Using Analysis of Time Series to Forecast numbers of The Patients with Malignant Tumors in Anbar Provinc

Transcription

1 Using Analysis of Time Series to Forecast numbers of The Patients with Malignant Tumors in Anbar Provinc /. ) ( ) / (Box & Jenkins).(.( ) ARIMA(2,1,0). Abstract: The aim of this research is to analysis time series with using (Box & Jenkins) method (Identification, Estimation, Diagnostic Checking of Model, Forecasting) to find the beast forecasting model to the number of patients with Malignant Tumors in Anbar Province by using the monthly data for the period ( ). The result of data analysis show that the proper and suitable model is Integrated Autoregressive model of order (2) ARIMA (2, 1, 0). According to this model the Research forecast the numbers of patients with Malignant Tumors the next two years in monthly bass, so the forecasting values represented the scours time series data that deal to the efficiency of the model

2 ( ). (Time Series).( ) ( ) ).( Box and Jenkins(B-J) ( ) :.(SPSS V.10 ) (Minitab) : (Wheel Wright & Markedis, 1978:60-64) MSE (1,2,1,2, ) (MSE) MSE (Dent and Min,1978 ). (A-F) (Box Jenkins) ARMA ( ) 372

3 MLE (100) (Ahtol, MSE J. and Tiao,1987:15-19) (p) (Wei:1990) ( 9-4:2000 ) ARIMA ARMA -990) (97-94) ( (Kaiser and Maravall:2001) ARIMA ARMA ARIMA (2009) ARMA (2,1) ARIMA (1,1,1) (59 :2009 ) (2008) (2004).VARIMA(2,1,0) -1 (B-J, 1976). Fundamental Concepts -1-1 Time Series : ) t 1, t 2,, t n (Z t1, Z t2,, Z tn ).( 373

4 (Statistical Series) n :(12-11 :2007 ) :. :.( ) : (Deterministic).. Sinusoidal ) (Periodic) : (Data : S : (Stationary in Variance). (Stationary in Mean).. Autocorrelation (AC) (k) :(Box&Pierce,1970, ) (-1 1) (1-1) : : ( 1/n) =0,1,2,3, : n (k=1,2,3, ) (k). (ACF) 374

5 (ACF) (k=q) (k) ( ) : : (ACF).( :9 ) (RACF) Residual Autocorrelation Function : Partial Autocorrelation (PACF) AR(P) 1996 ) (Autocorrelation Function) :(8: (PACF). (PACF). (k) (Anderson,1942: ) Stationary Time Series ) ( (Trend) Non stationary ). 375

6 (Homogenous :(20: 2007 ) ( ) (Back Shift Differences Operator) : (d).(nuno,1996:87) Box & Jenkins (B J) 2-1 Autoregressive Model (AR) :(13 :2010 ) : (p) (1-2) )3(1- : : i= 1, 2, 3,.P : : : p : : (Back shift operator) : B (exponential damping) AR(p).(17: 1981 ) p (PACF) (k) AR(p) AR(2) AR(1). (33-27:1989:27 ) : (1-2) (p=1) 376

7 . AR(1) : : : ( ACF) : ( =0 ) ) ( (exponentially) AR(1). ) ( : AR(1) (PACF) AR (2) (PACF) (1-2) (p=2) : ) AR(2) :,, : AR(2) : (k=1,2) (exponential AR(2) (B-J,1976:58-60) : damping) : 377

8 .(Wave damping sine) (ACF) : AR(2) ) (.) ( AR(2) (PACF) (B) Moving Average Model (MA) (q) :(17 :2010 ) :. : q (q) (MA). (17 :1981 ) (PACF) ( - ) Mixed Autoregressive Moving Average Model (ARMA) )6(1- (B-J,1976) (p, q) )7(1- :(B).(.( (,.. ) (B) :,, ) (B) : ).(19: 2010 ) 378

9 4-2-1 Autoregressive Integrated Moving Average Models (ARIMA). (ARIMA). AR(p) I(d) MA(q) (Auto Regressive Integrated Moving Average (Stationary) : (p,d,q) ARIMA Models). AR(p) : P. MA(q) : q. : d :2007 ), (Dent& Min,1978:33-45): (B) (30 : : ARIMA(p, d, q) :.(Kaiser,2001:34) ARMA ARIMA (1-8) 3-1 : (B-J, 1976 : ) 379

10 Identification Jenkins Box. (d=1). (d=2) ARIMA q d p. (B-J,1976:245) (1-7) (ACF) (PACF) (ACF) (PACF) (PACF) (ACF) :(18-16:1981 ) (PACF) (ACF).AR(P) (P) (PACF) (q) (ACF)).MA (q) (PACF) (ACF) ARMA (p,q) Estimation ( :Pirce,1971: ) Method of Ordinary Least Squares (O.L.S.E.).1. Maximum Likelihood Method

11 Diagnostic Checking of Model : (t-student) MA AR : (28-29 :2010 ) : Q (Ljung & Box) -1 : (Q). )9(1- : Q. =s =k =m : : -2 ( ) (Residuals) (0.95) ( ).(1\n) S.Makridakis, ) (AIC) (Akaike's Information Criterion) ) (1998:75 : (AIC ) ( (1-10). (p + q) : : (1-11) : (Schwartz) 381

12 (1-12) Forecasting (L) (Dougls, 1977:78-91) : (L) (1-13) : (L) AR(1) : (L) AR(2) : (L) MA(q) : (L) ARMA(p, q) (60) (1) (1) * Year Month January February March April May June July

13 August September October November December : * 2-2 (1) (Minitab) (2) (15) ( ) : (%95) : (Q.stat) Ljung & Box (2) ) (4) ( (B-J,1976). 383

14 ( ) (1) 384

15 (2) (3) 385

16 (4) 3-2 (Identification) (ACF) (PACF) (ACF) ( 4) (k) (PACF) (Cut-off) ARIMA(2,1,0) ARIMA(2,1,0) 386

17 ARIMA(1,1,0). (2) (2) Model order (p) Adj.SSE Risiduals.V AIC MAIC SBC ARIMA(1,1,0) ARIMA(2,1,0) : ARIMA(2, 1, 0) Or : Estimation 2-4 Ordinary ) (SPSS V.10) (Least Squares. Final Estimation of Parameters: T StDev Ceoff. Type AR AR Constant Differencing : 1 regular differenc Number of observation : original series 60,after defferencing 59 Analysis of Variance : DF Adj.sum of squares Residuals variance Residuals Standard error = Log Liklehood= AIC = MAIC = SBC = 387

18 5-2 (5).( ): (=5.5) [(Q.stat) (Ljung & Box)] (White Noise) (18.307) ( ). ARIMA(2,1,0) (6). (5) 388

19 (6) 6-2 (3-2) (3) ( ). (7) (3) ( ) Year Month January February March April May June July August September October November December

20 ( ) (7) (K). ).3 (SBC) (AIC) ).( 390

21 ARIMA (2,.1,0) ). ( :

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23 14. Pirece,A.D.(1971),"Least Squares Estimation in the Regression Model with Autoregresseion-Moving Average Errors",Biomatrika,Vol.58,P( ). 15. S. Makridakis, S. C. Wheelwright and R. J. Hyndman (1998), Forecasting Methods and Applications ", Third Edition, John Wiley & Sons, Inc. Publication, New York, USA. 16. Wheel Wright, S.G. & Markedis, S. (1973), "An Examination of the Use of Adaptive filtering in Forecasting O.P.Q", vol.24, No.1, P (60-64). 393