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I will assume you are using factors and gold returns that are contemporaneous. With that setup, you are essentially trying to explain or decompose gold returns. For an explanatory regression of a commodity (which is internationally traded), an $R^2$ of 36% is pretty good. Lots of factors can affect gold returns: Indian wedding season (a major effect on gold ...

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I might miss a point but if I understand your graph correctly, it seems that the parallelism between the two curves shows that your NN predicts roughly the current price in 2 days (hence the time lag). If you had no algorithm at all but just a prediction that Xt+2 = Xt, you would get a blue curve that exactly replicates the red one with the same lag. ...

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First of all, when you try nonlinear modelling, you should start with a linear model. Did you tried one? what was the result? It seems that your non linear model for day $d$ (blue curve) is close to the value the day before (red curve). You model may be close to $$\hat Y(d)=Y(d-1)+f(Y(d-1),Y(d-2),\ldots;X(d-1),X(d),\ldots),$$ where the non linear part $f(\... 1 I worry that power prices are very unlikely to be stationary. It is possible the mean does not vary wildly over time, and the price process may not be integrated, i.e. prices may not require differencing. However, prices (or returns) almost surely require correcting for heteroskedasticity. If you have a powerstack function estimated, perhaps you could use ... 0 You could ignore the problem, throw away returns for the first minute in each trading session, or you could keep those first-minute returns in a second dataset and analyze that to estimate the overnight gap volatility. Also, since you are an academic and using minute bars, I'm sure you are aware of the issues with bid-ask bounce and volatility estimation for ... 0 Have you thought about mirroring the data? So you would have in the missing data period the replication of what happened during the day, but in an inverse way. 3 Just by looking at the graphs, I'd say: Unit root Constant series Seasonality AR model No AC No AC 1 There is a multitude of texts which answer this question the easiest and free source is Rob Hyndmans from Monash Universities online text on forecasting, https://otexts.com/fpp2/, the topic is covered in many time series books and econometric texts, another good general reference is by Galit Schmueli who ran a course on Future learn for free on Time series ... 0 Lag length selection in Granger Causality tests is usually based on information criteria (AIC, BIC, etc.) instead of an F-test comparison. But Granger Causality seems not to be the adequate concept for your purpose to "measure what the lag is". Applying model selection criteria (e.g. information criteria) in Granger causality tests does not tell ... 2 When you carry out correlation coefficient between target variable (denoted as x) and feature variable (denoted as y), the correlation coefficient is a function of sample size:$ r = \frac{n \Sigma xy - (\Sigma x \Sigma y)}{\sqrt{(n\Sigma x^2 - \bar{x}^2 )(n\Sigma y^2 - \bar{y}^2 )}}\$ So daily data will impact on correlation.

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