What is considered "normal" in a dataset, relative to other datasets and through time? I currently have time series datasets of GDP across countries (lets say USA, Australia, and Japan). I want to be able to create a number from -1 to 1 for some point in time that both considers how large the GDP is at that day in time and how large the growth of the GDP is.
In order to do this, I need to think about what is thought of as "normal" levels for each of these countries both relative to themselves, each other, and across time (a "normal" value at one time, may not be the "normal" value at another time). Additionally, I need to consider how a country's value/growth is relative to other countries.
I'm confused how to go about standardizing/normalizing my datasets, in order to compare the differences (?) between them, and to come out with a value. Here's what I'm thinking right now (I've bolded some of my main questions — would be much appreciated if someone could give me some guidance on them).
Consider the average value of the GDP over the past 1 year, and that will be the "normal" value for the GDP for the past year. Thus, I can compare the current value of the GDP with this past 1 year average, and see if it is bigger/smaller (how do I go about determining how to quantify how much bigger/smaller it is — looking at the mean/SD of the entire historical dataset?). Similarly, how do I go about comparing the values of the GDP across countries? Do I look at the percent changes across time, and compare them?
 A: GDP across time in different currencies are not so easy to compare. Let us take the example of Canada and the USA.
The Canadian GDP growth rate as calculated quarterly and compared to the same quarter one year prior is as follows for the last ten years from the tradingeconomics website,
which is typically a quarterly amount of approximately 0.5% or 2% annualized. However during that same ten year period, the Canadian dollar took a nosedive compared to the USA dollar. For the relative value of the Canadian Dollar in USA dollars from the XE money transfer site website. Consequently, if one calculates the Canadian GDP in USA dollars it looks like this from the tradingeconomics site: That introduces a heavy correlation to the exchange rate, which muddies the concept of GDP within Canada itself.
Finally, how one runs the numbers depends on the purpose of performing the calculation. In our example above, if our purpose is to look at the USA purchasing power of the Canadian economy, the chart directly above would suffice. On the other hand, if one wants to calculate the purchasing power of the Canadian GDP within Canada, one would compare the Canadian GDP to the Canadian consumer price index, or in general, one would compare that GDP to the price trend for whatever one desires to purchase.
Calculating an SD would be not normally be performed. SD is a distance or displacement measure, a measure of expected change, and that role would be more typically obtained by comparing the GDP in a quarter to the GDP of the same quarter one year prior to mitigate the seasonal variation upon the GDP comparison of change. To recapitulate, comparison of GDP between countries should take into account what cost base is being used, for example, what that GDP means within each country compared to a target measurement of the purchasing power or other measure of utility of the GDP. For example, if one wishes to compare countries for what the GDP means within each country in terms of cost of living, that would be one kind of calculation, and if one wants to see what GDP means in terms of some other measurement, e.g., exchange rates, then one does that type of calculation.
