# A CONDITIONALLY HETEROSKEDASTIC TIME SERIES MODEL FOR SPECULATIVE PRICES AND RATES OF RETURN

@article{Bollerslev1987ACH, title={A CONDITIONALLY HETEROSKEDASTIC TIME SERIES MODEL FOR SPECULATIVE PRICES AND RATES OF RETURN}, author={Tim Bollerslev}, journal={The Review of Economics and Statistics}, year={1987}, volume={69}, pages={542-547} }

The distribution of speculative price changes and rates of return data tend to be uncorrelated over time but characterized by volatile and tranquil periods. A simple time series model designed to capture this dependence is presented. The model is an extension of the Autoregressive Conditional Heteroskedastic (ARCH) and Generalized ARCH (GARCH) models obtained by allowing for conditionally t-distributed errors. The model can be derived as a simple subordinate stochastic process by including an… Expand

#### 2,559 Citations

Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model

- Economics
- 1990

A multivariate time series model with time varying conditional variances and covariances, but constant conditional correlations is proposed. In a multivariate regression framework, the model is… Expand

Prediction in dynamic models with time-dependent conditional variances

- Mathematics
- 1992

Abstract This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with… Expand

A conditionally heteroskedastic time series model for certain South African stock price returns

- Economics
- 2010

ABSTRACT The distributional properties of returns data have important implications for financial models and are of particular importance in risk-scenario simulation, volatility prediction and in the… Expand

Correlated ARCH (CorrARCH): Modelling the time-varying conditional correlation between financial asset returns

- Economics, Computer Science
- Eur. J. Oper. Res.
- 2002

A bivariate GARCH covariance structure is proposed in which conditional variances can follow any GARCH-type process, while conditional correlation is generated by an explicit discrete-time stochastic process, the CorrARCH process. Expand

Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis

- Economics
- 2001

Daily returns of financial assets are frequently found to exhibit positive autocorrelation at lag 1. When specifying a linear AR(1) conditional mean, one may ask how this predictability affects… Expand

Autoregressive Conditional Heteroskedasticity Models and the Dynamic Structure of the Athens Stock Exchange

- Economics
- 2006

Autoregressive Conditional Heteroskedasticity (ARCH) models have been applied in modeling the relation between conditional variance and asset risk premium. The most important theoretical regularities… Expand

Modelling Dynamic Conditional Correlations in Spot , Forward and Futures Returns

- 2004

Volatility (or risk) is a key variable in many areas of finance, and there are many applications that require an accurate estimate of volatility. One important application is in designing optimal… Expand

Testing the CAPM with Time-Varying Risks and Returns

- Economics
- 1991

This paper draws on Robert F. Engle's autoregressive conditionally heteroskedastic modeling strategy to formulate a conditional capital asset pricing model with time-varying risk and expected… Expand

The Message in Daily Exchange Rates

- Mathematics
- 1989

Formal testing procedures confirm the presence of a unit root in the autoregressive ploynomial of the univariate time series representation of daily exchange-rate data. the first differences of the… Expand

Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects

- Economics
- 1990

This paper provides empirical support for the notion that autoregressive conditional heteroskedasticity in daily stock return data reflects time dependence in the process generating information flow… Expand

#### References

SHOWING 1-10 OF 32 REFERENCES

Modelling the persistence of conditional variances

- Economics
- 1986

This paper will discuss the current research in building models of conditional variances using the Autoregressive Conditional Heteroskedastic (ARCH) and Generalized ARCH (GARCH) formulations. The… Expand

The Distribution of Common Stock Price Changes: An Application of Transactions Time and Subordinated Stochastic Models

- Economics
- 1977

The empirical distributions of price changes for speculative assets (e.g., common stocks, bonds, etc.) measured over calendar time yield a higher frequency of observations near the mean and at the… Expand

Evidence of Nonlinearity in Daily Stock Returns

- Economics
- 1985

This article applies a newly developed statistical technique to time series of daily rates of return of 15 common stocks. The technique involves estimating the bispectrum of the observed time series.… Expand

Testing the Martingale Hypothesis in the Deutschmark/US dollar Futures and Spot Markets

- