Could you write a model that will tell you how fast your car is going, just by using math? Or are there innumerable latent variables which define a state space so large that the only meaningful prediction you could make is a short-term linear extrapolation?
I mean, what would make anyone think that there is any constant parameter set for a model that would predict COVID-19 case evolution, when governments and the population are taking active measures to combat spread, such as perhaps the most dramatic shift in the physical interconnectivity of human society in history? It's fundamentally impossible to predict something that is changing in an unpredictable manner.
The reason why we can make meaningful inferences about the accuracy of weather models is because we have a good understanding of the underlying physics which decribes the time evolution of the system. However, the combination of the chaotic dynamics of that system and the limitations of simulation yields accurate short-term probablistic predictions and inaccurate long-term probabilistic predictions.
SARIMAX, in contrast, doens't know if it's predicting shampoo sales, $GOOG, or epidemiology. Although I am curious what your exogenous regressors and lag/differencing/seasonal orders were, if you'd care to share. Did you fit them via an information criterion approach?
Could you write a model that will tell you how fast your car is going, just by using math? Or are there innumerable latent variables which define a state space so large that the only meaningful prediction you could make is a short-term linear extrapolation?
I mean, what would make anyone think that there is any constant parameter set for a model that would predict COVID-19 case evolution, when governments and the population are taking active measures to combat spread, such as perhaps the most dramatic shift in the physical interconnectivity of human society in history? It's fundamentally impossible to predict something that is changing in an unpredictable manner.
The reason why we can make meaningful inferences about the accuracy of weather models is because we have a good understanding of the underlying physics which decribes the time evolution of the system. However, the combination of the chaotic dynamics of that system and the limitations of simulation yields accurate short-term probablistic predictions and inaccurate long-term probabilistic predictions.
SARIMAX, in contrast, doens't know if it's predicting shampoo sales, $GOOG, or epidemiology. Although I am curious what your exogenous regressors and lag/differencing/seasonal orders were, if you'd care to share. Did you fit them via an information criterion approach?