Page 13 - Contributed Paper Session (CPS) - Volume 7

P. 13

```
CPS2014 Ma. S.B.P. et al.
a time series model as it produces consistent estimators of the variance of time
series statistics.
Nonparametric multivariate analysis simultaneously tracks the effects of
the array of explanatory variables on multiple variables of interest (response
variables) while letting the data speak for itself. Opsomer and Ruppert (1997)
came up with a bivariate additive model and fitted it by local polynomial
regression and showed that it has the same rate of convergence as its
univariate counterpart.
Friedman and Stuetzle (1981) suggested the use of an additive model
which assumes that the conditional expectation function of the response
variable can be written as the sum of smooth terms of covariates. Buja et al.
(1989) estimated an additive nonparametric regression model using linear
smoothers by the backfitting algorithm and provided proof on the
convergence of the method. The backfitting algorithm sequentially estimates
parameters of interest until convergence in an iterative manner. Hastie and
Tibshirani (1986) proposed the generalized additive model (GAM) which
replaces the sum of the linear covariates by a sum of smooth functions which
are iteratively estimated by the local scoring algorithm. Opsomer (2000)
derived recursive asymptotic bias and variance expressions for the backfitting
estimators on local polynomial regression smoothers.
This paper focuses on estimating the short bivariate time series given the
contemporaneous effects of predictors. The parameters in the bivariate
additive model will be estimated using a backfitting framework. The vector
autoregression at order one (VAR(1)) is used to estimate the output
autocorrelation coefficient ρ. The Generalized Additive Model (GAM) is used
for regressing the sparse components with the bivariate output series . It is
of interest to characterize the underlying empirical distribution function of the
estimates. After achieving initial parameter estimates, the residuals is used for
the sieve bootstrap procedure to give the final parameter estimates. The
performance of the model is evaluated through a simulation study and
application to the short data about the University of the Philippines on
teaching, research, and extension programs for the last two decades (1995 -
2015).
2. Methodology
The postulated model [2] is compared to the (1) process defined as
= −1 + , [1]
where is a 2 × 2 output autocorrelation matrix coefficient of the
immediate past −1 of a given bivariate time series data = ( , ) . is
1
2
a two-dimensional white noise process with time invariant positive definite
covariance matrix ( ′) = Σ .
2 | I S I W S C 2 0 1 9
```