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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Tue, 06 Dec 2011 19:41:11 -0500

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/2011/Dec/06/t1323218499j2nrbpmvly7l8ue.htm/, Retrieved Mon, 29 Apr 2024 03:40:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152059, Retrieved Mon, 29 Apr 2024 03:40:36 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

110

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]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Forecasting] [Unemployment] [2010-11-29 20:46:45] [b98453cac15ba1066b407e146608df68]
-    D      [ARIMA Forecasting] [WS 9 Forecasting ...] [2010-12-03 22:01:04] [8081b8996d5947580de3eb171e82db4f]
-   PD        [ARIMA Forecasting] [Workshop 9, Forecast] [2010-12-05 20:21:31] [3635fb7041b1998c5a1332cf9de22bce]
-   P           [ARIMA Forecasting] [ARIMA Extrapolati...] [2010-12-06 22:58:10] [3635fb7041b1998c5a1332cf9de22bce]
-   P             [ARIMA Forecasting] [Verbetering WS9] [2010-12-14 19:20:19] [3635fb7041b1998c5a1332cf9de22bce]
- R PD              [ARIMA Forecasting] [Ws9 ARIMA voorspe...] [2011-12-07 00:37:21] [43a0606d8103c0ba382f0586f4417c48]
- R                     [ARIMA Forecasting] [Ws9 ARIMA voorspe...] [2011-12-07 00:41:11] [635499bc27d9f41bf7bccae25a54e146] [Current]

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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	1 seconds
R Server	'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152059&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152059&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152059&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	1 seconds
R Server	'AstonUniversity' @ aston.wessa.net

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[60])
48	69	-	-	-	-	-	-	-
49	60	-	-	-	-	-	-	-
50	56	-	-	-	-	-	-	-
51	58	-	-	-	-	-	-	-
52	50	-	-	-	-	-	-	-
53	51	-	-	-	-	-	-	-
54	53	-	-	-	-	-	-	-
55	37	-	-	-	-	-	-	-
56	22	-	-	-	-	-	-	-
57	55	-	-	-	-	-	-	-
58	70	-	-	-	-	-	-	-
59	62	-	-	-	-	-	-	-
60	58	-	-	-	-	-	-	-
61	39	61.1105	38.7336	83.4874	0.0264	0.6074	0.5387	0.6074
62	49	53.5726	31.1449	76.0003	0.3447	0.8986	0.416	0.3494
63	58	59.1734	36.6557	81.691	0.4593	0.8121	0.5407	0.5407
64	47	49.6214	27.0037	72.2392	0.4101	0.2339	0.4869	0.2339
65	42	51.3275	28.7055	73.9496	0.2095	0.6461	0.5113	0.2816
66	62	52.848	30.2228	75.4732	0.2139	0.8263	0.4947	0.3277
67	39	37.0697	14.4432	59.6962	0.4336	0.0154	0.5024	0.0349
68	40	21.9551	-0.6715	44.5817	0.059	0.0699	0.4984	9e-04
69	72	55.0216	32.3949	77.6483	0.0707	0.9034	0.5007	0.3982
70	70	69.9889	47.3622	92.6157	0.4996	0.4309	0.4996	0.8505
71	54	62.0063	39.3796	84.6331	0.244	0.2443	0.5002	0.6357
72	65	57.9968	35.3701	80.6236	0.272	0.6354	0.4999	0.4999

