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If you have a linear/gaussian state space model and you're using a Kalman Filter, you can use maximum likelihood estimation or the EM algorithm. I personally prefer the former since you don't need to know anything about smoothing. If you use the EM, you do. If your observations are $z_1, \ldots, z_n$, then you can write down an innovations likelihood $$L(\...


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I will try to give a simple technique for Identifying $ARIMA(p,d,q)$ orders for a time series. It's an empirical technique, but the results are very closed to techniques based on $AIC$ or $BIC$ criterions. -Indentifying the Integration order $d$ : It's the first parameter to determine, indeed the ARMA models are based on the assumption that your time ...


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$(p_t,c_t)$ are respectively related to the put/call slopes of the total implied variance, not variance $$ w(k,t)=\sigma^2(k,t) t $$ Under SVI $$ w(k) = a + b \left(\rho(k-m) + \sqrt{(k-m)^2 + \sigma^2} \right) $$ such that $$ \frac{\partial w}{\partial k}(k) = b \left( \rho + \frac{k-m}{\sqrt{(k-m)^2+\sigma^2}} \right) $$ and $$ \lim_{k \to \pm \infty} \...


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The method The Cornish-Fisher expansion is a method that helps us to approximate the quantile of a target distribution $F$ in terms of another support distribution $\tilde{F}$, using the so-called cumulants of the target distribution. Cumulants are one way to (fully) describe a distribution function; i.e. if you know 'all' cumulants of a distribution ...


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To get "risk-neutral" parameters you must have prices of traded instruments on the interest rate, and not just historical data of (your estimate of) the spot rate, since the risk-neutral measure is inferred from market instruments. A good paper that might help you is the following: http://www.planchet.net/EXT/ISFA/1226.nsf/d512ad5b22d73cc1c1257052003f1aed/...


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A good article on adaptive Kalman filter tuning is: Introduction to the Kalman Filter and Tuning its Statistics for Near Optimal Estimates and Cramer Rao Bound The authors present an adaptive approach, which means that you make initial estimates of the noise covariances, and iterate the Kalman filter and the noise covariance estimates until all the ...


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Quoting George Box, "All models are wrong, but some are useful." The model with static parameters would be at least somewhat explanatory, but not necessarily predictive. By parameterizing too much one might stumble upon a perfect fit, which will fail miserably on future data.


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Basically there are at least two questions you have to ask yourself before believing "good backtests": Is there an economic or behavioural explanation why this should work (best would be to start from there in the first place). How many things did I try to arrive at this "good backtest". The following paper is quite helpful to learn some of the basics of ...


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