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CPS1111 Jitendra Kumar et al.
            for testing is based on credible interval. Using the posterior probability, the
            highest posterior density region is obtained as follows

                                                  
                                
             HPD    R;  P  y |      t s.  P .  HPD |  y                                     (15)

            4.  Merger and Acquire in Banking Industry: An application
                It  is  well  defined  that  banking  sector  has  strong  contribution  in  any
            economy. It has been adopted various approaches to smooth working in the
            global  front.  Merger  and  acquisition  is  one  of  the  finest  approaches  of
            consolidation that offers potential growth in Indian banking. State bank of
            India (SBI) is the largest bank in India. Recently SBI merged with five of its
            associate banks and Bharatiya mahila bank is becoming the largest lender in
            the list of top 50 banks in the world. The combined base of SBI is expected to
            increase  productivity,  reduce  geographical  risk  and  enhance  operating
            efficiency. In India, there are various channels to transfer the payment online.
            Mobile banking is one of the important channels to transfer the money using
            a mobile device which is introduced since 2002 and become popular after
            demonization as it is a very fast and effective performed using smart phone
            and tablet. For examine purpose, we have taken monthly data series of mobile
            banking of SBI and its associate banks over the period from November 2009
            to  November  2017.  Data  series  gives  information  about  the  number  of
            transactions  with  its  payment  in  a  specific  month  for  a  particular  bank.  In
            analysis, we have converted data into payment per transactions.
                The objective of the proposed study is to observe the impact of merger
            series. First, fitted an autoregressive model to mobile banking series to find
            out the most prefer order (lag) of SBI and its associate merger banks and then
            study more inferences. Table 1 shows the descriptive statistics and lag of AR
            model with estimated coefficients for each series. Once getting the lag (order)
            of each associate series, apply M-AR model to estimate the model parameters
            using OLS and Bayesian approach which are recorded in Table 2 and observed
            that there may be change in estimated value when considering merger in the
            series. From Table 1-2, we observed that there is a negative change happened
            due to SBBJ and SBP series because the sign of coefficient value is transform
            whereas other remaining series have a positive impact but not much affect on
            the  SBI  series.  To  know  the  impact  of  associate  banks  series,  testing  the
            presence  of merged  series  and  reported  in  Table  3.  Table 3  explained  the
            connection between associate banks with SBI and observed that banks merger
            has a significantly impact of SBI series and after the merger point, there is a
            decrease  in  the  mobile  banking  transactions.  All  assumed  test  is  correctly
            identifying the effect of merger.



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