Page 100 - Contributed Paper Session (CPS) - Volume 5

CPS1111 Jitendra Kumar et al.
the effectiveness of the merger model using various significance tests. The
performance of constructed model is demonstrated for recorded series of
merger of mobile banking transaction of SBI and its associate banks.

2. Merger Autoregressive (M-AR) Model:
Let us consider {yt: t = 1, 2, ……, T} is a time series from ARX(p1) model
associated with k time dependent explanatory variables up to a certain time
point called merger time Tm. After a considerable period, associated variables
are merged in the dependent series as AR model with different order p2. Then,
the form of time series merger model is We retrieved mother, neonatal and
child health (MNCH) data from Kenya.

 p 1 k r m


   1 i y t i   mj z m, t  j   t t  T m

1
 j

y t    i 1 m 1 1
   p 2  y   t  T
 2  2 i t i t m
  i 1 (1)
th
Where δm is merging coefficient of m series/variable and εt assumed to
be i.i.d. normal random variable. Without loss of generality one may assume
the number of merging series k as well as their merger time Tm and orders (pi:
i=1, 2) to be known. Model (1) can be casted in matrix notation before and
after the merger as follows
Y   1 l T m   1 X T m  Z  T m   T m (2)
T
m
Y T  T m  2 l T  T m   2 X T  T m   T  T m (3)
n
n
Combined eq (2) and eq (3) in vector form, produce the following equation
Y  l   X   Z    (4)
Model (4) is termed as merged autoregressive (M-AR(p1, m, p2)) model. The
purpose behind M-AR model is to make an impress about merger series with
acquisition series.

3. Inference for the Problem
The fundamental inference of any research is to utilize the given information
in a way that can easily understand and describe problem under study. In time
series, one may be interested to draw inference about the structure of model
through estimation as well as conclude the model by testing of hypothesis.
Thus, objective of present study is to establish the estimation and testing
procedure for which model can handle certain particular situation.

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