-15 09:56:32] [7506b5e9e41ec66c6657f4234f97306e]
-                   [ARIMA Forecasting] [Arima Forecasting] [2008-12-15 10:39:39] [4ddbf81f78ea7c738951638c7e93f6ee]
F                   [ARIMA Forecasting] [ARIMA] [2008-12-15 20:51:26] [28075c6928548bea087cb2be962cfe7e]
F                   [ARIMA Forecasting] [arima forecasting] [2008-12-15 22:36:09] [005293453b571dbccb80b45226e44173]
-                   [ARIMA Forecasting] [Forecasting] [2008-12-16 00:22:57] [c5e27150943bc3d623392efb0d98f8d3]
Feedback Forum
2008-12-16 16:07:25 [Glenn De Maeyer] [reply] 
De student trekt gedurende de 5 stappen de juiste conclusies. Hierop kan ik niet veel aanvullen. Het enige dat ik kan doen zijn de twee bekomen tabellen en hun gegevens verder verduidelijken.

De eerste tabel 'Univariate ARIMA Extrapolation Forecast' dienen we als volgt te interpreteren.

Time: de maanden, (vb. Time:50: 50e observatie = 50ste maand van de tijdreeks)

Y(t): de werkelijke waarde van onze tijdreeks

F(t)= de voorspelling van de werkelijke waarden door de software (deze begint pas van Time 50 aangezien de testing period 12 maanden omvat)

95% LB & UB (lower en upper bound): dit is het alomgekende betrouwbaarheidsinterval. Met een zekerheid van 95% ligt de waarde van F(t) tussen deze 2 grenzen. Cf. wetmatigheid economie ceteris paribus.

p-value (H0: Y[t] = F[t]): de 0 Hypothese stelt hier dat Y(t) = F(t) (werkelijke waarde = voorspelde waarde). In de realiteit is dat zo goed als onmogelijk, verschil zal er altijd zijn. De software toetst hier echter of het verschil significant is of aan het toeval toe te wijzen is. Indien p-value onder de 5% dan is de voorspelde waarde significant verschillend van de werkelijke waarde. Onder de ceteris paribus voorwaarde impliceert dit dat bij een significant verschil, er een verklaring moet zijn.

P(F[t]>Y[t-1]): In deze kolom vinden we de kans dat er een stijging is wanneer we 1 periode vooruit gaan. (We werken hier dus met maanden).
Zo zien we bijvoorbeeld dat wanneer we van periode 52 naar periode 53 gaan we een kans hebben van 85% dat er een stijging is. Dit impliceert dus ook dat er een kans is van +/- 15% op een daling.

P(F[t]>Y[t-s]): In deze kolom vinden we de kans dat er een stijging is t.o.v. dezelfde maand maar dan van het vorige jaar. Bij deze observaties zien we dat er over het algemeen de kans bestaat dat er een stijging is t.o.v. het vorige jaar.

P(F[t]>Y[48]): Hier vinden we de kans dat er een stijging is t.o.v.. de laatst gekende waarde (time=49).
2008-12-16 16:11:41 [Glenn De Maeyer] [reply] 
Bij de tweede tabel 'Univariate ARIMA Extrapolation Forecast Performance' zijn de voornaamste elementen:

Bij % S.E zien we de voorspellingsfout als je x-aantal perioden vooruit gaat voorspellen. Hoe verder we vooruit voorspellen, hoe groter de voorspellingsfout. Dit is vrij logisch aangezien het steeds moeilijker wordt om te voorspellen naarmate de tijd vordert
Bij PE zien we dan de werkelijke fout.

We dienen nu even de (absolute waarden van de) werkelijke fout te vergelijken met de voorspellingsfout.
Zo zien we bijvoorbeeld dat bij de periodes 56 en 52 de voorspellingsfout verschilt van de werkelijke fout.
2008-12-17 14:12:14 [Romina Machiels] [reply] 
De student heeft de vraag correct beantwoord. Hij heeft de 5 stappen goed gemaakt.
2008-12-19 15:19:59 [Kim De Vos] [reply] 
Ik ga akkoord met bovenvermelde opmerkingen
2008-12-22 20:23:17 [8e2cc0b2ef568da46d009b2f601285b2] [reply] 
De student toont aan de techniek te snappen en beantwoord de vragen correct. Hoewel de antwoorden uitgebreider hadden gekunt.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
92.66
94.2
94.37
94.45
94.62
94.37
93.43
94.79
94.88
94.79
94.62
94.71
93.77
95.73
95.99
95.82
95.47
95.82
94.71
96.33
96.5
96.16
96.33
96.33
95.05
96.84
96.92
97.44
97.78
97.69
96.67
98.29
98.2
98.71
98.54
98.2
96.92
99.06
99.65
99.82
99.99
100.33
99.31
101.1
101.1
100.93
100.85
100.93
99.6
101.88
101.81
102.38
102.74
102.82
101.72
103.47
102.98
102.68
102.9
103.03
101.29

