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I suggest to use R since it is open source and very powerful and thus is used by many companies and researchers. R does not only allow to deal with large amounts of data, it also allows to do state-of-art statistical analysis, including Tensorflow/Keras etc.

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First, T-test null hypothesis is that there are no differences between means of two samples. And p-value is the probability to observe the data, given that the null hypothesis is correct, so if p-value is small - you are likely to reject the null hypothesis. So in your case it is actually vice-versa to what you wrote: In case of StandardScaler your test ...

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Box-Cox transformation cannot work with negative values. You can try feeding negative values to the box-cox transformation and it will give you an error.

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You could try to use the following method. $$y=a\sin \left[\dfrac{\pi}{12}x-b\right]+ c$$ $$=a\left[\sin \dfrac{\pi}{12}x \cos b - \sin b \cos \dfrac{\pi}{12}x \right] +c$$ $$=a\sin \dfrac{\pi}{12}x \cos b - a \sin b \cos \dfrac{\pi}{12}x +c$$ The last equation indicates that we can switch to new parameters $w_1 = a\cos b$, $w_2=-a\sin b$, and $w_0=c$. ...

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These metrics are used to assess the performance of your model. If certain observations are not used by the model it would therefore not make sense to include them when calculating the model's metrics. You should therefore not take these type of records into account and only look at records that are processed by your model.

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Assuming by persistence you mean degree of autocorrelation. ACF is simply a function that can be derived for any stochastic process, whether stationary or not. But the estimation of ACF for non-stationary, which is what you are doing, is the problem. Generally, ACF is a function of both time, $t$ and lag, $h$: $$\gamma(t,t+h) \equiv Cov[X_t,X_{t+h}]$$ For ...

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