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I think you are doing it right... "I am not sure how to express the covariance matrix": but you specify variance to be 1, right? This is what you want? You just need to draw each time conditionally on drawing $X's$ in the right order: first draw first 10 $X's$, then the other five conditional on first five $X's$, and lastly draw $Y's$ condtional on 1, 5, 7,...


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But my question is, does the NN take all series in consideration when creating the forecasts for one series? Well, that depends your exact model. A typical choice might be a neural network $f$, with the model defined as: $p(x^k_t| x_{<t}; \theta) = \mathcal{N}(\mu^k, \sigma^k = f(x_{<t}, \theta))$ where $t$ indexes time, $k$ indexes over your 4 ...


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(NB: I started to write this before the question was edited; I don't comment here on the "empirical aspect", i.e., what is done in the literature, but rather on what "should" be done.) This is a good question, and I don't think there is a good answer. What I think is the following. Generally in statistics things are less "black and white" and it is much ...


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You can plot all the possible pairs of scatter plots. There are $n(n-1)/2$ of them, where $n$ is the number of features. It can be useful for data analysis as well. There's no rule as to which one to choose without having a specific/domain knowledge or having calculated the features importance. If $n$ is too large, and all features are equally important, ...


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If the random vectors $X, Y$ are independent, then, as functions of independent random variables are independent (see Functions of Independent Random Variables), $X_i$ and $Y_j$ are independent, since selecting one given component from a vector is a function. But the covariance of independent random variables are zero, that gives you the result. In your ...


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After fighting with the problem some more, in the end I did use an imputation approach: I adjusted the number of samples for all combinations of aquarium (this is the random factor) and sampling timepoint to 6, by randomly picking one (or two) of the available observations depending on how many were missing. Then I ran adonis2 with restricted permutations. I ...


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Simply put, the determinant really is a Jacobian determinant from a transformation. See, $\sigma$ is outside the exponential because it is a location scale family. If $y\sim N(\mu,\sigma)$ and $x\sim N(0,1)$, then $$ f_y(y) = \dfrac{1}{\sigma}f_x(\dfrac{y-\mu}{\sigma}). $$ This is because the Jacobian of the transformation is $\dfrac{1}{\sigma}$ One way to ...


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Yes. In fact, the multivariate logistic distribution is a member of the more general family of elliptically-contoured distributions, and can be derived from the univariate version. Both the univariate and multivariate normal distributions share the same probability density generator, which is proportional to $$ g(u) = exp(-u/2) $$ That is, if $u =\big(\...


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I think Li-Mak (Li & Mak, 1994) (univariate) and Ling-Li (Ling & Li, 1997) (multivariate) tests are suitable candidates for error diagnostics in univariate and multivariate GARCH models, respectively. Unlike some other (popular) tests*, they account for the fact that standardized residuals from GARCH models are not equal to true standardized ...


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While it is mentioned in a number of regression texts, the plot you have mentioned here does not seem particularly useful to me. A far better alternative is the added variable plot, which correctly represents the relationship between an individual explanatory variable and the response variable conditional on other explanatory variables. For the explanatory ...


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When applying multivariate GARCH models, you are supposed to use the Variance/Covariance approach. Let's assume that you have obtained the conditional variance forecast, say $H_t$. Then, assuming a vector of portfolio weights $w_t$ at time $t$, the portfolio variance will be $\sigma_p^2=w_t H_t w_t$. Depending on whether you have defined a level ...


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If you take cross correlation as measure for distance between curves For the curves in the Andrews plot $$f_x(t) = x_1 \frac{1}{\sqrt{2}} + x_2 \sin(t) + x_3 \cos(t) + x_4 \sin(2t)+ ...$$ The cross covariance $$\int_{-\pi}^{\pi} f_x(t) f_y(t) dt$$ can be simplified as separate products (because the trigonometric functions are orthogonal) $$ x_1 y_1 \...


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I think that you can use regression to analyze your data. In essence, you have described a regression with a single outcome, y (home price), with three predictor variables x1-x3 (proportion restaurant, proportion government, and proportion agriculture, respectively). You further have multiple home price observations in each of your sites, necessitating some ...


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It's better to operate on log domain in such cases. There are implementations (employing factorizations like Cholesky, LU) available in common languages: python: numpy, tensorflow R: msos, lme4


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Dynamic Time Warping might be a good choice if you are explicitly trying to use one time series to predict another. This method works by means of determining similarity between two sequences which vary, typically in either time or speed. From looking at your time series, it would not appear (at least visually) that there is a lag between the two time ...


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A repeated measures ANOVA doesn't require time-series data, although time series are common. At its core, the repeated measures ANOVA is an extension of a paired t-test, for cases when samples are not independent. The reason it often gets used with time series data is because the same measurement is taken from the same individual at different time points. ...


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