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Author

*The author of this computation has been verified*

R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Mon, 22 Dec 2008 06:21:52 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/22/t1229954177wtzl51r8dy69a7h.htm/, Retrieved Sun, 12 May 2024 18:36:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36067, Retrieved Sun, 12 May 2024 18:36:12 +0000

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Original text written by user:

in samenwerking met katrien bourdiaudhy, st�phanie claes en kevin engels

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

193

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

F     [Univariate Data Series] [blog 1e tijdreeks...] [2008-10-13 19:23:31] [7173087adebe3e3a714c80ea2417b3eb]
-   PD  [Univariate Data Series] [tijdreeksen opnie...] [2008-10-19 17:13:12] [7173087adebe3e3a714c80ea2417b3eb]
-   PD    [Univariate Data Series] [tijdreeksen opnie...] [2008-10-19 18:55:20] [7173087adebe3e3a714c80ea2417b3eb]
- RM        [Central Tendency] [central tendency ...] [2008-10-19 19:10:37] [7173087adebe3e3a714c80ea2417b3eb]
- RMP         [ARIMA Backward Selection] [arima backward st...] [2008-12-08 22:03:24] [7173087adebe3e3a714c80ea2417b3eb]
- RMP             [ARIMA Forecasting] [forecast bouwverg...] [2008-12-22 13:21:52] [95d95b0e883740fcbc85e18ec42dcafb] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36067&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36067&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36067&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value(H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[48])
36	9169	-	-	-	-	-	-	-
37	7701	-	-	-	-	-	-	-
38	9035	-	-	-	-	-	-	-
39	7158	-	-	-	-	-	-	-
40	8195	-	-	-	-	-	-	-
41	8124	-	-	-	-	-	-	-
42	7073	-	-	-	-	-	-	-
43	7017	-	-	-	-	-	-	-
44	7390	-	-	-	-	-	-	-
45	7776	-	-	-	-	-	-	-
46	6197	-	-	-	-	-	-	-
47	6889	-	-	-	-	-	-	-
48	7087	-	-	-	-	-	-	-
49	6485	6569.1467	5196.1388	7942.1546	0.4522	0.2299	0.0531	0.2299
50	7654	7500.3183	6028.3388	8972.2978	0.4189	0.9118	0.0205	0.709
51	6501	6800.3946	5272.0814	8328.7077	0.3505	0.1368	0.3233	0.3566
52	6313	7012.2897	5285.6901	8738.8892	0.2137	0.7192	0.0897	0.4662
53	7826	7494.3901	5667.6541	9321.1261	0.361	0.8975	0.2497	0.669
54	6589	6370.1315	4469.6246	8270.6385	0.4107	0.0666	0.2343	0.2299
55	6729	6403.6556	4402.3572	8404.954	0.375	0.428	0.274	0.2517
56	5684	6678.1279	4597.3419	8758.9139	0.1745	0.4809	0.2513	0.3501
57	8105	6749.2152	4601.5255	8896.9049	0.108	0.8345	0.1744	0.3789
58	6391	5963.1519	3746.7758	8179.528	0.3526	0.0291	0.4181	0.1601
59	5901	6765.1607	4486.7924	9043.529	0.2286	0.6262	0.4576	0.3909
60	6758	6996.2655	4662.4261	9330.105	0.4207	0.8212	0.4696	0.4696

