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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 computationSat, 10 Dec 2011 09:43:17 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/10/t13235282418ucxn6v5gfsg91o.htm/, Retrieved Sun, 05 May 2024 06:36:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153562, Retrieved Sun, 05 May 2024 06:36:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147

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]
- 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 P               [ARIMA Forecasting] [] [2011-12-02 16:20:33] [b1eb71d4db1ceb5d347df987feb4a25e]
- R PD                  [ARIMA Forecasting] [] [2011-12-10 14:43:17] [a1e1d0bae7c18896aaea36b6ddc51406] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12008,00
9169,00
8788,00
8417,00
8247,00
8197,00
8236,00
8253,00
7733,00
8366,00
8626,00
8863,00
10102,00
8463,00
9114,00
8563,00
8872,00
8301,00
8301,00
8278,00
7736,00
7973,00
8268,00
9476,00
11100,00
8962,00
9173,00
8738,00
8459,00
8078,00
8411,00
8291,00
7810,00
8616,00
8312,00
9692,00
9911,00
8915,00
9452,00
9112,00
8472,00
8230,00
8384,00
8625,00
8221,00
8649,00
8625,00
10443,00
10357,00
8586,00
8892,00
8329,00
8101,00
7922,00
8120,00
7838,00
7735,00
8406,00
8209,00
9451,00
10041,00
9411,00
10405,00
8467,00
8464,00
8102,00
7627,00
7513,00
7510,00
8291,00
8064,00
9383,00
9706,00
8579,00
9474,00
8318,00
8213,00
8059,00
9111,00
7708,00
7680,00
8014,00
8007,00
8718,00
9486,00
9113,00
9025,00
8476,00
7952,00
7759,00
7835,00
7600,00
7651,00
8319,00
8812,00
8630,00

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153562&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153562&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153562&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






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[84])
729383-------
739706-------
748579-------
759474-------
768318-------
778213-------
788059-------
799111-------
807708-------
817680-------
828014-------
838007-------
848718-------
8594869544.16798744.018710344.31710.44330.97850.34590.9785
8691138973.32948102.7939843.86580.37660.12420.81270.7173
87902510074.50749188.012110961.00270.01020.98320.90790.9986
8884768419.23577528.97729309.49410.45030.09120.58820.2553
8979528385.54587494.39249276.69920.17020.42120.64780.2323
9077598111.19157219.82489002.55820.21930.63680.54570.0911
9178358322.14327430.72579213.56070.14210.89220.04140.192
9276007614.19366722.7648505.62330.48760.31370.41830.0076
9376517598.01296706.58048489.44540.45360.49830.42850.0069
9483198145.22687253.79369036.660.35120.86140.61350.104
9588128042.25617150.82278933.68940.04530.27140.53090.0687
9686309101.76948210.33619993.20260.14980.7380.80060.8006

