Cardinal data as dependent variables I wanted to find out if there are any implications to using OLS when i have cardinal data as dependent variables.  So my dependent variables are counts of a certain outcome and they exist as natural numbers 0,1,2,3,...N
My independent variable is a series of realized volatility.
Is there a better way such data could be described?
 A: Yes, using OLS for cardinal/count data is suboptimal. See King (1988) for a comparison of OLS regression to exponential Poisson regression in a political science application. Here's a few excerpts:

The two models used most frequently in political science for analyzing this type of data are either misspecified (the OLS model...) or biased and inconsistent (the logged OLS model...). Since statistical theory is known only for unrealistically large sample sizes, I use Monte Carlo experiments to demonstrate the empirical unbiasedness of the EPR model in finite samples and the bias and inefficiency of the logged OLS model of event counts even in very large samples. [Emphasis added.]

Misspecification becomes apparent if OLS results in negative predictions, and near zero:

It makes the unrealistic assumption that the difference between zero and one event occurring in a particular time interval is the same as the difference between, say, 20 and 21 events. Thus, the true relationship is not linear, and a linear approximation would not in most cases even be a reasonable working assumption. OLS is an unbiased estimator of a linear conditional expectation function (CEF); the problem here is that the CEF is neither linear nor necessarily close to linear. 
Second, the statistical inefficiency (the variance of the estimates across samples) of the OLS estimator is much higher than it could be. By taking into account neither the heteroskedasticity, the particular asymmetric form of the heteroskedasticity, the correct functional form, nor the underlying Poisson distribution of the disturbances, OLS does not use all available information in the estimation. Insufficiency and inefficiency result. [Emphasis added.]
These statistical problems are more than just technical points. They usually result in substantively biased conclusions. In applications, coefficients will have the wrong size and will often have the incorrect sign. Questions such as "How many disruptive events will occur next month if unemployment decreases to 10 percent?" will many times yield nonsensical answers like, "The estimates indicate that there will be about negative four disruptive events." (This does not mean that there will be four less events; it means that the predicted number of events is -4.0.) Furthermore, estimates will often be very imprecise, making many empirical analyses inconclusive. In fact, since the standard errors and test statistics are themselves biased, there will usually be no indication of this imprecision. Unfortunately, these serious criticisms of the OLS model apply to most existing analyses of event count data in political science.

Poisson regression isn't ideal for every dataset of counts, because the Poisson distribution's mean and variance are defined as equal. When variance is greater than the mean, overdispersion results, and underdispersion is its opposite. These can be addressed with generalized alternatives presented by King (1989) using the negative binomial distribution. The UCLA Statistical Consulting Group (2007) offers a good overview of other alternatives for modeling zero-inflation and random effects.
If your dataset is a time-series, you probably have many more analyses to consider than these alone.
References
- King, G. (1988). Statistical models for political science event counts: Bias in conventional procedures and evidence for the exponential Poisson regression model. American Journal of Political Science, 32(3), 838–863. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.214.8814&rep=rep1&type=pdf.
- King, G. (1989). Variance specification in event count models: From restrictive assumptions to a generalized estimator. American Journal of Political Science, 33(3), 762–784. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.214.8157&rep=rep1&type=pdf.
- Statistical Consulting Group. (2007, April).  Regression models with count data. UCLA. Retrieved from http://www.ats.ucla.edu/stat/stata/seminars/count_presentation/count.htm.
