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A key aspect of the STS models is that the pursuit of stationarity is not necessary since the time series components such as trend and, seasonal and cyclical factors can accommodate evolving distributions over time.
This is counter-intuitive, as we would expect that a model that includes the significant ARMA time series component (Model 2) should outperform one that did not contain any time series components (Model 3).
We now compare the performance of our model, as defined by equation (1), with three other models, in order to investigate the effect of different covariates and time series components upon outbreak signature detection.
Paul, the random weekly and daily time series components in Model 1 yield higher sensitivities, compared to including a day-of-week covariate plus ARMA errors in Model 2, and day-of-week covariate plus no ARMA errors in Model 3.
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In this section, special attention is devoted to the time series component of the data series under consideration.
Component g j is known as a detailed (high-frequency) component of the time series; component fj − m is known as the smoothed component of the time series.
Figure 7 shows the time series for the estimated optimum process noise values at stations 0098 and 0032 for each coordinate time series component.
Accordingly, in the first stage, the model is used to process one time series component and then, the obtained values are used as inputs for the second model to analyze another component.
The model fit for the data in each city was assessed using diagnostic plots (time series plots, normal quantile plots, autocorrelation and partial autocorrelation plots, and the spectral estimates) of the estimated innovations of the time series component.
Within outbreaks the value of Rt (which has value R0 at time 0) should be allowed to change (i.e. decrease), which could perhaps be done by including a time series component in the MCMC approach.
Then main time series of input(s) and output records were decomposed into sub-time series components using wavelet transform.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com