forecast_peak

Since Harvey and Kattuman (2021) show that $$g_{y,t+\ell|T}
= \exp\{\delta_{T|T}+\ell \gamma_{T|T}\}+\gamma_{T|T},$$ we can compute the
$\ell$ for which $g_{y,t}=0$ and then will fall below zero. This
$\ell$ is given by
$$\ell = \frac{\ln(-\gamma_{T|T})-\delta_{T|T}}{\gamma_{T|T}}.$$ This is
predicated on $\gamma_{T|T}&lt;0$, else there is super-exponential growth
and no peak in sight. Of course, it only makes sense to investigate an
upcoming peak for $g_{y,T|T}&gt;0$ (when cases are growing). The estimates
of $\delta_{T|T}$ and $\gamma_{T|T}$ are extracted from the
<code>KFS</code> object passed to the function.

The 'tsgc' package provides comprehensive tools for the analysis and forecasting of epidemic trajectories.
It is designed to model the progression of an epidemic over time while accounting for the various uncertainties
inherent in real-time data. Underpinned by a dynamic Gompertz model, the package adopts a state space approach,
using the Kalman filter for flexible and robust estimation of the non-linear growth pattern commonly observed in
epidemic data. The reinitialization feature enhances the model’s ability to adapt to the emergence of new waves.
The forecasts generated by the package are of value to public health officials and researchers who need to
understand and predict the course of an epidemic to inform decision-making. Beyond its application in public
health, the package is also a useful resource for researchers and practitioners in fields where the trajectories
of interest resemble those of epidemics, such as innovation diffusion. The package includes functionalities for
data preprocessing, model fitting, and forecast visualization, as well as tools for evaluating forecast accuracy.
The core methodologies implemented in 'tsgc' are based on well-established statistical techniques as described in
Harvey and Kattuman (2020) <doi:10.1162/99608f92.828f40de>, Harvey and Kattuman (2021)
<doi:10.1098/rsif.2021.0179>, and Ashby, Harvey, Kattuman, and Thamotheram (2024)
<https://www.jbs.cam.ac.uk/wp-content/uploads/2024/03/cchle-tsgc-paper-2024.pdf>.

Craig Thamotheram

tsgc

Time Series Methods Based on Growth Curves

forecast_peak function

<dl><dt>kfs_out</dt>
<dd>The <code>KFAS::KFS</code> object for which the forecast peak is to
be calculated. This would be the <code>output</code> element of a model estimated
in the <code>SSModelDynamicGompertz</code> or <code>SSModelDynamic</code></dd></dl>

Arguments

Returns forecast of number of periods until peak given
KFAS::KFS output. — forecast_peak

<dl>

<dt>kfs_out</dt>
<dd>The <code>KFAS::KFS</code> object for which the forecast peak is to
be calculated. This would be the <code>output</code> element of a model estimated
in the <code>SSModelDynamicGompertz</code> or <code>SSModelDynamic</code></dd>

</dl>

forecast_peak: Returns forecast of number of periods until peak given `KFAS::KFS` output.

Description

Usage

Value

Arguments

Examples