\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[48]) \tabularnewline
36 & 9169 & - & - & - & - & - & - & - \tabularnewline
37 & 7701 & - & - & - & - & - & - & - \tabularnewline
38 & 9035 & - & - & - & - & - & - & - \tabularnewline
39 & 7158 & - & - & - & - & - & - & - \tabularnewline
40 & 8195 & - & - & - & - & - & - & - \tabularnewline
41 & 8124 & - & - & - & - & - & - & - \tabularnewline
42 & 7073 & - & - & - & - & - & - & - \tabularnewline
43 & 7017 & - & - & - & - & - & - & - \tabularnewline
44 & 7390 & - & - & - & - & - & - & - \tabularnewline
45 & 7776 & - & - & - & - & - & - & - \tabularnewline
46 & 6197 & - & - & - & - & - & - & - \tabularnewline
47 & 6889 & - & - & - & - & - & - & - \tabularnewline
48 & 7087 & - & - & - & - & - & - & - \tabularnewline
49 & 6485 & 6569.1467 & 5196.1388 & 7942.1546 & 0.4522 & 0.2299 & 0.0531 & 0.2299 \tabularnewline
50 & 7654 & 7500.3183 & 6028.3388 & 8972.2978 & 0.4189 & 0.9118 & 0.0205 & 0.709 \tabularnewline
51 & 6501 & 6800.3946 & 5272.0814 & 8328.7077 & 0.3505 & 0.1368 & 0.3233 & 0.3566 \tabularnewline
52 & 6313 & 7012.2897 & 5285.6901 & 8738.8892 & 0.2137 & 0.7192 & 0.0897 & 0.4662 \tabularnewline
53 & 7826 & 7494.3901 & 5667.6541 & 9321.1261 & 0.361 & 0.8975 & 0.2497 & 0.669 \tabularnewline
54 & 6589 & 6370.1315 & 4469.6246 & 8270.6385 & 0.4107 & 0.0666 & 0.2343 & 0.2299 \tabularnewline
55 & 6729 & 6403.6556 & 4402.3572 & 8404.954 & 0.375 & 0.428 & 0.274 & 0.2517 \tabularnewline
56 & 5684 & 6678.1279 & 4597.3419 & 8758.9139 & 0.1745 & 0.4809 & 0.2513 & 0.3501 \tabularnewline
57 & 8105 & 6749.2152 & 4601.5255 & 8896.9049 & 0.108 & 0.8345 & 0.1744 & 0.3789 \tabularnewline
58 & 6391 & 5963.1519 & 3746.7758 & 8179.528 & 0.3526 & 0.0291 & 0.4181 & 0.1601 \tabularnewline
59 & 5901 & 6765.1607 & 4486.7924 & 9043.529 & 0.2286 & 0.6262 & 0.4576 & 0.3909 \tabularnewline
60 & 6758 & 6996.2655 & 4662.4261 & 9330.105 & 0.4207 & 0.8212 & 0.4696 & 0.4696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36067&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[48])[/C][/ROW]
[ROW][C]36[/C][C]9169[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]7701[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]9035[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]7158[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]8195[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]8124[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]7073[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]7017[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]7390[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]7776[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]6197[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]6889[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]7087[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]6485[/C][C]6569.1467[/C][C]5196.1388[/C][C]7942.1546[/C][C]0.4522[/C][C]0.2299[/C][C]0.0531[/C][C]0.2299[/C][/ROW]
[ROW][C]50[/C][C]7654[/C][C]7500.3183[/C][C]6028.3388[/C][C]8972.2978[/C][C]0.4189[/C][C]0.9118[/C][C]0.0205[/C][C]0.709[/C][/ROW]
[ROW][C]51[/C][C]6501[/C][C]6800.3946[/C][C]5272.0814[/C][C]8328.7077[/C][C]0.3505[/C][C]0.1368[/C][C]0.3233[/C][C]0.3566[/C][/ROW]
[ROW][C]52[/C][C]6313[/C][C]7012.2897[/C][C]5285.6901[/C][C]8738.8892[/C][C]0.2137[/C][C]0.7192[/C][C]0.0897[/C][C]0.4662[/C][/ROW]
[ROW][C]53[/C][C]7826[/C][C]7494.3901[/C][C]5667.6541[/C][C]9321.1261[/C][C]0.361[/C][C]0.8975[/C][C]0.2497[/C][C]0.669[/C][/ROW]
[ROW][C]54[/C][C]6589[/C][C]6370.1315[/C][C]4469.6246[/C][C]8270.6385[/C][C]0.4107[/C][C]0.0666[/C][C]0.2343[/C][C]0.2299[/C][/ROW]
[ROW][C]55[/C][C]6729[/C][C]6403.6556[/C][C]4402.3572[/C][C]8404.954[/C][C]0.375[/C][C]0.428[/C][C]0.274[/C][C]0.2517[/C][/ROW]
[ROW][C]56[/C][C]5684[/C][C]6678.1279[/C][C]4597.3419[/C][C]8758.9139[/C][C]0.1745[/C][C]0.4809[/C][C]0.2513[/C][C]0.3501[/C][/ROW]
[ROW][C]57[/C][C]8105[/C][C]6749.2152[/C][C]4601.5255[/C][C]8896.9049[/C][C]0.108[/C][C]0.8345[/C][C]0.1744[/C][C]0.3789[/C][/ROW]
[ROW][C]58[/C][C]6391[/C][C]5963.1519[/C][C]3746.7758[/C][C]8179.528[/C][C]0.3526[/C][C]0.0291[/C][C]0.4181[/C][C]0.1601[/C][/ROW]
[ROW][C]59[/C][C]5901[/C][C]6765.1607[/C][C]4486.7924[/C][C]9043.529[/C][C]0.2286[/C][C]0.6262[/C][C]0.4576[/C][C]0.3909[/C][/ROW]
[ROW][C]60[/C][C]6758[/C][C]6996.2655[/C][C]4662.4261[/C][C]9330.105[/C][C]0.4207[/C][C]0.8212[/C][C]0.4696[/C][C]0.4696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36067&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36067&T=1

