Just like what I am asking in the title. I see nearly all the financial datas take logs before the data analysing step, Why? Dose it have nice properties?
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$\begingroup$ You probably need to meet certain assumptions on the distributions of the variables before applying certain models, hence the need for such a transformation. $\endgroup$– Black MilkCommented Aug 7, 2014 at 1:06
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$\begingroup$ This is answered here: stats.stackexchange.com/questions/18844/…. Also, look at the comments below the question there. One of the commenters provides links for further insight. Also, this might help too ats.ucla.edu/stat/mult_pkg/faq/general/… $\endgroup$– Black MilkCommented Aug 7, 2014 at 1:50
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$\begingroup$ Variance of annual return based on variance of monthly return is also relevant $\endgroup$– TooToneCommented Aug 7, 2014 at 18:55
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3 Answers
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Finance data tends to be money-related and as such incorporates many potential multiplicative effects - things like inflation or interest for example.
The variables tend to be right skew, in some cases close to lognormal.
The effects of things like scale changes (cents to dollars or billions to millions) are simple location shifts on the log scale. Multiplicative/percentage effects (like 10% increase, say) convert to shifts as well.
Variables often exhibit exponential growth, at least in the short term.
All these things make working on the log scale much more sensible/easy.
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Most common financial data (prices, returns, etc) have a Lognormal distribution. Second of all, for some modelling, it does not make sense to have negative values so by taking logs, you are ensuring that you will not get negative values in your calculations.
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$\begingroup$ Though a log of a negative number is nonexistent, so modeling on those records would just throw them away, right? $\endgroup$ Commented Aug 7, 2014 at 2:01
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$\begingroup$ What kind of negative numbers? -12 percent GDP growth is the same as 88% of the previous quarter's GDP. This transformation preserves that data point, even under logarithmic transformation. It's inappropriate to take the log of a negative number, but that doesn't mean it's ok to throw out the data... that's a recipe for a bad/biased model. $\endgroup$– Sycorax ♦Commented Aug 7, 2014 at 2:11
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$\begingroup$ After take log my data are all negative,because my original data are like all around 0.4,so shall I not take logs just use the original data? $\endgroup$ Commented Aug 8, 2014 at 19:58
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$\begingroup$ taking logs is usually done on level data (prices, output, money, ...); it is not used on changes in level (returns, growth rates). So in this reply the 'returns' slipped in incorrectly. Note that taking logs of levels is also convenient to compute (approximate) returns/growth rates: you can just use difference of log value to obtain approximate growth rates. $\endgroup$ Commented Jul 8, 2015 at 10:40
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One of the major reasons in econometrics is that money tends to have diminishing marginal returns/effects. \$1 simply means less to you if you have \$1 million than if you have $10. A log transform accommodates this.
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$\begingroup$ +1 to @Glen_b who highlighted this already, I just wanted to make sure the proper economics term was used. $\endgroup$ Commented Aug 7, 2014 at 1:58