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast \tabularnewline
time & Y[t] & F[t] & 95% LB & 95% UB & p-value(H0: Y[t] = F[t]) & P(F[t]>Y[t-1]) & P(F[t]>Y[t-s]) & P(F[t]>Y[60]) \tabularnewline
48 & 69 & - & - & - & - & - & - & - \tabularnewline
49 & 60 & - & - & - & - & - & - & - \tabularnewline
50 & 56 & - & - & - & - & - & - & - \tabularnewline
51 & 58 & - & - & - & - & - & - & - \tabularnewline
52 & 50 & - & - & - & - & - & - & - \tabularnewline
53 & 51 & - & - & - & - & - & - & - \tabularnewline
54 & 53 & - & - & - & - & - & - & - \tabularnewline
55 & 37 & - & - & - & - & - & - & - \tabularnewline
56 & 22 & - & - & - & - & - & - & - \tabularnewline
57 & 55 & - & - & - & - & - & - & - \tabularnewline
58 & 70 & - & - & - & - & - & - & - \tabularnewline
59 & 62 & - & - & - & - & - & - & - \tabularnewline
60 & 58 & - & - & - & - & - & - & - \tabularnewline
61 & 39 & 61.1105 & 38.7336 & 83.4874 & 0.0264 & 0.6074 & 0.5387 & 0.6074 \tabularnewline
62 & 49 & 53.5726 & 31.1449 & 76.0003 & 0.3447 & 0.8986 & 0.416 & 0.3494 \tabularnewline
63 & 58 & 59.1734 & 36.6557 & 81.691 & 0.4593 & 0.8121 & 0.5407 & 0.5407 \tabularnewline
64 & 47 & 49.6214 & 27.0037 & 72.2392 & 0.4101 & 0.2339 & 0.4869 & 0.2339 \tabularnewline
65 & 42 & 51.3275 & 28.7055 & 73.9496 & 0.2095 & 0.6461 & 0.5113 & 0.2816 \tabularnewline
66 & 62 & 52.848 & 30.2228 & 75.4732 & 0.2139 & 0.8263 & 0.4947 & 0.3277 \tabularnewline
67 & 39 & 37.0697 & 14.4432 & 59.6962 & 0.4336 & 0.0154 & 0.5024 & 0.0349 \tabularnewline
68 & 40 & 21.9551 & -0.6715 & 44.5817 & 0.059 & 0.0699 & 0.4984 & 9e-04 \tabularnewline
69 & 72 & 55.0216 & 32.3949 & 77.6483 & 0.0707 & 0.9034 & 0.5007 & 0.3982 \tabularnewline
70 & 70 & 69.9889 & 47.3622 & 92.6157 & 0.4996 & 0.4309 & 0.4996 & 0.8505 \tabularnewline
71 & 54 & 62.0063 & 39.3796 & 84.6331 & 0.244 & 0.2443 & 0.5002 & 0.6357 \tabularnewline
72 & 65 & 57.9968 & 35.3701 & 80.6236 & 0.272 & 0.6354 & 0.4999 & 0.4999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152059&T=1

