TESTING TIMESERIES FORCASTING MODELS ON INFLUENZA CASES IN NAKHON SI THAMMARAT

Abtract:

Sangtien  Youthao *, Mullica  Jaroensutasinee , Krisanadej  Jaroensutasinee

CX-KURUE & Computational Sience Graduate Program, Institute of  Science,  Walailak University,  222 Thasala District,  Nakhon Si Thammarat, 80160, Thailand.

This study tested  the forcasting model  from   Timeseries of   influenza cases  per month  data  in   Nakhon  Si  Thammarat   between  1994   to  2003 with a total of 120   months. Calculating   forcasting   values from 7   timeseries   forcasting   models by     Mathermatica. In this study calculated forcasting values from each   model and calculated   error values between actual values and forcasting values. After calculated that to compare error values from each  models  by  using  analysis  of   variance   and  calculated post test  by using  Student Newman Keuls method for checking the good model  and different or not from other model. The result from this study showed  that  minimum error values from  SES0.8 model  (Single Exponential   Smoothing   Model   by   using   constant  values  0.8 )  and  not  different  from  Single  Exponential  Smoothing  Model   by   using  constant   values  0.8   and  start  value at  0.2 (SES0.8,0.2)  but  result of  two model different  from other model and maximum error values from Global Linear Trend Model (GLT).

Methodology:  Timeseries forcasting models in this study were chosen from more than 20 models as follow in table.

Table 1 Timeseries model

 

Model	Name
1	Global Constant Mean Model (GCM)
2	Single Moving Average Model (SMA)
3	Single Exponential Smoothing using constant value 0.8 Model (SES0.8)
4	Single Exponential Smoothing using constant value 0.8 start at 0.2 (SES0.8,0.2)
5	Global Linear Trend Model (GLT)
6	Double Moving Average Model (DMA)
7	Brown’s Linear Exponential Smoothing Model (BLES)

          Calculation  all  of  forcasting  values  from  7  models  by  using  statistics and mathermatics command from Mathermatica.  The  technique  were  chosen  in  this  study for checking different of error value from forcasting value and actual values in 120 month of influenza cases per month data  were ANOVA  (Analysis of  Variance).  In post test of ANOVA technique were chosen Student Newman Keuls technique for comparison mean test to find different or not from 7 models.

 

Table 2     and SD of error values from model

 

Error of Model	Mean( ) ± SD
GCM	36.8206  ±  57.512
SMA	45.6102  ±  56.8118
SES0.8	12.145    ±  15.5268
SES0.8,0.2	12.6777  ±  15.8907
GLT	98.6625  ±  101.172
DMA	68.9368  ±  85.5289
BLES	22.7559  ±  28.6806

 
 

Table 3 Comparison mean of error value from model

                  

Source of Variation	df	SS	MS	F
Model	3	26.2935	8.7645	6.12795*
Error	16	22.884	1.43025
Total	19	49.1775

                                                                                                

 

Table 4 Comparison Mean of error from seven models by Post test ANOVA Student Newman Keuls technique

 

Error of Model	Rank	StudentNewmanKeuls Test
SES0.8	1
SES0.8,0.2	2
BLEBrown’s Linear Exponential Model	3
Global Constant mean Model	4
Single Moving Average	5
Doble Moving Average	6
Global Linear Trend Model	7

Figure 1 Observal Influenza cases 1994-2003 and its forcasting values from SES0.8 Model

Results, Discussion and Conclusions  

From table 2 data of influenza cases in Nakhon Si Thammarat taken in seven model to study. The result showed the Single Exponential Smoothing Technique Model used constant value 0.8 (SES0.8) had minimum error value.

From table 3 testing by ANOVA calculated to test comparison means of error values had significant at 0.01 (F _3,16  = 6.12795 , P<0.01).  Result from ANOVA test that showed the error value of one pair or more had different error value.

From table 4 taken Student Newman Keuls test for check  error values of  forecasting value  and  data of  Influenza  cases resulted  showed  that  the Single Exponential Smoothing Technique Model  use  constant  0.8  not different  from  error values by Single Exponential Smoothing Technique Model use constant  0.8  and start at 0.2  but two models took the error value different from other models. Number of influenza cases in Nakhon Si Thammarat had pattern nearly Single Exponential Smoothing Model.

            Result of this study when we try to take double exponential smoothing in Brown’s Linear Exponential Model for give the new forcasting value its had more error from single smoothing method.  Its happen in the both technique Exponential smoothing and Moving average. The Global Linear Trend Model (GLT) had maximum error values showed that the data of influenza cases in Nakhon Si Thammarat had not pattern in linear.
 

Acknowledgement: This study was supported by CX-KURUE WU Thailand. We thank the Nakhon Si Thammarat Province Health Office, Ministry of public Health for influenza data.

 
References:

1.Lohjeerachunkul W., Sutayarukwit S., Jitathawat J. and Pinsukanjana A. (1996). Forcasting Technique. Applied Statistics Centre: NIDA, Bangkok,16-111.

2.Mugglin, A.S.,Cressie,N. and Gemmell,I.(2002). Hierarchical statistical modeling of influenza epidemic dynamics in space and time. Stat. Med., 21, 2703-2721.