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CPS2014 Ma. S.B.P. et al.

                              Data boosting on short bivariate time series data
                                              by sieve bootstrap
                     Ma. Salvacion B. Pantino , Erniel B. Barrios , Joseph Ryan G. Lansangan
                    1  Mathematics Program, College of Science, University of the Philippines Cebu, Philippines
                       2  School of Statistics, University of the Philippines Diliman, Quezon City, Philippines

                  A  model  is  postulated  given  a  short  bivariate  time  series  data  with  high-
                  dimensional  inputs.  The  correlated  response  vectors  are  functions  of  the
                  contemporaneous  effects  of  the  input  series.  The  model  is  then  estimated
                  using a hybrid of methods embedded into the backfitting algorithm. It is noted
                  from  the  simulation  studies  that  the  estimation  procedure  produces
                  parameter  estimates  with  lower  relative  bias  and  better  predictive  ability
                  compared to (1). The estimation method is also robust to misspecification

                  Short  bivariate  time  series  data;  high-dimensional  inputs;  backfitting

                  1.  Introduction
                      Data are being collected at various lengths and frequencies depending on
                  their  availability  and  cost.  Optimizing  the  use  of  the  database  of  various
                  industries  have  been  the  trend  towards  answering  questions  about
                  productivity,  prediction,  and  diagnoses  of  arising  problems  that  could  be
                  resolved by crafting solutions based on what was observed. Considering the
                  contemporaneous effects of a set of variables has been a concern towards
                  determining their dynamic effects over time. More so, insightful explanations
                  could be derived if a wide array of covariates would be considered to explain
                  two or more interrelated variables of interest.
                      Shen and Huang (2008) proposed the sparse principal component analysis
                  via regularized singular value decomposition (sPCA-rSVD) which solves a low-
                  rank matrix approximation problem by imposing regularization penalties to
                  produce  sparse  principal  component  (PC)  loadings.  Witten  et  al.  (2009)
                  developed  a  method  using  penalized  matrix  decomposition  (PMD)  which
                  decomposes the wide array of covariates using sparse vectors.
                      The  bootstrap  method  of  resampling  proposed  by  Efron  (1979)  has
                  become a powerful nonparametric method for estimating the distribution of a
                  statistical  quantity.  Bühlmann  (1997)  developed  the  sieve  bootstrap  as  a
                  method of generating a bootstrap sample by resampling from the residuals of

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