ppt variasi kalender putri 116 & rizka 126.ppt

8/10/2019 PPT Variasi Kalender Putri 116 & Rizka 126.ppt

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Forecasting Total Passenger Train In SumatRegion By Using Model Variations Calend

Period 2006-2013

By : Putri Milakhul Khasanah (1311100116) | Rizka Fauzia (1311100126

Lecture : Dr. Irhamah, M.Si.


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Background

the importance of transport for the

people of Indonesia are caused byseveral factors, among others, thegeographical situation of Indonesia

which consists of thousands islands,waters which consists of mostly sea,

rivers and lakes that allow thetransport is done by land, water, and

air to reach all areas Indonesia

The train is one of transportation canbe quite economical than that in

terms of railway safety has little risk interms of traffic accidents compared to

other means of transportation.

on the day of Eid

rail spike, many pcelebrate Eid wi

Precisely passoccurred in Sum

tickets majorsPalembang, Soutto H-1 Idul Fitri 143

o

Calendar variation effects on theresults of the forecast time series datahas been studied, among others, by

Bell and Hillmer who studied the effectof trading-day effects and holiday

In the months in which these days are,passenger data will tend to be high.Due to the determination of the dateof Eid follow the Islamic calendar, it is

the celebration of the Christiancalendar will be shifted forward eachyear. This is called the calender effectwhich shifts on the calendar effect on

time series data


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B. Autoregressive Integrated Moving Average atau ARIMA Model


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C. Diagnostic Checking


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D. Variations Calendar Model


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Data Sources and research variables

The data used in this research issecondary data, data on the

number of passenger trains inIndonesia period 2006-2013(people) who are taken in theadan Pusat S tatistics

website(www.bps.go.id). Research

variables used in this study is thenumber of train passengers in

Sumatra January 2006 to May2013. Data on the number of

passenger trains in Sumatra asmany as 101 data. In this study, adummy variable that is used only

during the month of Eid.

Tahun

Tanggal

2006

23-24 Oktober

2007

12-13 Oktober

2008 01-02 Oktober

2009 21-22 September

2010 10-11 September

2011

30-31 Agustus

2012 19-20 Agustus

2013

08-09 Agustus


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Step Analysis

1. Draw a time series plot of the data to determine the number of passengers aboard the d

2. The data is divided into two, namely the data in sample and out of sample. Data in the ssamples of data and the data out as much as 5 data.3. Eliminate the effect of variations in the calendar of the response variables using dummy

model.4. To test the white noise on the Nt Nt see ACF plot. If you meet the assumption of whi

proceed to step 8. If not, then do modeling Nt with Box-Jenkins ARIMA method.5. ARIMA model obtained in step 2 is used to model the data on the number of passenge

dummy variable on the calendar variations as input simultaneously modeled in order to ob

such as first equation6. Test the significance of the parameters by using the t test and diagnostic checks using ttest and Kolmogorov-Smirnov up at meet the assumption of white noise and normally di

7. Selection of the best model based on the value RMSEin (data insample) or RMSEo sample) the smallest.8. Forecasting the number of rail passengers using the best model.


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Characteristic of DataVariable Mean StDev Minimum Maximum

2006 276,9 38,6 226,0 346,02007 284,6 56,8 210,0 401,02008 328,3 57,5 262,0 436,02009 343,3 58,2 248,0 441,02010 411,8 73,9 327,0 588,02011 441,3 62,8 354,0 568,02012 365,3 46,3 299,0 482,02013 332,9 44,4 276,0 425,0

From the descriptive statistics tableabove it can be seen that the number

of passengers traveling by Train inSumatra, most are in 2010 and 2011 with

a maximum value of 588 and 568thousand passengers. While the fewest

number of passengers was in 2006.

pattern d

betw

Decembwas diffe

dispersio

passen

Sumatra

S


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Time Series Plot of Data JumlahPenumpang KA Sumatra

painca

p

pThto

pet


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A suitable method to predict the number of passengers Railway in Sumatra is due to the var

calendar every year there is a fairly high rise and the increase from year to year on the skids, m

the increase in the number of passengers who jumped higher than the annual retreat around


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Equation :

KA di SUMATRA = 339 + 1,6 D1,t + 61,6 D2,t + 96,6 D3,t+ 102 D4,t + 249 D5,t+ 229 DD7,t+ 52,6 D8,t

perform a linear regression between the danumber of passengers with Dummy coding (D

the variable y (the number of railway pass

Sumatra).


