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5

I personally use the simple Garch(1,1) for volatility filtering in the risk management area. In fact in most cases I don't even estimate the parameters, I stick 0.94 for mean reversion, 0.04 for the squared error and I get the constant by matching the series variance. My experience is that there is no point pretending to finetune parameters when vol is ...

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Very interesting question. I am not an expert on the subject, however, I was able to find a collection of papers on the subject that should get you started. Here is a good and very informative paper that walks you through several tick by tick volatility estimators that seek to reduce the volatility imposed by market micro-structure: Efficient estimation of ...

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Did you try solving for $w_k$? $$\bar{r}_t = \sum_{k=0}^p w_k r_{t-k}$$ $$\bar R = W R$$ Since you probably have $t>>k$, you can solve for $W$ using OLS $$\bar R = W R +\varepsilon$$ -- UPDATE You can try applying Kalman filter. Here, your state evolution is $$r_t=\mu+\varepsilon_t$$. You introduce new vector $x_t=(r_t, r_{t-1}, \dots, ... 1 For any continuous distribution we can define $$VaR_{\alpha}=-F^{-1}(1-\alpha)$$ where$F^{-1}$is the inverse of the CDF. Now suppose that you have a distribution which comes from a location-scale family with location parameter$\mu$and scale parameter$\sigma$then $$F^{-1}(1-\alpha)=\mu+\sigma \phi^{-1}(1-\alpha)$$ where$\phi^{-1}$is the inverse CDF ... 1 If$\log{(|R_t|)}$is your first term, I'm not sure why this is a matrix. Modulus (determinant herein) applied to a matrix$R_t$gives a scalar. If your implementation in python produces a matrix, that's likely because modulus is treated as an element-wise abs() function for each element of a matrix. It may be easier and faster to use rugarch (univariate ... 1 The$\lambda$value used in the original paper is arbitrary, but you can estimate that by assuming (in the simplest case) 2 assets and running the following model:$\sigma^2_{12,t+1}=\lambda$$*$$\sigma^2_{12,t-1}$$+$$(1-\lambda)$$r_{1,t}$$*$$r_{2,t}; given r_{1,t} and r_{2,t} respectively as the returns for the asset 1 and 2 and ... 1 Yes, these are the fundamental building blocks for a money making strategy. To partially solve the issues you mention (small/low positive means/profits with large standard errors), you can investigate on many assets simultaneously. The idea is to take the advantage of Central Limit Theorem. Assuming the signal for each asset are i.i.d., and each signal ... 1 Approach 1 is parametric regression, whereas approach 2 is non-parametric regression. How are they related: non-parametric regression models the entire distribution of all possible function forms, and then do the integration to calculate a single value E[Y|X]. It is function-form free. In contrast, parametric linear regression ASSUMES that the function ... 1 You can apply the Kolmogorov-Smirnov test. I simply quote from the entry: "The two-sample K–S test is one of the most useful and general nonparametric methods for comparing two samples, as it is sensitive to differences in both location and shape of the empirical cumulative distribution functions of the two samples." There is an R-implementation too. 1 Thanks @Aksakal for suggesting Kalman Filter. Here I provide more details. We will view it as a state-space model:$$ \begin{split} z_t &= A_t z_{t-1} + B_t u_t + \epsilon_t, \\ y_t &= C_t z_t + D_t u_t + \delta_t, \\ \epsilon_t &\sim \mathcal{N}(0, Q_t),\ \delta_t \sim \mathcal{N}(0, R_t), \end{split}  where $z_t$ is the latent variable, ...

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