# How to standardize data with low variance?

I have quarterly data of federal fund rate (test set), e.g.:

[2.18, 2.18, 2.18, 2.18, 2.18, 2.18, 2.18, 2.18, 2.18, 2.18, 2.18, 2.18, 2.19, 2.19, 2.19, 2.19, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.19, 2.2, 2.2, 2.2, 2.2, 2.19, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.19, 2.2, 2.2, 2.19, 2.2, 2.19, 2.19, 2.19, 2.19, 2.2, 2.2, 2.2, 2.4, 2.4, 2.4]


Train data description is:

Mean: 1.003916
Variance: 0.203896
Std: 0.4514


I want to use this data as an input feature for the LSTM model. For this, I apply standardization, as follows:

$x'(i)&space;=&space;\frac{x(i)&space;-&space;\mu}{\sigma&space;^{2}}$

I am forced to use training data mean and variance, since I need to avoid look ahead bias at dev and test sets. However, after applying it turns out that the data standardizes to even larger values.

This can't be used as an input to neural network, since it causes some features to be more weighted than others. Moreover, rest of features are within -1, 1 range.
I have also tried using Min-Max normalization, but in this case NN does not converge on some data points.

What should I do in this case?

• The fact that NN doesnt converge on fed funds variable standardized with the range is a red herring. This cant be the reason – Aksakal Apr 23 at 20:21
• standard scaling means dividing by the standard deviation $\sigma$, while your equation shows you dividing by the variance $\sigma^2$. After scaling you should check that $x'$ has mean zero and variance one; and you should expect to see a mix of positive and negative values roughly between -2 and 2. Also, the example data set you provide doesn't look like it has mean 1.0039 and variance 0.2039 like you claim. Unless the omitted values are very different than the ones shown, I would expect something like a mean of 2.2, variance .002, and standard deviation of .046. – olooney Apr 23 at 20:43
• @olooney, you're right as stated above, I use mean and std from the train set and then apply to dev and test data(given above) – sokolov Apr 23 at 20:48

Usually you standardize by the volatility (std deviation) $$\sigma$$ not the variance $$\sigma^2$$. You want the unitless variable, but in your case the units stay. For instance, the interest rates are in inverse time units $$year^{-1}$$ so, your new variable is going to be in time units, years.
• I'm not sure why you think -3 and +3 range is not valid. If you really want to get them into $[-1,1]$ interval you either use the range instead of the standard deviation or as a quick fix get $3\sigma$ in denominator. – Aksakal Apr 23 at 20:16