Fisher information matrix of binary time series

by   Xu Gao, et al.

The standard approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating the historical data as covariate inputs, standard errors of estimates of GLM parameters computed using the empirical Fisher information do not fully account the auto-correlation in the data. To overcome this serious limitation, we derive the exact conditional Fisher information matrix of a general logistic autoregressive model with endogenous covariates for any series length T. Moreover, we also develop an iterative computational formula that allows for relatively easy implementation of the proposed estimator. Our simulation studies show that confidence intervals derived using the exact Fisher information matrix tend to be narrower than those utilizing the empirical Fisher information matrix while maintaining type I error rates at or below nominal levels. Further, we establish that the exact Fisher information matrix approaches, as T tends to infinity, the asymptotic Fisher information matrix previously derived for binary time series data. The developed exact conditional Fisher information matrix is applied to time-series data on respiratory rate among a cohort of expectant mothers where it is found to provide narrower confidence intervals for functionals of scientific interest and lead to greater statistical power when compared to the empirical Fisher information matrix.


page 1

page 2

page 3

page 4


Higher order approximation for constructing confidence intervals in time series

For time series with high temporal correlation, the empirical process co...

Multivariate time series models for mixed data

We introduce a general approach for modeling the dynamic of multivariate...

Matrix Autoregressive Model with Vector Time Series Covariates for Spatio-Temporal Data

In this paper, we propose a new model for forecasting time series data d...

Statistical Inference for Cox Proportional Hazards Models with a Diverging Number of Covariates

For statistical inference on regression models with a diverging number o...

Flexible Bivariate INGARCH Process With a Broad Range of Contemporaneous Correlation

We propose a novel flexible bivariate conditional Poisson (BCP) INteger-...

Using Simulation to Analyze Interrupted Time Series Designs

We are sometimes forced to use the Interrupted Time Series (ITS) design ...

Fitting stochastic predator-prey models using both population density and kill rate data

Most mechanistic predator-prey modelling has involved either parameteriz...

Please sign up or login with your details

Forgot password? Click here to reset