Numbers Count

Numbers Count

Autocorrelation is the cross-correlation of a datum with itself. The kernel estimation method is a nonparametric procedure for testing economic models.

The two preceding sentences make little sense unless understood in the bigger context.

Statistical tools have been of considerable help to the economics, finance, business and accounting industries. A solid grounding in derivatives and mathematical notation is a must if one wants to work through countless proofs and demonstrations ubiquitous in econometric literature.

In mathematics, an asymptotic function portrayed graphically looks like a normal distribution bell curve with tails that never touch the horizon. Some definitions lists include that financial analysis models can be multivariate and univariate. Also, the martingale is a mathematical property used in financial modeling.

Financial forecasts are a complex task to say the least. Bollerslev (2001) shows that financial time series analysis is further complicated with market volatility. Through time, price changes follow market activity, clouding forecasts further.

Building on realized power variation, Barndorff-Nielsen & Shephard (2003) introduced the concept of realized bipower variation. Is bipower variation robust to jumps? The authors demonstrate that under certain circumstances, it can accurately predict integrated variance even with jumps.

Numbers count. Photo by Elena

Most undergraduate business or commerce programs have required mathematics courses as minimum conditions for entry. The mathematical background program is usually Linear Algebra and Calculus I and II, or any combination thereof. The prerequisites make perfect sense. Lacking a grasp on such foundations as the compound Poisson process and normal inverse Gaussian distribution, at least in the case of financial econometrics, the material would be all but impossible to comprehend. Nonetheless, the GraphPad Software Website provides an online calculator enabling computation of Binomial, Gaussian and Poisson probabilities.

Skewness refers to a situation in statistical analysis where the data group towards one side. Distributions can be normal, left-skewed or right-skewed. While skewness focuses on tails, kurtosis measures the peaks of the distribution.

Another statistical predictor has to do with least squares. According to the least squares estimation – respecting certain assumptions – determined model parameters would be good estimates of the parameters of the mechanism that brought forth the sample.

A financial econometrician wants to find the joint conditional density, to estimate expected return of market portfolios. Engle (2001) potential multivariate extensions to techniques estimating conditional densities.

The prevalence of subdivisions and overlapping of academic fields makes it somewhat harder to pin point the exact concepts that apply to financial econometrics. Still, it would be difficult to imagine this branch without mentioning these key ideas. Hopefully, the above has introduced the theoretical framework of the subject matter and related branches of learning such as mathematical finance.

References:

    Barndorff-Nielsen, O. E. & Shephard, N. (2003). Power and bipower variation with stochastic volatility and jumps. Working paper series No.152. CAF: Centre for Analytical Finance. University of Aarhus – Aarhus School of Business.

    Bollerslev, T. (2001). Financial econometrics: Past developments and future challenges. Journal of Econometrics, 100 (1): 41-51.

    Engle, R. (2001). Financial econometrics – A new discipline with new methods. Journal of Econometrics, 100 (1): 53-56.

    Raible, S. (1998). Levy processes in finance: Theory, numerics, and empirical facts. PhD Thesis. Mathematics Faculty, Freiburg University, Freiburg.