Fisher information matrix of binary time series

Abstract

A common 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 time series with short length. By treating the historical data as covariate inputs, standard errors of estimates of GLM parameters computed from 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, as T tends to infinity, the exact Fisher information matrix approaches 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.

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Acknowledgements

Data collection for the maternal cohort was supported by US PHS (NIH) grant RO1 HD-060628 to Pathik D. Wadhwa.

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Correspondence to Xu Gao.

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Gao, X., Gillen, D. & Ombao, H. Fisher information matrix of binary time series. METRON 76, 287–304 (2018). https://doi.org/10.1007/s40300-018-0145-3

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Keywords

  • Binary time series
  • Correlated binary data
  • Empirical Fisher information
  • Exact Fisher information matrix
  • Logistic autoregressive model