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31780&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31780&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31780&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 time1 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[49])
3796.92-------
3899.06-------
3999.65-------
4099.82-------
4199.99-------
42100.33-------
4399.31-------
44101.1-------
45101.1-------
46100.93-------
47100.85-------
48100.93-------
4999.6-------
50101.88101.4867101.0135101.95980.0516111
51101.81101.75101.0808102.41920.43030.351711
52102.38102.2514101.4318103.07090.37920.854411
53102.74102.6661101.7198103.61250.43920.723311
54102.82102.6507101.5927103.70880.37690.434311
55101.72101.6561100.497102.81510.4570.024510.9997
56103.47103.3337102.0818104.58560.41550.99420.99981
57102.98103.2335101.8952104.57190.35520.36460.99911
58102.68103.6102102.1907105.02970.09950.80790.99991
59102.9103.401101.9047104.89730.25580.82750.99961
60103.03103.1892101.6199104.75850.42120.6410.99761
61101.29101.9079100.2688103.5470.230.08980.99710.9971

\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[49]) \tabularnewline
37 & 96.92 & - & - & - & - & - & - & - \tabularnewline
38 & 99.06 & - & - & - & - & - & - & - \tabularnewline
39 & 99.65 & - & - & - & - & - & - & - \tabularnewline
40 & 99.82 & - & - & - & - & - & - & - \tabularnewline
41 & 99.99 & - & - & - & - & - & - & - \tabularnewline
42 & 100.33 & - & - & - & - & - & - & - \tabularnewline
43 & 99.31 & - & - & - & - & - & - & - \tabularnewline
44 & 101.1 & - & - & - & - & - & - & - \tabularnewline
45 & 101.1 & - & - & - & - & - & - & - \tabularnewline
46 & 100.93 & - & - & - & - & - & - & - \tabularnewline
47 & 100.85 & - & - & - & - & - & - & - \tabularnewline
48 & 100.93 & - & - & - & - & - & - & - \tabularnewline
49 & 99.6 & - & - & - & - & - & - & - \tabularnewline
50 & 101.88 & 101.4867 & 101.0135 & 101.9598 & 0.0516 & 1 & 1 & 1 \tabularnewline
51 & 101.81 & 101.75 & 101.0808 & 102.4192 & 0.4303 & 0.3517 & 1 & 1 \tabularnewline
52 & 102.38 & 102.2514 & 101.4318 & 103.0709 & 0.3792 & 0.8544 & 1 & 1 \tabularnewline
53 & 102.74 & 102.6661 & 101.7198 & 103.6125 & 0.4392 & 0.7233 & 1 & 1 \tabularnewline
54 & 102.82 & 102.6507 & 101.5927 & 103.7088 & 0.3769 & 0.4343 & 1 & 1 \tabularnewline
55 & 101.72 & 101.6561 & 100.497 & 102.8151 & 0.457 & 0.0245 & 1 & 0.9997 \tabularnewline
56 & 103.47 & 103.3337 & 102.0818 & 104.5856 & 0.4155 & 0.9942 & 0.9998 & 1 \tabularnewline
57 & 102.98 & 103.2335 & 101.8952 & 104.5719 & 0.3552 & 0.3646 & 0.9991 & 1 \tabularnewline
58 & 102.68 & 103.6102 & 102.1907 & 105.0297 & 0.0995 & 0.8079 & 0.9999 & 1 \tabularnewline
59 & 102.9 & 103.401 & 101.9047 & 104.8973 & 0.2558 & 0.8275 & 0.9996 & 1 \tabularnewline
60 & 103.03 & 103.1892 & 101.6199 & 104.7585 & 0.4212 & 0.641 & 0.9976 & 1 \tabularnewline
61 & 101.29 & 101.9079 & 100.2688 & 103.547 & 0.23 & 0.0898 & 0.9971 & 0.9971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31780&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[49])[/C][/ROW]