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(a). ACF results residuals (b). PACresidual results

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1,0

0,80,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

Autocorrelation

Autocorrelation Function for RESI1(with 5% significance limits for the autocorrelations)

2018161412108642

1,0

0,80,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

PartialAutocorrelation

Partial Autocorrelation Function for RESI1(with 5% significance limits for the partial autocorrelations)

2001000-100-200

99,9

99

95

90

80

7060504030

20

10

5

1

0,1

RESI1

Percent

Mean -3,48758E-13

StDev 65,93

N 96

KS 0,084

P -Valu e 0,094

Probability Plot of RESI1Normal

. Normallity

(a). (b).

residual white noise that is not

marked by any lag are out of

bounds. From the results of the

ACF and PACF plots are then

carried differencing to

determine the order of the AR

and MA


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Residual ACF differencing resultsand the residual PACF differenciresults.

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1,0

0,8

0,6

0,4

0,2

0,0

-0,2-0,4

-0,6

-0,8

-1,0

Lag

Auto

correlation

Autocorrelation Function for diff_resid(with 5% significance limits for the autocorrelations)

161412108642

1,0

0,8

0,6

0,4

0,2

0,0

-0,2

-0,4

-0,6

-0,8

-1,0

Lag

Partial

Autocorrelation

Partial Autocorrelation Function for d(with 5% significance limits for the partial autoco


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all variablessignificantly a

number of rapassengers insince the p-vathan 0.05.

ARIMA ([12],1,[1,12]), D1,t ,D2,t,D3,t,D4,t D5,t, D6,t+1, D7,t, D8,t.

Parameter Estimate P-value LagMA1,1 0.57514


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Normality Test

Lag P-value6 0.0561

12 0.2563

18 0.2268

24 0.3390

Test P-ValueShapiro-Wilk 0.6067Kolmogorov-Smirnov 0.0582Cramer-von Mises >0.2500Anderson-Darling >0.2500

Test of White Noise Residual

residual has met the assumpwhite noise. Tests conduc

bengan L-jung Box test. In thelag, p-value produced has greater than the value of a(0.05) thus obtained decisialready white noise residu

These four types of noshowed that the residunormal distribution of d

indicated by the p-valwere greater than the va

(0.05).


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Models :Yt = 63.18006 D1,t + 115.61399 D2,t + 137.38636 D3,t+ 147.83242 D4,t + 244.80187 D5,t+

D6,t+2+ 107.18506 D7,t+ 107.11171 D8,t+ Nt


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Forecast for 5 months

Bulan JumlahPenumpangJanuari 2014 374.2385Februari 2014 321.6586Maret 2014 343.5865April 2014 330.4124

Mei 2014 372.3364


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C. Diagnostic Checking

1 Conclusions

Pattern number of railway passengers inSumatra experienced a significant increase on theeve of certain days, especially Eid. The resultsobtained from the analysis of descriptive statisticalanalysis of known patterns of data dissemination isthe number of passengers in September.

The best model to predict the number ofpassengers in January, February, March, April, andMay in 2014 is ARIMA ([12], 1, [1.12]), D1,t;D2,t; D3,t; D4,t; D5,t; D6,t+1; D7,t; D8,t. Themodel is obtained by using the method of time seriesregression with a dummy variable regression modelvariations calendar effects and dummy trend.NilaiMAPE generated is equal to 13.6614% thatdeclared the model is good enough.

2 Suggestions

Analyzed the number of passeaffected by the number of holidaoccur in widths, but for further aneeds to be done on their vacat

July, which also resulted in the inin the number of passengers. Itneeds to be done forecasting

other modeling approache


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efferences

[1] Abdulkadir, Muhammad. (1998). Hukum Pengangkutan Niaga. Bandung: PT Citra Aditya

[2] Bell, W. R. & Hillmer, S. C. (1983). Modeling Time series with Calendar Variation. Journal ofAmerican Statistical Association, 78(383): 526-534.[3] BPS. (2012). Data Jumlah Penumpang Kereta Api 2006-2016 (orang).Dari : http://www.bp

go.id/tab_sub/view.php?tabel=1&daftar=1&id_s ubyek=17&notab=16, diakses pada tanNovember 2014.

[4] Cryer. (2004). Time Series Analysis with Application in R (2nd edition).New York : Springer ([5] Liu, L. M. (1980).Analysis of Time series with Calendar Effects. Management Science, 26(1 112.[6] Harapan, Sinar. (2014). Jumlah Penumpang KA di Sulawesi Meningkat. Dari: http://

sinarharapan.co/index.php/news/read/140715003/tiket-ka-jurusan-lubuklinggau-palemba

habis-terjual-.html, diakses pada tanggal 21 November 2014.[7] Wei, W. W. S.. (2006). Time Series Analysis: Univariate and Multivariate Methods. New York Pearson Education Inc.

ppt variasi kalender putri 116 & rizka 126.ppt

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