Normalize Return Series with a Shared Mean and Standard Deviation

Summary

The document discusses how to normalize stock data when comparing series, such as through correlation analysis. Its responses recommend working with returns rather than raw prices because price levels are generally nonstationary, and favor subtracting a common mean and dividing by a common standard deviation when the goal is to place the series on a comparable scale. One response also notes that normalization can set a series to mean zero and standard deviation one.

The advice is brief and does not specify how to estimate the common mean and standard deviation, how to handle changing volatility, or whether returns should be simple or logarithmic. It also gives little justification beyond the concern about nonstationary prices and a general appeal to standardization. The recommendation is therefore a starting point for comparing return series, not a complete statistical procedure or evidence that a particular normalization is suitable for every analysis.

Key ideas

• For comparing stock series, the responses recommend using returns instead of raw prices.
• The suggested approach uses a shared mean and standard deviation to standardize return data.
• Standardization places observations on a comparable scale, often with zero mean and unit standard deviation.
• The document gives limited guidance on estimating scaling parameters or adapting them to changing market conditions.

Tags

# Small question about normalization


# Small question about normalization












Lets assume I want to normalize some stock data ( prices or log prices) to compare for different types of correlation for example.

And here is the question how should I normalize:

a) by subtracting common mean of prices of interest and divide it by common sd?

b) or should I use individual means and sd's in this procedure?

## Answer by Drew (score 1)

https://quant.stackexchange.com/a/17390

The point of normalization is to put everything on the same level (i dont mean price level.) Prices are usually nonstationary, so CLT doesnt apply, while returns arent. So @siegel 's answer is correct in saying use a) with return data.

## Answer by siegel (score 0)

https://quant.stackexchange.com/a/17388

I would prefer choice a), however, I'd work with returns, not prices.

## Answer by Barnaby (score 0)

https://quant.stackexchange.com/a/17398

You normalize for example by having a mean of 0 and a standard deviation of 1 for the data Use in R the scale function.

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