[ROW][C]37[/C][C]96.92[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]99.06[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]99.65[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]99.82[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]99.99[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]100.33[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]99.31[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]101.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]101.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]100.93[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]100.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]100.93[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]99.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]101.88[/C][C]101.4867[/C][C]101.0135[/C][C]101.9598[/C][C]0.0516[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]51[/C][C]101.81[/C][C]101.75[/C][C]101.0808[/C][C]102.4192[/C][C]0.4303[/C][C]0.3517[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]52[/C][C]102.38[/C][C]102.2514[/C][C]101.4318[/C][C]103.0709[/C][C]0.3792[/C][C]0.8544[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]53[/C][C]102.74[/C][C]102.6661[/C][C]101.7198[/C][C]103.6125[/C][C]0.4392[/C][C]0.7233[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]54[/C][C]102.82[/C][C]102.6507[/C][C]101.5927[/C][C]103.7088[/C][C]0.3769[/C][C]0.4343[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]55[/C][C]101.72[/C][C]101.6561[/C][C]100.497[/C][C]102.8151[/C][C]0.457[/C][C]0.0245[/C][C]1[/C][C]0.9997[/C][/ROW]
[ROW][C]56[/C][C]103.47[/C][C]103.3337[/C][C]102.0818[/C][C]104.5856[/C][C]0.4155[/C][C]0.9942[/C][C]0.9998[/C][C]1[/C][/ROW]
[ROW][C]57[/C][C]102.98[/C][C]103.2335[/C][C]101.8952[/C][C]104.5719[/C][C]0.3552[/C][C]0.3646[/C][C]0.9991[/C][C]1[/C][/ROW]
[ROW][C]58[/C][C]102.68[/C][C]103.6102[/C][C]102.1907[/C][C]105.0297[/C][C]0.0995[/C][C]0.8079[/C][C]0.9999[/C][C]1[/C][/ROW]
[ROW][C]59[/C][C]102.9[/C][C]103.401[/C][C]101.9047[/C][C]104.8973[/C][C]0.2558[/C][C]0.8275[/C][C]0.9996[/C][C]1[/C][/ROW]
[ROW][C]60[/C][C]103.03[/C][C]103.1892[/C][C]101.6199[/C][C]104.7585[/C][C]0.4212[/C][C]0.641[/C][C]0.9976[/C][C]1[/C][/ROW]
[ROW][C]61[/C][C]101.29[/C][C]101.9079[/C][C]100.2688[/C][C]103.547[/C][C]0.23[/C][C]0.0898[/C][C]0.9971[/C][C]0.9971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31780&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31780&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[49])
3796.92-------
3899.06-------
3999.65-------
4099.82-------
4199.99-------
42100.33-------
4399.31-------
44101.1-------
45101.1-------
46100.93-------
47100.85-------
48100.93-------
4999.6-------
50101.88101.4867101.0135101.95980.0516111
51101.81101.75101.0808102.41920.43030.351711
52102.38102.2514101.4318103.07090.37920.854411
53102.74102.6661101.7198103.61250.43920.723311
54102.82102.6507101.5927103.70880.37690.434311
55101.72101.6561100.497102.81510.4570.024510.9997
56103.47103.3337102.0818104.58560.41550.99420.99981
57102.98103.2335101.8952104.57190.35520.36460.99911
58102.68103.6102102.1907105.02970.09950.80790.99991
59102.9103.401101.9047104.89730.25580.82750.99961
60103.03103.1892101.6199104.75850.42120.6410.99761
61101.29101.9079100.2688103.5470.230.08980.99710.9971






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
500.00240.00393e-040.15470.01290.1135
510.00346e-0400.00363e-040.0173
520.00410.00131e-040.01650.00140.0371
530.00477e-041e-040.00555e-040.0213
540.00530.00161e-040.02870.00240.0489
550.00586e-041e-040.00413e-040.0185
560.00620.00131e-040.01860.00150.0394
570.0066-0.00252e-040.06430.00540.0732
580.007-0.0097e-040.86520.07210.2685
590.0074-0.00484e-040.2510.02090.1446
600.0078-0.00151e-040.02540.00210.046
610.0082-0.00615e-040.38180.03180.1784

