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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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