# Time Series or Regression

I'd like to research the impact of certain events and characteristics on the liquidity of the stocks over time. I've got a sample of 200 stocks and I use several measures of liquidity (Amihud, Bid-Ask spread, etc.). I've got around 5000 trading days and the data consists of all values of interest over time.

For example I made an index of Corporate Governance of the firm, allowing it to have a score from 1 to 10. Or I have a variable expressing the media coverage on that firm. And of course market cap, number of outstanding shares, free float, price, etc.

My first task, I'd guess, would be to model/measure 'normal liquidity' that is without certain events occurring.

Is this just regression with a lot of control variables or is this time series analysis? Or a combination... how should I start? Any introductionary resources would be welcomed.

Definitely time series analysis. What you essentially want to do is some form of impact analysis. this can be done naturally using multivariate time series models like Vector Auto Regression models. Also when working with data to model liquidity you might want to use some specialized procedures like GARCH and ACD. Further there are methods to model non stationarities and there are extensions to non-linearities as well. Definitely time series analysis.

• Thanks for your reply. According to Wikipedia: A VAR model describes the evolution of a set of k variables (called endogenous variables) over the same sample period (t = 1, ..., T) as a linear function of only their past values. Is this what I want? The concept of regression came up because I'd figure the liquidity would depend on certain characterstics (that in turn could change over time) and not only depend on previous values. Oct 16 '13 at 8:44
• Am I not looking a fixed effect panel data regression of some sorts? Oct 16 '13 at 10:03
• look you can call it whatever you want to. i seriously believe that regression is a very general term. time series analysis is a more specific field of analysis which is completely suited to the problem you have mentioned. hence that would be my choice. and it might be similar or same to a lot of other methods but it is a specialized field of study and self contained so you need not worry about other things when using time series analysis. Oct 16 '13 at 13:38

Breakpoint approaches

Test based

To be well received in a financial econometrics journal, you want test-based approaches. Depending on your question it is common to see a linear regression (least squares) where the parameter suspected of breaking is interacted with an indicator function $I(E)$ where $E$ is the event in question; this function assumes a unit value when $E$ occurs. This is almost always specified exogenously; see e.g. the contagion literature.

This is less common but in some applications a VAR or VECM is what you want. You will want to review Joyeux (2007) for various test based breaking models within a VECM framework. Note that data generating process of your model is going to be restricted simply because the asymptotics haven't been worked out for many alternatives - this logically follows from how recent Johansen's framework is as well as the complexity of VARs/VECMs versus completely linear single equation models. It may be interesting to look at the impulse response functions of the models in different regimes.

Endogenous approaches also fall under test based approaches. Here it is typical to analyse the residuals of an unbroken model and to determine the time location where the residuals is statistically 'large'.

Another typical approach is to fit a market model around the event and do a test on the cumulative abnormal returns. There is a dauntingly deep literature on how to get an unbiased test statistic in this instance. You may want to look into the 1980s paper by Sefcik and Thompson and GLS/WLS derivatives of this paper. They provide a dummy breakpoint framework which is statistically equivalent to the CAR approaches, and in my opinion more interpretable.

Other avenues:

• Contagion literature (truly gigantic).
• Financial integration literature (stock and bond markets).

Non test based

These are harder to publish: event studies basically need a test. But to get a truly thorough idea of what's happening - much better than a test in my opinion in all real world applications - to all your time series around the event, look at a power spectrum of your time series. This is done with the click of a button in the biwavelet package in R (there are around 10 others).

This is for qualitative understanding - no official test comes from this. It is therefore not likely to publish (unless you're going for econophysics journals such as Physica A where you might not get an economist reviewer).

Before you start, you might like to consider the following.

If you have a method to measure 'normal liquidity', you next might like to 'black out' the periods within your time series that are around your past events. This would require some logic and common sense. You can then calculate your measure of 'normal liquidity' with and without these events included.