Z-Score Normalization Does Not Bound Indicators to a Fixed Range

# How to normalize various indicators into one column?


# How to normalize various indicators into one column?












I've seen this video which talks about how to compress different indicators into a sin

https://www.youtube.com/watch?v=sDu6CudKa0Q

I tried to do the same by this way:

```
data_hist['sma10']  = talib.SMA(data_hist['close'].values, 10)  
data_hist['difsma'] = data_hist['close'] - data_hist['sma10']  
data_hist['cci10']  = talib.CCI(data_hist['high'].values, data_hist['low'].values, data_hist['close'].values, 10)  
data_hist['mom5']   = talib.MOM(data_hist['close'].values, 5)

data_hist.dropna(inplace=True)  

cols = ['cci10', 'mom5', 'difsma']  
data_hist['norm'] = ( data_hist[cols].sum(axis=1) - data_hist[cols].mean(axis=1) ) / data_hist[cols].std(axis=1)
```

But this is an example of output data (it's not between -1 and 1...)

```
2013-09-11 00:00:00+00:00   -1.557247
2013-09-12 00:00:00+00:00   -1.686368
2013-09-13 00:00:00+00:00   -2.160459
2013-09-16 00:00:00+00:00   -2.805381
2013-09-17 00:00:00+00:00   -2.770916
2013-09-18 00:00:00+00:00   -1.726371
2013-09-19 00:00:00+00:00   -1.610760
2013-09-20 00:00:00+00:00   -1.645410
2013-09-23 00:00:00+00:00    2.143846
2013-09-24 00:00:00+00:00    1.863802
2013-09-25 00:00:00+00:00    1.847545
2013-09-26 00:00:00+00:00    1.956981
2013-09-27 00:00:00+00:00    2.507031
2013-09-30 00:00:00+00:00   -0.856816
2013-10-01 00:00:00+00:00    1.422277
2013-10-02 00:00:00+00:00    1.604809
```

What am I missing out? Any alternative to compress various indicators in a single column?

## Answer by SRKX (score 1, accepted)

https://quant.stackexchange.com/a/32406

Normalized data are not supposed to be in $[-1,1]$, but they're supposed to be "centered" around 0 (because you subtract the mean of the sample) and with values spread from 0 in a way which makes it comparable between different variable size (because you divide by the standard deviation of the sample).

A quick example is let's say you compare two random sample $X$ and $Y=7 \cdot X$. It could be somewhat "difficult" to see that the points in $X$ and $Y$ are in fact distributed in a same way but for a scaling factor, just by looking at the values.

But the normalized data will show that they're actually exactly the same:

$$X_\text{normalized} = \frac{X-\mu_X}{\sigma_X}$$ $$\begin{align} Y_\text{normalized} &= \frac{Y-\mu_Y}{\sigma_Y} \\ &= \frac{7X-7\mu_X}{7\sigma_X} \\ &= \frac{X-\mu_X}{\sigma_X} \\ & = X_\text{normalized} \end{align}$$

This, however, does not imply it will be contained between -1 and 1.