1. PREDICTION OF FUTURE PASSENGER SALES
BASED ON
CURRENT SALES
FOR AN AIRLINE COMPANY
BY
DIPIKA PATRA
2. The project aims in constructing a Time Series Model
using Auto Regressive Integrated Moving Average
Process with parameters (p , d , q) to forecast future
passenger sales.
Analysis Software used:
Statistical Analytical Software
&
Microsoft Excel
3. Explanation of Auto Regressive Integrated Moving
Average Model i.e. ARIMA(p, d, q):-
In practical problem most Time Series are non stationary.
To forecast a model we difference the observed Time Series
until it is Stationary.
Here the parameter “d” imply the “d” the order difference is
Stationary.
Now ARMA(p, q) Model fitted on the differenced series. i.e.
A(L)xt=B(L)et
Where A(L)=1-a1L-a2L^2-……-apL^p
B(L)=1-b1L-b2L^2-……-bqL^q
9. Now we have to fit ARMA model on DIF12_DIF_LOG_AIR
PROC ARIMA DATA = DIPIKA.D;
IDENTIFY VAR = DIF12_DIF_LOG_AIR MINIC;
RUN;
Suggest to fit ARMA(3,0) as Minimum BIC.
Minimum Information Criterion
Lags MA 0 MA 1 MA 2 MA 3 MA 4 MA 5
AR 0 -6.24 -6.32 -6.30 -6.32 -6.29 -6.27
AR 1 -6.33 -6.29 -6.28 -6.29 -6.26 -6.23
AR 2 -6.32 -6.28 -6.25 -6.25 -6.22 -6.20
AR 3 -6.35 -6.31 -6.27 -6.24 -6.24 -6.22
AR 4 -6.33 -6.29 -6.25 -6.25 -6.21 -6.19
AR 5 -6.30 -6.26 -6.22 -6.23 -6.19 -6.16
Considering all possible “p” & “q” in the neighbourhood suggested by SAS & for
each of them generate the value of AIC & BIC & calculate the average of them
, select 6 models based on the relative lower value of average.
Next calculating Minimum of MEAN ABSOLUTE % ERROR select the best model
ARMA(0,3).
11. FITTED MODEL
Model for variable DIF12_DIF_LOG_AIR
Estimated Mean 0.001
1 - 0.31 B**(1) + 0.072 B**(2) - 0.21 B**(3)
12. GRAPHICAL REPRESENTATION OF ACTUAL &
FORECASTED SALE REPORT FOR THE YEAR 1960:-
0
100
200
300
400
500
600
700
FORCASTED
ACTUAL
13. GRAPHICAL REPRESENTATION OF ACTUAL & FORECASTED
SALE REPORT FOR THE YEAR 1949 to 1960:-
0
100
200
300
400
500
600
700
S
a
l
e
s
v
a
l
u
e
actual for 1949 to 1960
forecast for 1949 to 1960
