# Time series analysis on illiquid price data?

Say for example I have the following company in some specialized industry:

A - Company that is about to be listed in Exchange 1, i.e., no price history

B - Company that produce similar products as Company A, listed on Exchange 1 as well, however B has very thin volume and price could stay the same for weeks.

C - Similar to company A but listed on Exchange 2, again, thin trading volume

D - Similar to company B but listed on Exchange 2, also thin trading volume

For companies B, C and D, I have their historical EOD price for the past two years.

Exchange 1 and 2 are listed in different continents and there is very little correlation between the two, also, there is no index for this industrial sector. (However the price between company C&D and A&B should be correlated). Also, we can not assume the price time series is non-stationary as the products those company produce could be seasonal in nature.

I would like to figure out the "correct" market price for Company A before it is listed, based on the information above. And my results so far shows that each of the price time series that I have has a different ARIMA model.

Therefore, my question is how can I tackle these price data to start my analysis? Bearing in mind that those are all the data I have and can get.

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I would strongly discourage you to estimate the first trading price of A as function of current (and even historical time series) of comparable companies. The opening trading price is best estimated from A's own fundamentals as well as subscription price, support period price bands, which banks underwrote the stock, how much the company intents to float, public interest, .... You are in for a tough exercise with tons of margin for error if you attempt to price the trading range based on where comparables trade(d) – Matt Wolf Sep 16 '13 at 2:10
@MattWolf I agree, however that is exactly the point. Initially when the stock start to get traded, the price is somewhat "mis-priced" and assuming that it will eventually revert to the theoretical mean, that would represent a trading opportunity. – AZhu Sep 16 '13 at 2:38
what makes you think it is initially mispriced? And towards which theoretical mean, given there is no reference level to gravitate towards? As said, using other asset's time series is possibly one of the worst proxies you could pick. But that is just my 2 cents without exhaustive research on the topic. Why don't you test on your theory on past IPOs? – Matt Wolf Sep 16 '13 at 2:46
@MattWolf Just like what you have mentioned, this is something I do not know and I am trying to find out, the industry is pretty unique in a way that it is small and the data is limited, hence if you compare this to say the IPO of FB, where there are already tonnes of data for similar companies, it won't be the same. – AZhu Sep 16 '13 at 10:57

I suggest you to start by reading the literature on the market illiquidity proxies and the relative effect of market illiquidity on the stock market returns; some of my favourite authors about this topic are Amihud & Mendelson, that developed this research field with their seminal paper in 1986:

Amihud, Yakov, and Haim Mendelson. "Asset pricing and the bid-ask spread." Journal of financial Economics 17.2 (1986): 223-249.

Browsing on google scholar who cited this paper, you can find other interesting papers about the topic.

As regards your question, particularly, you could examine how the illiquidity of a security B influences the illiquidity of security C, or vice versa (since the relative markets are on different continents, they pretty surely trade on different hours), since, if they are comparable, they should move in the same way and be correlated.

Said that, since it is proven that empirically this relationship holds:

$R_{t+1}$ = $\alpha$ + $\beta$*$ILLIQ_t$ + $\epsilon$

where:

• $R_{t+1}$: stock return at time $t+1$;
• $ILLIQ_t$: market illiquidity proxy;
• $\alpha$ and $\beta$: linear regression coefficients;

particularly when you measure the portfolio returns on the portfolio illiquidity.

You could be able to find a trading opportunity.

Alternatively, you could test a pair trading strategy based on security illiquidity; look, for instance, if there exist a granger causality between these two stocks.

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