Page 12 - Contributed Paper Session (CPS) - Volume 7

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

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

Abstract
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
errors.

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

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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