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LeeCarter Model
The phrase "stochastic model" brings to mind models whose output are random. For example, the CoxIngersollRoss interest rate model, where outputs depend on a random error term.
For LeeCarter model, I can't quite wrap my head around why it's considered "stochastic". To me, it seems once the parameters are properly calibrated with past data, the projection of future mortality rates are deterministicln(mu_xt) = alpha_x + beta_x * kappa_t. So why is this classified as stochastic? My thoughts: is it because in the framework, we assumed that there is an error term, although we're not actually projecting it? Or is it because kappa_t is a variable indexed by time? Thanks.
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The K_t is a functional of Normal distrn. If you look close enough, it's a random walk with a constant drift, or a AR(1) process in time series.
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