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast[/C][/ROW]
[ROW][C]time[/C][C]Y[t][/C][C]F[t][/C][C]95% LB[/C][C]95% UB[/C][C]p-value(H0: Y[t] = F[t])[/C][C]P(F[t]>Y[t-1])[/C][C]P(F[t]>Y[t-s])[/C][C]P(F[t]>Y[60])[/C][/ROW]
[ROW][C]48[/C][C]69[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]60[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]56[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]58[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]50[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]51[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]53[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]37[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]22[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]55[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]70[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]62[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]58[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]39[/C][C]61.1105[/C][C]38.7336[/C][C]83.4874[/C][C]0.0264[/C][C]0.6074[/C][C]0.5387[/C][C]0.6074[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]53.5726[/C][C]31.1449[/C][C]76.0003[/C][C]0.3447[/C][C]0.8986[/C][C]0.416[/C][C]0.3494[/C][/ROW]
[ROW][C]63[/C][C]58[/C][C]59.1734[/C][C]36.6557[/C][C]81.691[/C][C]0.4593[/C][C]0.8121[/C][C]0.5407[/C][C]0.5407[/C][/ROW]
[ROW][C]64[/C][C]47[/C][C]49.6214[/C][C]27.0037[/C][C]72.2392[/C][C]0.4101[/C][C]0.2339[/C][C]0.4869[/C][C]0.2339[/C][/ROW]
[ROW][C]65[/C][C]42[/C][C]51.3275[/C][C]28.7055[/C][C]73.9496[/C][C]0.2095[/C][C]0.6461[/C][C]0.5113[/C][C]0.2816[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]52.848[/C][C]30.2228[/C][C]75.4732[/C][C]0.2139[/C][C]0.8263[/C][C]0.4947[/C][C]0.3277[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]37.0697[/C][C]14.4432[/C][C]59.6962[/C][C]0.4336[/C][C]0.0154[/C][C]0.5024[/C][C]0.0349[/C][/ROW]
[ROW][C]68[/C][C]40[/C][C]21.9551[/C][C]-0.6715[/C][C]44.5817[/C][C]0.059[/C][C]0.0699[/C][C]0.4984[/C][C]9e-04[/C][/ROW]
[ROW][C]69[/C][C]72[/C][C]55.0216[/C][C]32.3949[/C][C]77.6483[/C][C]0.0707[/C][C]0.9034[/C][C]0.5007[/C][C]0.3982[/C][/ROW]
[ROW][C]70[/C][C]70[/C][C]69.9889[/C][C]47.3622[/C][C]92.6157[/C][C]0.4996[/C][C]0.4309[/C][C]0.4996[/C][C]0.8505[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]62.0063[/C][C]39.3796[/C][C]84.6331[/C][C]0.244[/C][C]0.2443[/C][C]0.5002[/C][C]0.6357[/C][/ROW]
[ROW][C]72[/C][C]65[/C][C]57.9968[/C][C]35.3701[/C][C]80.6236[/C][C]0.272[/C][C]0.6354[/C][C]0.4999[/C][C]0.4999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152059&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152059&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[60])
48	69	-	-	-	-	-	-	-
49	60	-	-	-	-	-	-	-
50	56	-	-	-	-	-	-	-
51	58	-	-	-	-	-	-	-
52	50	-	-	-	-	-	-	-
53	51	-	-	-	-	-	-	-
54	53	-	-	-	-	-	-	-
55	37	-	-	-	-	-	-	-
56	22	-	-	-	-	-	-	-
57	55	-	-	-	-	-	-	-
58	70	-	-	-	-	-	-	-
59	62	-	-	-	-	-	-	-
60	58	-	-	-	-	-	-	-
61	39	61.1105	38.7336	83.4874	0.0264	0.6074	0.5387	0.6074
62	49	53.5726	31.1449	76.0003	0.3447	0.8986	0.416	0.3494
63	58	59.1734	36.6557	81.691	0.4593	0.8121	0.5407	0.5407
64	47	49.6214	27.0037	72.2392	0.4101	0.2339	0.4869	0.2339
65	42	51.3275	28.7055	73.9496	0.2095	0.6461	0.5113	0.2816
66	62	52.848	30.2228	75.4732	0.2139	0.8263	0.4947	0.3277
67	39	37.0697	14.4432	59.6962	0.4336	0.0154	0.5024	0.0349
68	40	21.9551	-0.6715	44.5817	0.059	0.0699	0.4984	9e-04
69	72	55.0216	32.3949	77.6483	0.0707	0.9034	0.5007	0.3982
70	70	69.9889	47.3622	92.6157	0.4996	0.4309	0.4996	0.8505
71	54	62.0063	39.3796	84.6331	0.244	0.2443	0.5002	0.6357
72	65	57.9968	35.3701	80.6236	0.272	0.6354	0.4999	0.4999

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
61	0.1868	-0.3618	0	488.8754	0	0
62	0.2136	-0.0854	0.2236	20.9086	254.892	15.9653
63	0.1942	-0.0198	0.1557	1.3768	170.3869	13.0532
64	0.2326	-0.0528	0.13	6.8719	129.5082	11.3802
65	0.2249	-0.1817	0.1403	87.003	121.0071	11.0003
66	0.2184	0.1732	0.1458	83.7587	114.799	10.7144
67	0.3114	0.0521	0.1324	3.7261	98.9315	9.9464
68	0.5258	0.8219	0.2186	325.6187	127.2674	11.2813
69	0.2098	0.3086	0.2286	288.2656	145.1561	12.0481
70	0.1649	2e-04	0.2057	1e-04	130.6405	11.4298
71	0.1862	-0.1291	0.1988	64.1013	124.5915	11.1621
72	0.199	0.1208	0.1923	49.0444	118.2959	10.8764

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
61 & 0.1868 & -0.3618 & 0 & 488.8754 & 0 & 0 \tabularnewline
62 & 0.2136 & -0.0854 & 0.2236 & 20.9086 & 254.892 & 15.9653 \tabularnewline
63 & 0.1942 & -0.0198 & 0.1557 & 1.3768 & 170.3869 & 13.0532 \tabularnewline
64 & 0.2326 & -0.0528 & 0.13 & 6.8719 & 129.5082 & 11.3802 \tabularnewline
65 & 0.2249 & -0.1817 & 0.1403 & 87.003 & 121.0071 & 11.0003 \tabularnewline
66 & 0.2184 & 0.1732 & 0.1458 & 83.7587 & 114.799 & 10.7144 \tabularnewline
67 & 0.3114 & 0.0521 & 0.1324 & 3.7261 & 98.9315 & 9.9464 \tabularnewline
68 & 0.5258 & 0.8219 & 0.2186 & 325.6187 & 127.2674 & 11.2813 \tabularnewline
69 & 0.2098 & 0.3086 & 0.2286 & 288.2656 & 145.1561 & 12.0481 \tabularnewline
70 & 0.1649 & 2e-04 & 0.2057 & 1e-04 & 130.6405 & 11.4298 \tabularnewline
71 & 0.1862 & -0.1291 & 0.1988 & 64.1013 & 124.5915 & 11.1621 \tabularnewline
72 & 0.199 & 0.1208 & 0.1923 & 49.0444 & 118.2959 & 10.8764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152059&T=2

