sarima - دانشگاه تبریز
TRANSCRIPT
SARIMA*
. .
)SARIMA( .
88613851392
1393 . . .
:.JEL:G21D22C45Q41.
*
1390.**
/ / /-
:////
.....
1-
.
.
.13851391
.551385200,21391
.)ATM(1
1000)600(
000,10)1389 :3 .(
.
. .
)ANN(2
1 Automated Teller Machine2 Artificial Neural Networks
/ /
.
.
)SARIMA(11 -3 -8ANN
.88613851392-
. .
)23 (...
.
.SARIMA
.2-
. .
.
1 Seasonal Autoregressive Moving Integrated Average Model2 POS3 Pin-Pad
.....
.1)1994 (
)ACP(2000,5019901991 .3)2003 (
)AR ()ARMA(4
)MPE(5
.5140
17 .ARMA
.6)2007 (
2007-2012AR .7)2008 (ATM
ATMANN-.
.8)1999 (12
1 Engle & Russell.2 Autoregressive Conditional Duration Model3 Maass, Koehler, Kalden, Costa, Parlitz, Merkwirth & Wichard.4 Wavelet Technique
5 Mean percentage error = t tY Y
n6 Egan, Tubin & Vyas7 Rimvydas Simutis, Darius Dilijonas & Lidija Bastina8 Snellman & Vesala
/ /
.)POS (
1988199619972006 .3)2000 (
41986-2000)VECM(5 .
. .
6)2005 ( .
) : (...37
)PNN(8)MLFN(9 .
.10)2010 (ATM
2003AR .ATM
1 Panel Data2 Fixed Effect3 Adam4 Johansen & Juselius (1995)5 Vector Error Correction Model6 Gan, Clemes, Limsombunchai & Weng.7 logistic regression8 probability neural network9 multi-layer feed-forward neural network10 Paul & Mukherjee
.....
.
.)1391 ( .1380-1391
)2005(
12
)GMDH(3
.80
. .
.)2003 (
6 .)2005 (
.
1 Radial basis function2 Generalize Regression Network3 Group Method of Data Handling
/ /
.1
3-
1360 .13701371
.1372
.POS8/1
POSATM
.ATM
POS
)1384 :35 -36 .(1380
.) (1381
.-POSATM .
6 .
1()ATM(2()POS (3()Pin-Pad(4(5()(
:)().(
.....
()(
3 .
... .
6 .)1 (13851392.
)1:( :..
1389 .-
.1389
1388)1390 :93-94 .(
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
/ /
13901391 .
91-1390 . .
1392 .
5-
-1 .- .
.
2007283 .
13851392)88 (6
..
1 Box-Jenkins2 Matlab 20073 Eviews 8
.....
6-
.
)12003 (2
)1381 ( .
3
.
]10 [ .45
)1998 :44 .(-
11- .18/0
1000,500000 .
]10 [.)61994(
min
max min
in
X XXX X
)1(
1 Guoqiang Zhang2 Back Propagation
...
4 Sigmoid tangent transfer function5 Hyperbolic6 Simon Haykin
/ /
:6-1-
)) (( .
. .
. .
) .12007 :2 :11 -13( .
.2)1995 (
.6-2-
.3
)1993()1379 ()AR ( .4)1992(
)1991 ( .
.6-3-
1 Howard, Demuth and Mark Beale.2 Yves Chauvin and David E. Rumelhart3 Zaiyong Tang and Paul A. Fishwick4 Sharda and Patil
.....
.-
)MSE(1)RMSE(2
)MAPE(34)MAD()2R(5U6.
.7090.
6-4-)1382 :206 (
.
.)
71998 .(
1 Mean Squared Error = 2ˆ( )t tY Yn
2 Root of Mean Square Error = MSE
3 Error Mean Absolute Percentage =t̂ t
t
Y YY
n
4 Mean Absolute Deviation = Mean percentage error = t tY Y
n5 R Squared = 2
2
ˆ( )1 ˆ
t t
t
Y YY
6 Theil Inequality coefficient Bias Proportion =2
21
ˆ( )
( )
t t
t t
Y Yn
Y Yn
7 G. Zhang, B. Eddy Patuwo and Michael Hu.
/ /
. .
6-5-
1234 .
.56
) .1381(. .-
.)
( . .
. -)LM(7
8 .001/0100
.
1 learning rate2 Epochs3 Goal4 Traning Function5 Supervised6 Unsupervised7 Levenberg–Marquardt algorithm8 Gradient Descent
.....
7-
.
.3831 .
1-3-8ANN)1 ( .8812.
100)2 (.100
MSEMSE00032/0.
)1:( :
)2 :(1 -3 -8ANN :
/ /
8-SARIMA
1 . .
)ARIMA (p,d,qpd
q .d
.)ARMA (p,q:
01 1
p q
t i t i j t j ti j
Y Y u )2(
.)SARIMA (p,d,q) (P,D,Q
pqPQ .
)21389( .–3.
)ADF(4)1 (.
)I(1.
1 Diagnostic tests2 Jack Johnston & John Dinardo.3 Stationary4 Augmented Dickey-Fuller Unit Root Test
.....
)1:(1
ADF510
5949/2-9450/1-6140/1-3980/05921/2-9446/1-6142/1-8795/8-
:
2
)3 (
3 .) (
.