\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[84]) \tabularnewline
72 & 9383 & - & - & - & - & - & - & - \tabularnewline
73 & 9706 & - & - & - & - & - & - & - \tabularnewline
74 & 8579 & - & - & - & - & - & - & - \tabularnewline
75 & 9474 & - & - & - & - & - & - & - \tabularnewline
76 & 8318 & - & - & - & - & - & - & - \tabularnewline
77 & 8213 & - & - & - & - & - & - & - \tabularnewline
78 & 8059 & - & - & - & - & - & - & - \tabularnewline
79 & 9111 & - & - & - & - & - & - & - \tabularnewline
80 & 7708 & - & - & - & - & - & - & - \tabularnewline
81 & 7680 & - & - & - & - & - & - & - \tabularnewline
82 & 8014 & - & - & - & - & - & - & - \tabularnewline
83 & 8007 & - & - & - & - & - & - & - \tabularnewline
84 & 8718 & - & - & - & - & - & - & - \tabularnewline
85 & 9486 & 9544.1679 & 8744.0187 & 10344.3171 & 0.4433 & 0.9785 & 0.3459 & 0.9785 \tabularnewline
86 & 9113 & 8973.3294 & 8102.793 & 9843.8658 & 0.3766 & 0.1242 & 0.8127 & 0.7173 \tabularnewline
87 & 9025 & 10074.5074 & 9188.0121 & 10961.0027 & 0.0102 & 0.9832 & 0.9079 & 0.9986 \tabularnewline
88 & 8476 & 8419.2357 & 7528.9772 & 9309.4941 & 0.4503 & 0.0912 & 0.5882 & 0.2553 \tabularnewline
89 & 7952 & 8385.5458 & 7494.3924 & 9276.6992 & 0.1702 & 0.4212 & 0.6478 & 0.2323 \tabularnewline
90 & 7759 & 8111.1915 & 7219.8248 & 9002.5582 & 0.2193 & 0.6368 & 0.5457 & 0.0911 \tabularnewline
91 & 7835 & 8322.1432 & 7430.7257 & 9213.5607 & 0.1421 & 0.8922 & 0.0414 & 0.192 \tabularnewline
92 & 7600 & 7614.1936 & 6722.764 & 8505.6233 & 0.4876 & 0.3137 & 0.4183 & 0.0076 \tabularnewline
93 & 7651 & 7598.0129 & 6706.5804 & 8489.4454 & 0.4536 & 0.4983 & 0.4285 & 0.0069 \tabularnewline
94 & 8319 & 8145.2268 & 7253.7936 & 9036.66 & 0.3512 & 0.8614 & 0.6135 & 0.104 \tabularnewline
95 & 8812 & 8042.2561 & 7150.8227 & 8933.6894 & 0.0453 & 0.2714 & 0.5309 & 0.0687 \tabularnewline
96 & 8630 & 9101.7694 & 8210.3361 & 9993.2026 & 0.1498 & 0.738 & 0.8006 & 0.8006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153562&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[84])[/C][/ROW]
[ROW][C]72[/C][C]9383[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]73[/C][C]9706[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]74[/C][C]8579[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]75[/C][C]9474[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]76[/C][C]8318[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]77[/C][C]8213[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]78[/C][C]8059[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]79[/C][C]9111[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]80[/C][C]7708[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]81[/C][C]7680[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]82[/C][C]8014[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]83[/C][C]8007[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]84[/C][C]8718[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]85[/C][C]9486[/C][C]9544.1679[/C][C]8744.0187[/C][C]10344.3171[/C][C]0.4433[/C][C]0.9785[/C][C]0.3459[/C][C]0.9785[/C][/ROW]
