Latent Gaussian Count Time Series

Changepoint detection in autocorrelated ordinal categorical time series

“…As the categories of Y t are determined through Z t , temporal dependence in {Z t } induces temporal dependence in {Y t }. The relationship between the autocovariance of {Z t } and the autocovariance of {Y t } is examined in Jia et al (2021). The autoregressive latent Gaussian process {Z t } is Markov; however, its categorized variable {Y t } is not Markov since the Gaussian clipping transformation between Z t and Y t in (1) is not one-to-one.…”

“…For example, if the true 𝜌 = −0.75, the estimate might be −0.6. To handle this scenario, an upper bound in the function optim is set to the lag 1 autocorrelation of Jia et al, 2021).…”

“…The autocovariance and autocorrelation functions of $$$ \left\{{Z}_t\right\} $$$ are both $$$ {\rho}^h $$$ at lag $$$ h\ge 0 $$$. This setting was recently used in Jia et al (2021) for a stationary autoregressive latent Gaussian process.…”

“…As the categories of $$$ {Y}_t $$$ are determined through $$$ {Z}_t $$$, temporal dependence in $$$ \left\{{Z}_t\right\} $$$ induces temporal dependence in $$$ \left\{{Y}_t\right\} $$$. The relationship between the autocovariance of $$$ \left\{{Z}_t\right\} $$$ and the autocovariance of $$$ \left\{{Y}_t\right\} $$$ is examined in Jia et al (2021). The autoregressive latent Gaussian process $$$ \left\{{Z}_t\right\} $$$ is Markov; however, its categorized variable $$$ \left\{{Y}_t\right\} $$$ is not Markov since the Gaussian clipping transformation between $$$ {Z}_t $$$ and $$$ {Y}_t $$$ in (1) is not one‐to‐one.…”

The negative binomial process: A tractable model with composite likelihood‐based inference

“…A limitation of our model is that it can capture only positive autocorrelation. A possible way to extend it to include both positive and negative autocorrelation is to follow the approach recently proposed by Jia et al (2018). More specifically, let be a stationary ARMA Gaussian model with zero mean and unit variance and define , where F (·) and are the cumulative distribution function of the gamma and standard normal distributions, respectively.…”