11. Introduction: Definitions and Concepts

Financial markets can be regarded from various points of view. First of all there are economic theories which make assertions about security pricing. Different economic theories exist in different markets (currency, interest rates, stocks, derivatives, etc.). The well known examples include the purchasing power parity for exchange rates, interest rate term structure models, the capital asset pricing model (CAPM) and the Black-Scholes option pricing model. Most of these models are based on theoretical concepts which, for example, involve the formation of expectations, utility functions and risk preferences. Normally it is assumed that individuals in the economy act `rationally', have rational expectations and are risk averse. Under this situation prices and returns can be determined in equilibrium models (as, for example, the CAPM) which clear the markets, i.e., supply equals aggregate demand. A different Ansatz pursues the arbitrage theory (for example, the Black-Scholes model), which assumes that a riskless profit would be noticed immediately by market participants and be eliminated through adjustments in the price. Arbitrage theory and equilibrium theory are closely connected. The arbitrage theory can often get away with fewer assumptions, whereas the equilibrium theories reach more explicitly defined solutions for complex situations.

The classical econometric models are formulated with the economically interpreted parameters. One is interested in the following empirical questions:

  1. How well can a specific model describe a given set of data (cross section or time series)?
  2. Does the model help the market participants in meeting the relative size of assertions made on future developments?
  3. What do the empirical findings imply for the econometric model? Will it eventually have to be modified? Can suggestions actually be made which will influence the functioning and structural organization of the markets?
In order to handle these empirical questions, a statistical inquiry is needed. Since as a rule with financial market data the dynamic characteristics are the most important, we will concentrate mainly on the time series analysis. First of all, we will introduce the concepts of univariate analysis. Then we will move to the multivariate time series. The interdependence of financial items can be modelled explicitly as a system.

Certain terms, which are often used in time series analysis and in the analysis of financial time series, are introduced in a compact form. We will briefly define them in the next section.