[ROW][C]86[/C][C]9113[/C][C]8973.3294[/C][C]8102.793[/C][C]9843.8658[/C][C]0.3766[/C][C]0.1242[/C][C]0.8127[/C][C]0.7173[/C][/ROW]
[ROW][C]87[/C][C]9025[/C][C]10074.5074[/C][C]9188.0121[/C][C]10961.0027[/C][C]0.0102[/C][C]0.9832[/C][C]0.9079[/C][C]0.9986[/C][/ROW]
[ROW][C]88[/C][C]8476[/C][C]8419.2357[/C][C]7528.9772[/C][C]9309.4941[/C][C]0.4503[/C][C]0.0912[/C][C]0.5882[/C][C]0.2553[/C][/ROW]
[ROW][C]89[/C][C]7952[/C][C]8385.5458[/C][C]7494.3924[/C][C]9276.6992[/C][C]0.1702[/C][C]0.4212[/C][C]0.6478[/C][C]0.2323[/C][/ROW]
[ROW][C]90[/C][C]7759[/C][C]8111.1915[/C][C]7219.8248[/C][C]9002.5582[/C][C]0.2193[/C][C]0.6368[/C][C]0.5457[/C][C]0.0911[/C][/ROW]
[ROW][C]91[/C][C]7835[/C][C]8322.1432[/C][C]7430.7257[/C][C]9213.5607[/C][C]0.1421[/C][C]0.8922[/C][C]0.0414[/C][C]0.192[/C][/ROW]
[ROW][C]92[/C][C]7600[/C][C]7614.1936[/C][C]6722.764[/C][C]8505.6233[/C][C]0.4876[/C][C]0.3137[/C][C]0.4183[/C][C]0.0076[/C][/ROW]
[ROW][C]93[/C][C]7651[/C][C]7598.0129[/C][C]6706.5804[/C][C]8489.4454[/C][C]0.4536[/C][C]0.4983[/C][C]0.4285[/C][C]0.0069[/C][/ROW]
[ROW][C]94[/C][C]8319[/C][C]8145.2268[/C][C]7253.7936[/C][C]9036.66[/C][C]0.3512[/C][C]0.8614[/C][C]0.6135[/C][C]0.104[/C][/ROW]
[ROW][C]95[/C][C]8812[/C][C]8042.2561[/C][C]7150.8227[/C][C]8933.6894[/C][C]0.0453[/C][C]0.2714[/C][C]0.5309[/C][C]0.0687[/C][/ROW]
[ROW][C]96[/C][C]8630[/C][C]9101.7694[/C][C]8210.3361[/C][C]9993.2026[/C][C]0.1498[/C][C]0.738[/C][C]0.8006[/C][C]0.8006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153562&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153562&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[84])
729383-------
739706-------
748579-------
759474-------
768318-------
778213-------
788059-------
799111-------
807708-------
817680-------
828014-------
838007-------
848718-------
8594869544.16798744.018710344.31710.44330.97850.34590.9785
8691138973.32948102.7939843.86580.37660.12420.81270.7173
87902510074.50749188.012110961.00270.01020.98320.90790.9986
8884768419.23577528.97729309.49410.45030.09120.58820.2553
8979528385.54587494.39249276.69920.17020.42120.64780.2323
9077598111.19157219.82489002.55820.21930.63680.54570.0911
9178358322.14327430.72579213.56070.14210.89220.04140.192
9276007614.19366722.7648505.62330.48760.31370.41830.0076
9376517598.01296706.58048489.44540.45360.49830.42850.0069
9483198145.22687253.79369036.660.35120.86140.61350.104
9588128042.25617150.82278933.68940.04530.27140.53090.0687
9686309101.76948210.33619993.20260.14980.7380.80060.8006