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast Performance[/C][/ROW]
[ROW][C]time[/C][C]% S.E.[/C][C]PE[/C][C]MAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][/ROW]
[ROW][C]61[/C][C]0.1868[/C][C]-0.3618[/C][C]0[/C][C]488.8754[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]0.2136[/C][C]-0.0854[/C][C]0.2236[/C][C]20.9086[/C][C]254.892[/C][C]15.9653[/C][/ROW]
[ROW][C]63[/C][C]0.1942[/C][C]-0.0198[/C][C]0.1557[/C][C]1.3768[/C][C]170.3869[/C][C]13.0532[/C][/ROW]
[ROW][C]64[/C][C]0.2326[/C][C]-0.0528[/C][C]0.13[/C][C]6.8719[/C][C]129.5082[/C][C]11.3802[/C][/ROW]
[ROW][C]65[/C][C]0.2249[/C][C]-0.1817[/C][C]0.1403[/C][C]87.003[/C][C]121.0071[/C][C]11.0003[/C][/ROW]
[ROW][C]66[/C][C]0.2184[/C][C]0.1732[/C][C]0.1458[/C][C]83.7587[/C][C]114.799[/C][C]10.7144[/C][/ROW]
[ROW][C]67[/C][C]0.3114[/C][C]0.0521[/C][C]0.1324[/C][C]3.7261[/C][C]98.9315[/C][C]9.9464[/C][/ROW]
[ROW][C]68[/C][C]0.5258[/C][C]0.8219[/C][C]0.2186[/C][C]325.6187[/C][C]127.2674[/C][C]11.2813[/C][/ROW]
[ROW][C]69[/C][C]0.2098[/C][C]0.3086[/C][C]0.2286[/C][C]288.2656[/C][C]145.1561[/C][C]12.0481[/C][/ROW]
[ROW][C]70[/C][C]0.1649[/C][C]2e-04[/C][C]0.2057[/C][C]1e-04[/C][C]130.6405[/C][C]11.4298[/C][/ROW]
[ROW][C]71[/C][C]0.1862[/C][C]-0.1291[/C][C]0.1988[/C][C]64.1013[/C][C]124.5915[/C][C]11.1621[/C][/ROW]
[ROW][C]72[/C][C]0.199[/C][C]0.1208[/C][C]0.1923[/C][C]49.0444[/C][C]118.2959[/C][C]10.8764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152059&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152059&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
61	0.1868	-0.3618	0	488.8754	0	0
62	0.2136	-0.0854	0.2236	20.9086	254.892	15.9653
63	0.1942	-0.0198	0.1557	1.3768	170.3869	13.0532
64	0.2326	-0.0528	0.13	6.8719	129.5082	11.3802
65	0.2249	-0.1817	0.1403	87.003	121.0071	11.0003
66	0.2184	0.1732	0.1458	83.7587	114.799	10.7144
67	0.3114	0.0521	0.1324	3.7261	98.9315	9.9464
68	0.5258	0.8219	0.2186	325.6187	127.2674	11.2813
69	0.2098	0.3086	0.2286	288.2656	145.1561	12.0481
70	0.1649	2e-04	0.2057	1e-04	130.6405	11.4298
71	0.1862	-0.1291	0.1988	64.1013	124.5915	11.1621
72	0.199	0.1208	0.1923	49.0444	118.2959	10.8764

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 1.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

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

R code (references can be found in the software module):

par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,par1))
(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.mape1 <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.mse1 <- 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$pred[i]
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
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[1] = abs(perf.pe[1])
perf.mse[1] = abs(perf.se[1])
for (i in 2:fx) {
perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
perf.mape1[i] = perf.mape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
}
perf.rmse = sqrt(perf.mse1)
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:par1] <- 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.mape1[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse1[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