# Tag Info

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Let’s take a simple example to answer a broad but interesting question: Imagine that we have a daily return serie denoted $r_{t}$ ( which is assumed to be stationary) and let's take a little time to define main concepts : Mean Process (First moment process) The unconditional mean of $r_{t}$ denoted $u$ is just its expectation $E(r_{t})$. It is not time ...

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To get it out the way: you cannot ask 'what model is better' without a reference to what its use is. Do you want to test for the mean or the AR parameter to trade it? Do you want to calculate VaR? Do you want to forecast volatility over one period? Or over 1000 periods? Or higher moments? Do you want to simulate volatility over one period? Or longer? For ...

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A good rule of thumb is to "test" your models by doing forecasts and to choose the best one. Note however that your choice will be based upon the loss function you selected. If you are concerned about outliers you should (for instance) use Median Squared Errors, if you don't you can use Mean Square Errors. In your particular case the Information Criteria ...

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I think you fail to understand Multivariate Garch model such as DCC models since they do take into account non linearity. They are interested in jointly modeling the time series behavior of multiple conditional variance processes. Each couple of series has its own particular conditional correlation process evolving trough time in a non-linear way. In fact ...

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The code you posted is wrong since you do not model the time series behavior of the up/down process (ie if you have 10 up move and consequently 10 down move it is not the same as the opposite ie 10 down and after 10 up..). I would recommend you to use standards Arma Garch models apply on returns instead of modeling the process of up/down. These are (at ...

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Thr second sum should be: $$\sum_{i=6}^{10}u_i = 0.10039773$$ This gives a mean of $0.0067648$ and a standard deviation of $\sigma=.028836$. To avoid these errors you should use something to automate your calculations. Something like a spreadsheet.

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I solved the problem. The implementation which I was using from Mathworks is not very robust and has particular problems at the endpoint. After some more googling I found this other implementation which is much more robust and provide me with correct results of HHT.

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I agree on Richard. the simpler you choose, the better it is so as to get reliable estimates. What's your data frequency? purpose? For model construction as far as I am concerned, daily data from 2010 is enough. Otherwise, you could use a proxy asset for asset D depending on its nature. To clarify, if D is an ETF let's say CAC 40 ETF, concatenate its return ...

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What you need is more mutual information rather than Shannon entropy. It is dedicated to capture the influence of one variable on another (you can think about it as a non linear version of Pearson correlations). They are closely related since the mutual information $I$ between two variables $X$ and $Y$ reads: $$I(X;Y) = H(X,Y) - H(X|Y) - H(Y|X)$$ where $H$ ...

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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 ...

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You can consider old prices for Stocks B, C and D to be "missing data" and apply techniques used by Statisticians to deal with such missing data. One approach, the EM algorithm, suggests you estimate the covariance for the common period, use that covariance matrix and the available data to generate pseudo data for the back period for the third stock and ...

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The short answer: Take all time series starting from 2010 (at most). The covarianc-matrix tells you something about the assets for a certain amount of time. E.g. if I estiamte the covaraince matrix of those 4 assets taking into account data from the last year (!) then I can expect that this matrix remains valid for the coming 1-3 months - if the markets ...

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There is no particular issue with your polynomials. However if you really want them to both start with a 1, you can apply a change of variable by defining : $$Y_t = -\frac{1}{4}X_t$$ Then your polynomials $\Phi_y(B)$ and $\Theta(B)$ such that : $$\Phi_y(B)Y_t=\Theta(B)Z_t$$ will both start with a $1$. It ...

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