Statistical inference for stochastic coefficient regression models
The classical multiple regression model plays a very important role in statistical analysis.
The typical assumption is that changes in the response variable, due to a
small change in a given regressor, is constant over time. In other words, the
rate of change is not influenced by any unforeseen external variables and remains the same over the entire
time period of observation. This strong assumption may, sometimes, be unrealistic, for
example, in areas like social sciences, environmental sciences etc. In view of this, we propose
stochastic coefficient regression (SCR) models with stationary, correlated
random errors and consider their statistical inference.
We assume that the coefficients are stationary processes,
where each admits a linear process representation. We propose a frequency domain method of
estimation, the advantage of this method is that no assumptions on
the distribution of the coefficients are necessary. We illustrate the methodology
with simulations and compare their performance. These models are fitted to two real data sets
and their predictive performance are also examined.