As an alternative you can also use a QR Code:

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

Univariate ARIMA Extrapolation Forecast
time	Y[t]	F[t]	95% LB	95% UB	p-value(H0: Y[t] = F[t])	P(F[t]>Y[t-1])	P(F[t]>Y[t-s])	P(F[t]>Y[48])
36	9169	-	-	-	-	-	-	-
37	7701	-	-	-	-	-	-	-
38	9035	-	-	-	-	-	-	-
39	7158	-	-	-	-	-	-	-
40	8195	-	-	-	-	-	-	-
41	8124	-	-	-	-	-	-	-
42	7073	-	-	-	-	-	-	-
43	7017	-	-	-	-	-	-	-
44	7390	-	-	-	-	-	-	-
45	7776	-	-	-	-	-	-	-
46	6197	-	-	-	-	-	-	-
47	6889	-	-	-	-	-	-	-
48	7087	-	-	-	-	-	-	-
49	6485	6569.1467	5196.1388	7942.1546	0.4522	0.2299	0.0531	0.2299
50	7654	7500.3183	6028.3388	8972.2978	0.4189	0.9118	0.0205	0.709
51	6501	6800.3946	5272.0814	8328.7077	0.3505	0.1368	0.3233	0.3566
52	6313	7012.2897	5285.6901	8738.8892	0.2137	0.7192	0.0897	0.4662
53	7826	7494.3901	5667.6541	9321.1261	0.361	0.8975	0.2497	0.669
54	6589	6370.1315	4469.6246	8270.6385	0.4107	0.0666	0.2343	0.2299
55	6729	6403.6556	4402.3572	8404.954	0.375	0.428	0.274	0.2517
56	5684	6678.1279	4597.3419	8758.9139	0.1745	0.4809	0.2513	0.3501
57	8105	6749.2152	4601.5255	8896.9049	0.108	0.8345	0.1744	0.3789
58	6391	5963.1519	3746.7758	8179.528	0.3526	0.0291	0.4181	0.1601
59	5901	6765.1607	4486.7924	9043.529	0.2286	0.6262	0.4576	0.3909
60	6758	6996.2655	4662.4261	9330.105	0.4207	0.8212	0.4696	0.4696

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
49	0.1066	-0.0128	0.0011	7080.6646	590.0554	24.2911
50	0.1001	0.0205	0.0017	23618.0751	1968.1729	44.3641
51	0.1147	-0.044	0.0037	89637.0986	7469.7582	86.4278
52	0.1256	-0.0997	0.0083	489006.019	40750.5016	201.8675
53	0.1244	0.0442	0.0037	109965.1061	9163.7588	95.7275
54	0.1522	0.0344	0.0029	47903.3988	3991.9499	63.1819
55	0.1595	0.0508	0.0042	105848.9771	8820.7481	93.9188
56	0.159	-0.1489	0.0124	988290.3444	82357.5287	286.98
57	0.1624	0.2009	0.0167	1838152.4722	153179.3727	391.3814
58	0.1896	0.0717	0.006	183054.0035	15254.5003	123.5091
59	0.1718	-0.1277	0.0106	746773.7354	62231.1446	249.4617
60	0.1702	-0.0341	0.0028	56770.4687	4730.8724	68.7813

