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I am looking at a report of a company. They are saying they are normalizing data. They have time-series data (i.e. data for certain parameters for sequence of time). They first generate new variables as $100\cdot(x/lag(x)-1)$ Then they do Kernel density estimation. I thought normalizing is subtracting mean and dividing by sd, wasn't it?

1) So, is $100\cdot(x/lag(x)-1)$ a normalization for time-series? EDIT: as I understand this is just calculating the ratio of one year by another year. Is it considered normalization?

2) What is the kernel used for in here then? Just smoothing?

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  • $\begingroup$ If you write $lag$, do you mean logarithm $\log$? $\endgroup$
    – Karel Macek
    Commented Oct 23, 2015 at 13:40
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    $\begingroup$ "Normalization" is a very overloaded term -- much like "linear." $\endgroup$
    – Sycorax ♦
    Commented Oct 23, 2015 at 13:56
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    $\begingroup$ Subtracting the mean and dividing by the SD is usually called standardization (although some people overload that term, too). $\endgroup$
    – whuber ♦
    Commented Oct 23, 2015 at 14:33
  • $\begingroup$ @user777, could you clarify what you mean by "overloaded"? Do you mean that there are different meanings to it? $\endgroup$
    – user3349993
    Commented Nov 15, 2015 at 12:56
  • $\begingroup$ @user3349993 I mean that there are many meanings of "normalization." It sounds like the company's definition and yours are not the same -- and since companies' procedures tend to be etched in stone, changing their mind will be like shouting into a hurricane. 0-mean, unit variance normalization is one method; but some people "normalize" by putting everything in the $[-1,1]$ or $[0,1]$ intervals. Or they are referring to normalized vectors... Or any of a number of other examples. $\endgroup$
    – Sycorax ♦
    Commented Nov 15, 2015 at 18:26

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I assume that $lag$ is the lagged variable. Somehow $lag(x_t)=x_{t-1}$.

Therefore it is not normalization that is performed. They just turn a (price/value?) series into a series of (returns?) ratios : $\tilde{x}_t=\frac{x_t-x_{t-1}}{x_{t-1}}$. The 100 multiplier is just a way to express these ratios in percentage I guess.

Then there is nothing wrong with fitting any distribution on the returns. Kernel estimation is indeed smoother (than producing the empirical distribution).

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