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Well, given that either LM or BHHH is supposed to stop when the Kuhn-Tucker condition is satisfied, I infer it has to be stepwise. I would say otherwise if, say, they were potentially using something like SALO (simulated annealing with local optimization), where one algorithm could profitably run in full as a sub-step of the other.


An AR(1), once the time series and lags are aligned and everything is set-up, is in fact a standard regression problem. Let's look, for simplicity sake, at a "standard" regression problem. I will try to draw some conclusions from there. Let's say we want to run a linear regression where we want to approximate $y$ with $$h_(x) = \sum_0^n \theta_i x_i = ...


Inhomogeneous time/sampling. Autocorrelation. Stochastic volatility. Jumps. Leverage.


It appears to be related to behavioral psychology. In "space," there will be a statistical chance to two asteroids colliding, and a much larger number of near misses. But no asteroid will observe the "near miss" of two other asteroids and adjust its behavior or trajectory accordingly. In human affairs, a "near miss" could produce just the result that was ...


A naive reason has been explained by Nassim Nicholas Taleb in his book titled Black Swan. In a deeper look, one should be aware that no historical data analysis can truly estimate the real tail risk of financial markets. By the same token, standard deviation, max drawdown, expected shortfall, VaR, Conditional Var... No single or combination of such ...


Volatility changes over time. Even if daily returns are normal, assuming the conditional volatility each day is known, the unconditional distribution of daily returns will have excess kurtosis. For example, if daily returns have a standard deviation of 1%, 90% of the time, and a standard deviation of 3%, 10% of the time, the presence of the high-volatility ...


Extreme events in financial markets, like the crash of 1987, occur more frequently in the real world than a normal distribution would predict. The economic facts that drive those extreme events are varying. Such extreme declines have been observed over many different time periods (Tulip-mania for instance), which suggests that it is more likely inherent to ...

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