In my view, the Case-Shiller Index describes the development in house prices and does not provide a separation with respect to the driving factors, i.e. whether the evolution is driven by fundamental or speculative factors. For this question, you need to decompose the Case-Shiller Index into these components, based on an econometric model for the fundamental evolution.

I am not sure whether something similar is useful for Kazakhstan. For example, in case of rising housing prices, US households could get higher credit from banks to finance additional consmption, as they can provide higher collateral. In Kazakhstan, financial markets are less developed.

It might be a good idea to develop indicators for the early detection of crisis, but in the case of Kazakhstan, energy prices should be included in this measure. Probably also exchange rates, foreign reserves, FDI etc

INDEX: Indication of change by specifying a reference point (based year) and then track changes in subsequent period relative to that based year's value. Can this be used as predictor of crisis or upcoming bubble? Probably not a good tool. Time series regression with 1 lag would be more useful since 1 year lag is more accurate than 5 or 10 years apart by base year reference.

KAZAKHSTAN USE OF INDICES: There are currently 2 indices used in Kazakhstan, namely (i) GDP deflator with based year value fixed on 2007 dollars and (ii) inflation, average CPI with based year fixed on 2000 dollars. As of the end of 2013, the GDP deflator index for Kzakhstan is 298.54 compared to 100 base year in 2007. The inflation (average CPI) index at at end if 2013 is 392.634 compared to 100 based year in 2000. The reading of these types of indices allow use to compare the present to the past. It tells us where we have been? where we are now in reference to our past? See IMF figures attached Excel file.

CASE-SHILLER INDEX: Probably such index may not be feasible due to availability of data. Case-Shiller index is used for the housing market. Does the real estate market in Kazakhstan show movement in prices and has enough data to track?

REFERENCE: See attached file for IMF World Economic Report. For various types of index, see link to Wolfram site.

http://mathworld.wolfram.com/IndexNumber.html

Yes and no. Yes, you can create an index. If you have sales prices and attributes, then use standard hedonics. If you have only prices, then use repeat sales models. But no, the index will not tell you when there is a bubble. 

Developing the housing index should require data. If you have characteristics of the dwellings then you could use hedonic methods. I'm not sure about repeated sale (it depends on the amount if data). For instance, in Bucharest there are limited numbers of repeated sales, so this is out of the question.