)3:( :
ARSARMASMA
ARSARMASMA .
1 Mackinnon (1996)2 Correlogram
/ /
1
.
)2 (.
)2(SARIMA
t2MAAR
C7366/423618/40000/0
AR(1)8988/08313/80000/0
SAR(1)4750/07252/10887/0
MA(1)9380/0-997/7 -0000/0
SMA(1)8420/0-363/3-0012/0
F4697/3)0118/0(2R7597/0
D.W9454/1F34967/1)2252/0(
F-40348/0)9657/0(
:
15
10)D.W (F -
F
.F2R
75
.
1 Akaike info criterion2 Inverse Roots3 Ramsey Reset test4 Breusch-Godfrey
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
AR rootsMA roots
.....
MAAR
.
9-1-3-8ANN)3 (
.MSE
RMSEMAPEMADU2R .SARIMA
)3 (.
)3:(
2RUMADMAPERMSEMSE
ANN9994/02833/001012/013113/001789/000032/0SARIMA7597/090807/06511/10718399/02087/17509/30698
:
)3 (SARIMA
.10-
13921393ANN1
.13)4 (.
1 Simulation
/ /
)4:( :
)4 (
13933000.
.
.)ATMPOSPin-Pad (
.)5 (91 -13861
1387 .
.
0500
100015002000250030003500
1385
_413
85_9
1386
_213
86_7
1386
_12
1387
_513
87_
1013
88_3
1388
_813
89_1
1389
_613
89_
1113
90_4
1390
_913
91_2
1391
_713
91_
1213
92_5
1392
_10
1393
_313
93_8
ANN
.....
)5:( :
13875/013901391
.
.
.
.
/ /
11-
13933000 .
.1389 .
1389
ATM .
. .
.
.91 -1390
.
.
.....
.
.
910 -1386 . .
12-
.
.)ATMPOSPin-
Pad (... .
.
.
)IRF(1.
1 Impulse Response Function
/ /
.).1381 .(12 :69 -96.
.) .1382 .(.
.)1389 .(.
.) .1390 .(
..) .1389 .(
7)2( :27-56..) .1386 .(-
60 :19-42..) .1388 .(
..) .1390 .(
..) .1381 .(
)ANN(12 :97-125.
.) .1384 .()ATMPOS)( -(
.11.) .1389 .(
ATM
.1. Adam, Christopher. (2000). The Transactions Demand for Money in
Chile, Research Department of the Central Bank of Chile.
.....
2. Chauvin, Y. and Rumelhart D.E. (1995). Backpropagation: Theoryarchitectures, and applications, Hillsdale, NJ: Erlbaum.
3. Egan, Bob and George Tubin and Charul Vyas. (2007). US MobileBanking Forecast: 2007-2012, www.TowerGroup.com.
4. Engle, Robert F. and Jeffrey R. Russell. (1994). ForecastingTransactions Rates: The Autoregressive Conditional Duration Model,Working Papers, National Bureau of Economic Research, Cambridge.
5. Gan, Christopher and Mike Clemes and Visit Limsombunchai andAmy Weng. (2005), Consumer Choice Prediction: Artificial NeuralNetworks versus Logistic Model, Commerce Division, LincolnUniversity Canterbury, No. 104.
6. Haykin, Simon S. (1994). Neural Networks: A ComprehensiveFoundation, Macmillan College Publishing.
7. Howard, Demuth and Mark Beale. (2007). Neural Network ToolboxUser’s Guide, www.mathworks.com.
8. Maass, Peter and Torsten Koehler and Jan Kalden and Roza Costa andUlrich Parlitz and Christian Merkwirth and Jörg Wichard. (2003).Mathematical methods for forecasting bank transaction data, Zentrumfür Technomathematik.
9. Paul, Justin and Anirban Mukherjee. (2010). ATMs and Cash DemandForecasting: A Study of Two Commercial Banks, Journal of RegionalDevelopment, vol.2, no.2, pp: 653-671.
10. Sharda, R. and R.B Patil. (1992). Connectionist approach to time seriesprediction: An empirical test, Journal of Intelligent Manufacturing 3,pp: 317–323.
11. Simutis, Rimvydas and Darius Dilijonas and Lidija Bastina. (2008).Cash Demand Forecasting for ATM Using Neural Networks andSupport Vector Regression Algorithms, 20th EURO Mini Conference:Continuous Optimization and Knowledge-Based Technologies,Vilnius, Lithuania, pp: 416–421.
12. Snellman, Jussi and Jukka Vesala. (1999). Forecasting theElectronification of Payments with Learning Curves: The Case ofFinland, Discussion Papers, Bank of Finland, Research Department.
13. Tang, Zaiyong and and Fishwick Paul A. (1993), Feedforward NeuralNets as Models for Time Series Forecasting, Journal on Computing,vol.5, no.4, pp:374-385.
14. Zhang, G. and B. Eddy Patuwo and Michael Hu. (1998). Forecastingwith artificial neural network: the state of art, International Journal ofForecasting, vol.14, pp: 35-62.
15. Zhang, Peter .G. (2003). Time series forecasting using a hybridARIMA and neural network model, Neuro Computing, vol.50, pp:159-175