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.1066 & -0.0128 & 0.0011 & 7080.6646 & 590.0554 & 24.2911 \tabularnewline
50 & 0.1001 & 0.0205 & 0.0017 & 23618.0751 & 1968.1729 & 44.3641 \tabularnewline
51 & 0.1147 & -0.044 & 0.0037 & 89637.0986 & 7469.7582 & 86.4278 \tabularnewline
52 & 0.1256 & -0.0997 & 0.0083 & 489006.019 & 40750.5016 & 201.8675 \tabularnewline
53 & 0.1244 & 0.0442 & 0.0037 & 109965.1061 & 9163.7588 & 95.7275 \tabularnewline
54 & 0.1522 & 0.0344 & 0.0029 & 47903.3988 & 3991.9499 & 63.1819 \tabularnewline
55 & 0.1595 & 0.0508 & 0.0042 & 105848.9771 & 8820.7481 & 93.9188 \tabularnewline
56 & 0.159 & -0.1489 & 0.0124 & 988290.3444 & 82357.5287 & 286.98 \tabularnewline
57 & 0.1624 & 0.2009 & 0.0167 & 1838152.4722 & 153179.3727 & 391.3814 \tabularnewline
58 & 0.1896 & 0.0717 & 0.006 & 183054.0035 & 15254.5003 & 123.5091 \tabularnewline
59 & 0.1718 & -0.1277 & 0.0106 & 746773.7354 & 62231.1446 & 249.4617 \tabularnewline
60 & 0.1702 & -0.0341 & 0.0028 & 56770.4687 & 4730.8724 & 68.7813 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36067&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]49[/C][C]0.1066[/C][C]-0.0128[/C][C]0.0011[/C][C]7080.6646[/C][C]590.0554[/C][C]24.2911[/C][/ROW]
[ROW][C]50[/C][C]0.1001[/C][C]0.0205[/C][C]0.0017[/C][C]23618.0751[/C][C]1968.1729[/C][C]44.3641[/C][/ROW]
[ROW][C]51[/C][C]0.1147[/C][C]-0.044[/C][C]0.0037[/C][C]89637.0986[/C][C]7469.7582[/C][C]86.4278[/C][/ROW]
[ROW][C]52[/C][C]0.1256[/C][C]-0.0997[/C][C]0.0083[/C][C]489006.019[/C][C]40750.5016[/C][C]201.8675[/C][/ROW]
[ROW][C]53[/C][C]0.1244[/C][C]0.0442[/C][C]0.0037[/C][C]109965.1061[/C][C]9163.7588[/C][C]95.7275[/C][/ROW]
[ROW][C]54[/C][C]0.1522[/C][C]0.0344[/C][C]0.0029[/C][C]47903.3988[/C][C]3991.9499[/C][C]63.1819[/C][/ROW]
[ROW][C]55[/C][C]0.1595[/C][C]0.0508[/C][C]0.0042[/C][C]105848.9771[/C][C]8820.7481[/C][C]93.9188[/C][/ROW]
[ROW][C]56[/C][C]0.159[/C][C]-0.1489[/C][C]0.0124[/C][C]988290.3444[/C][C]82357.5287[/C][C]286.98[/C][/ROW]
[ROW][C]57[/C][C]0.1624[/C][C]0.2009[/C][C]0.0167[/C][C]1838152.4722[/C][C]153179.3727[/C][C]391.3814[/C][/ROW]
[ROW][C]58[/C][C]0.1896[/C][C]0.0717[/C][C]0.006[/C][C]183054.0035[/C][C]15254.5003[/C][C]123.5091[/C][/ROW]
[ROW][C]59[/C][C]0.1718[/C][C]-0.1277[/C][C]0.0106[/C][C]746773.7354[/C][C]62231.1446[/C][C]249.4617[/C][/ROW]
[ROW][C]60[/C][C]0.1702[/C][C]-0.0341[/C][C]0.0028[/C][C]56770.4687[/C][C]4730.8724[/C][C]68.7813[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36067&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36067&T=2

As an alternative you can also use a QR Code:

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

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
49	0.1066	-0.0128	0.0011	7080.6646	590.0554	24.2911
50	0.1001	0.0205	0.0017	23618.0751	1968.1729	44.3641
51	0.1147	-0.044	0.0037	89637.0986	7469.7582	86.4278
52	0.1256	-0.0997	0.0083	489006.019	40750.5016	201.8675
53	0.1244	0.0442	0.0037	109965.1061	9163.7588	95.7275
54	0.1522	0.0344	0.0029	47903.3988	3991.9499	63.1819
55	0.1595	0.0508	0.0042	105848.9771	8820.7481	93.9188
56	0.159	-0.1489	0.0124	988290.3444	82357.5287	286.98
57	0.1624	0.2009	0.0167	1838152.4722	153179.3727	391.3814
58	0.1896	0.0717	0.006	183054.0035	15254.5003	123.5091
59	0.1718	-0.1277	0.0106	746773.7354	62231.1446	249.4617
60	0.1702	-0.0341	0.0028	56770.4687	4730.8724	68.7813

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code