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Complex Systems in Finance and Econometrics pp 340–352Cite as

Financial Economics, Non-linear Time Series in

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Article Outline

Glossary

Definition of the Subject

Introduction

Basic Nonlinear Financial Time Series Models

Future Directions

Bibliography

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Abbreviations

Arbitrage:

The possibility of producing a riskless profit by exploiting price differences between identical or linked assets.

Market efficiency:

A market is called efficient when all available information is reflected accurately, instantly and fully in the prices of traded assets. Depending on the definition of the available information set, private, public or that contained in historical prices, market efficiency is considered as strong, semi‐strong or weak, respectively. The market price of an asset in an efficient market is an unbiased estimate of its true value. Systematic excess profits, which cannot be justified on the basis of the underlying risk, are not possible in such a market.

Martingale:

The term was originally used to describe a particular gambling strategy in which the stake is doubled following a losing bet. In probability theory it refers to a stochastic process that is a mathematical model of ‘fair play’. This has been one of the most widely assumed processes for financial prices. It implies that the best forecast for tomorrow's price is simply today's price or, in other words, that the expected difference between any two successive prices is zero. Assuming a positive (negative) expected difference leads to the more general and realistic class of submartingale (supermartingale) processes. The martingale process implies that price differences are serially uncorrelated and that univariate linear time series models of prices have no forecasting value. However, martingales do not preclude the potential usefulness of nonlinear models in predicting the evolution of higher moments, such as the variance. The efficient market hypothesis is often incorrectly equated to the so‐called random walk hypothesis, which roughly states that financial prices are martingales.

Option:

A call (put) option is a contractual agreement which gives the holder the right to buy (sell) a specified quantity of the underlying asset, within a specified period of time, at a price that is agreed when the contract is executed. Options are derivative assets since their value is based upon the variation in the underlying, which is typically the price of some asset such as a stock, commodity, bond, etc. Other basic types of derivatives include futures, forwards and swaps. An option is real, in contrast to financial, when the corresponding right refers to some business decision, such as the right to build a factory.

Portfolio theory:

The study of how resources should be optimally allocated between alternative investments on the basis of a given time investment horizon and a set of preferences.

Systematic risk:

Reflects the factors affecting all securities or firms in an economy. It cannot be reduced by diversification and it is also known as market risk. In the context of one of the most popular financial models, the Capital Asset Pricing Model (CAPM), systematic risk is measured by the beta coefficient.

Unsystematic risk:

This is the part of risk that is unique to a particular security or firm and can be reduced through diversification. This risk cannot be explained on the basis of fluctuations in the market as whole and it is also known as residual or idiosyncratic risk.

Volatility:

A measure of overall risk for an asset or portfolio which represents the sum of systematic and unsystematic risk. While several different approaches have been proposed for approximating this unobservable variable, the simplest one is based on the annualized standard deviation estimated using a historical sample of daily returns.

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Author information

Authors and Affiliations

  1. Department of Economics, Loughborough University, Loughborough, UK

    Terence C. Mills & Raphael N. Markellos

  2. Department of Management Science and Technology, Athens University of Economics and Business, Athens, Greece

    Raphael N. Markellos

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  1. Terence C. Mills
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Mills, T.C., Markellos, R.N. (2009). Financial Economics, Non-linear Time Series in. In: Meyers, R. (eds) Complex Systems in Finance and Econometrics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7701-4_19

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