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Asif  Alıyev: Forecasting of Engel Curve Components with the Application of ARIMA Method

                    The general form of ARIMA(p,d,q) is expressed as below:

                                                                       
                                                                                         (4)
                                            
                                                      
                                                                             
                             (1 − ∑       ) (1 −   )    =    + (1 + ∑       )   
                                                                                 
                                                                           
                                          
                                                         
                                     =1                                =1

                    Where, the drift of ARIMA(p,d,q) proces is        ,  d – is the degree of differentiation.
                                                              1−∑      

                    ARIMA(p,d,q) process has the factor properties of polynomials with the difference
                          ′
                       =    −   . ARIMA process is a particular case of an ARMA(p+d, q) process which
                    has the autoregressive polynomial with d unit roots. When nonstationary processes
                    are  brought into the ARIMA process they become stationary or weakly stationary.

                    ARIMA  as  a  time  series  forecasting  process  is  based  on  Box-Jenkins  (2016)
                    methodology. The method is built from four steps:
                     1.  Identification. The adequate values of p, d and q are identified by using the
                         correlogram and partial correlogram outputs.

                     2.  Calculation.  Next,  the  parameters  p  and  q  terms  of    the  AR  and  MA  are
                         identified  and  included  in  the  model  using  simple  least  squares  method,  but
                         sometimes nonlinear (in parameter) calculation methods is also possible. For this
                         purpose statistical tools (Eviews e.g.) are applied; the AR və MA parameters are
                         obtained for each  (p,d,q) set.

                     3.  Diagnostic checking. The BJ methodology is applied as an iterative process for
                         the selection of adequate ARIMA model. Having computed the parameters of
                         the alternative models, the chosen one must be checked whether the residuals are
                         white noise or not; if not, the process must be started over.


                     4.  Forecasting.  The  ARIMA  modeling  is  notable  in  forecasting  due  to  its
                         credibility  compared  to  the  econometric  modeling,  especially  for  short-term
                         forecasts.

                    The  Box-Jenkins  methodology  is  the  ground  for  selection  of  proper  forecasting
                    method among AR, MA, ARMA, and ARIMA (Gujarati, 2004).









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