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
850.0428-0.006103383.500800
860.04950.01560.010819507.870611445.6857106.9845
870.0449-0.10420.04191101465.826374785.7325612.1975
880.05390.00670.03313222.1906281894.847530.9377
890.0542-0.05170.0369187961.9872263108.2751512.9408
900.0561-0.04340.0379124038.848239930.0372489.8265
910.0546-0.05850.0409237308.501239555.532489.4441
920.0597-0.00190.036201.4595209636.273457.8605
930.05990.0070.03282807.6312186655.3128432.0362
940.05580.02130.031630197.1121171009.4927413.5329
950.05660.09570.0375592505.7453209327.3338457.523
960.05-0.05180.0387222566.3215210430.5828458.7271

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
85 & 0.0428 & -0.0061 & 0 & 3383.5008 & 0 & 0 \tabularnewline
86 & 0.0495 & 0.0156 & 0.0108 & 19507.8706 & 11445.6857 & 106.9845 \tabularnewline
87 & 0.0449 & -0.1042 & 0.0419 & 1101465.826 & 374785.7325 & 612.1975 \tabularnewline
88 & 0.0539 & 0.0067 & 0.0331 & 3222.1906 & 281894.847 & 530.9377 \tabularnewline
89 & 0.0542 & -0.0517 & 0.0369 & 187961.9872 & 263108.2751 & 512.9408 \tabularnewline
90 & 0.0561 & -0.0434 & 0.0379 & 124038.848 & 239930.0372 & 489.8265 \tabularnewline
91 & 0.0546 & -0.0585 & 0.0409 & 237308.501 & 239555.532 & 489.4441 \tabularnewline
92 & 0.0597 & -0.0019 & 0.036 & 201.4595 & 209636.273 & 457.8605 \tabularnewline
93 & 0.0599 & 0.007 & 0.0328 & 2807.6312 & 186655.3128 & 432.0362 \tabularnewline
94 & 0.0558 & 0.0213 & 0.0316 & 30197.1121 & 171009.4927 & 413.5329 \tabularnewline
95 & 0.0566 & 0.0957 & 0.0375 & 592505.7453 & 209327.3338 & 457.523 \tabularnewline
96 & 0.05 & -0.0518 & 0.0387 & 222566.3215 & 210430.5828 & 458.7271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153562&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]85[/C][C]0.0428[/C][C]-0.0061[/C][C]0[/C][C]3383.5008[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]86[/C][C]0.0495[/C][C]0.0156[/C][C]0.0108[/C][C]19507.8706[/C][C]11445.6857[/C][C]106.9845[/C][/ROW]
[ROW][C]87[/C][C]0.0449[/C][C]-0.1042[/C][C]0.0419[/C][C]1101465.826[/C][C]374785.7325[/C][C]612.1975[/C][/ROW]
[ROW][C]88[/C][C]0.0539[/C][C]0.0067[/C][C]0.0331[/C][C]3222.1906[/C][C]281894.847[/C][C]530.9377[/C][/ROW]
[ROW][C]89[/C][C]0.0542[/C][C]-0.0517[/C][C]0.0369[/C][C]187961.9872[/C][C]263108.2751[/C][C]512.9408[/C][/ROW]
[ROW][C]90[/C][C]0.0561[/C][C]-0.0434[/C][C]0.0379[/C][C]124038.848[/C][C]239930.0372[/C][C]489.8265[/C][/ROW]
[ROW][C]91[/C][C]0.0546[/C][C]-0.0585[/C][C]0.0409[/C][C]237308.501[/C][C]239555.532[/C][C]489.4441[/C][/ROW]
[ROW][C]92[/C][C]0.0597[/C][C]-0.0019[/C][C]0.036[/C][C]201.4595[/C][C]209636.273[/C][C]457.8605[/C][/ROW]
[ROW][C]93[/C][C]0.0599[/C][C]0.007[/C][C]0.0328[/C][C]2807.6312[/C][C]186655.3128[/C][C]432.0362[/C][/ROW]
[ROW][C]94[/C][C]0.0558[/C][C]0.0213[/C][C]0.0316[/C][C]30197.1121[/C][C]171009.4927[/C][C]413.5329[/C][/ROW]
[ROW][C]95[/C][C]0.0566[/C][C]0.0957[/C][C]0.0375[/C][C]592505.7453[/C][C]209327.3338[/C][C]457.523[/C][/ROW]
[ROW][C]96[/C][C]0.05[/C][C]-0.0518[/C][C]0.0387[/C][C]222566.3215[/C][C]210430.5828[/C][C]458.7271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153562&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153562&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
850.0428-0.006103383.500800
860.04950.01560.010819507.870611445.6857106.9845
870.0449-0.10420.04191101465.826374785.7325612.1975
880.05390.00670.03313222.1906281894.847530.9377
890.0542-0.05170.0369187961.9872263108.2751512.9408
900.0561-0.04340.0379124038.848239930.0372489.8265
910.0546-0.05850.0409237308.501239555.532489.4441
920.0597-0.00190.036201.4595209636.273457.8605
930.05990.0070.03282807.6312186655.3128432.0362
940.05580.02130.031630197.1121171009.4927413.5329
950.05660.09570.0375592505.7453209327.3338457.523
960.05-0.05180.0387222566.3215210430.5828458.7271


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; 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 = 1 ; par7 = 1 ; par8 = 2 ; 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,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')