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
50 & 0.0024 & 0.0039 & 3e-04 & 0.1547 & 0.0129 & 0.1135 \tabularnewline
51 & 0.0034 & 6e-04 & 0 & 0.0036 & 3e-04 & 0.0173 \tabularnewline
52 & 0.0041 & 0.0013 & 1e-04 & 0.0165 & 0.0014 & 0.0371 \tabularnewline
53 & 0.0047 & 7e-04 & 1e-04 & 0.0055 & 5e-04 & 0.0213 \tabularnewline
54 & 0.0053 & 0.0016 & 1e-04 & 0.0287 & 0.0024 & 0.0489 \tabularnewline
55 & 0.0058 & 6e-04 & 1e-04 & 0.0041 & 3e-04 & 0.0185 \tabularnewline
56 & 0.0062 & 0.0013 & 1e-04 & 0.0186 & 0.0015 & 0.0394 \tabularnewline
57 & 0.0066 & -0.0025 & 2e-04 & 0.0643 & 0.0054 & 0.0732 \tabularnewline
58 & 0.007 & -0.009 & 7e-04 & 0.8652 & 0.0721 & 0.2685 \tabularnewline
59 & 0.0074 & -0.0048 & 4e-04 & 0.251 & 0.0209 & 0.1446 \tabularnewline
60 & 0.0078 & -0.0015 & 1e-04 & 0.0254 & 0.0021 & 0.046 \tabularnewline
61 & 0.0082 & -0.0061 & 5e-04 & 0.3818 & 0.0318 & 0.1784 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31780&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]50[/C][C]0.0024[/C][C]0.0039[/C][C]3e-04[/C][C]0.1547[/C][C]0.0129[/C][C]0.1135[/C][/ROW]
[ROW][C]51[/C][C]0.0034[/C][C]6e-04[/C][C]0[/C][C]0.0036[/C][C]3e-04[/C][C]0.0173[/C][/ROW]
[ROW][C]52[/C][C]0.0041[/C][C]0.0013[/C][C]1e-04[/C][C]0.0165[/C][C]0.0014[/C][C]0.0371[/C][/ROW]
[ROW][C]53[/C][C]0.0047[/C][C]7e-04[/C][C]1e-04[/C][C]0.0055[/C][C]5e-04[/C][C]0.0213[/C][/ROW]
[ROW][C]54[/C][C]0.0053[/C][C]0.0016[/C][C]1e-04[/C][C]0.0287[/C][C]0.0024[/C][C]0.0489[/C][/ROW]
[ROW][C]55[/C][C]0.0058[/C][C]6e-04[/C][C]1e-04[/C][C]0.0041[/C][C]3e-04[/C][C]0.0185[/C][/ROW]
[ROW][C]56[/C][C]0.0062[/C][C]0.0013[/C][C]1e-04[/C][C]0.0186[/C][C]0.0015[/C][C]0.0394[/C][/ROW]
[ROW][C]57[/C][C]0.0066[/C][C]-0.0025[/C][C]2e-04[/C][C]0.0643[/C][C]0.0054[/C][C]0.0732[/C][/ROW]
[ROW][C]58[/C][C]0.007[/C][C]-0.009[/C][C]7e-04[/C][C]0.8652[/C][C]0.0721[/C][C]0.2685[/C][/ROW]
[ROW][C]59[/C][C]0.0074[/C][C]-0.0048[/C][C]4e-04[/C][C]0.251[/C][C]0.0209[/C][C]0.1446[/C][/ROW]
[ROW][C]60[/C][C]0.0078[/C][C]-0.0015[/C][C]1e-04[/C][C]0.0254[/C][C]0.0021[/C][C]0.046[/C][/ROW]
[ROW][C]61[/C][C]0.0082[/C][C]-0.0061[/C][C]5e-04[/C][C]0.3818[/C][C]0.0318[/C][C]0.1784[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31780&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31780&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
500.00240.00393e-040.15470.01290.1135
510.00346e-0400.00363e-040.0173
520.00410.00131e-040.01650.00140.0371
530.00477e-041e-040.00555e-040.0213
540.00530.00161e-040.02870.00240.0489
550.00586e-041e-040.00413e-040.0185
560.00620.00131e-040.01860.00150.0394
570.0066-0.00252e-040.06430.00540.0732
580.007-0.0097e-040.86520.07210.2685
590.0074-0.00484e-040.2510.02090.1446
600.0078-0.00151e-040.02540.00210.046
610.0082-0.00615e-040.38180.03180.1784


Figures (Output of Computation)

Input Parameters & R Code

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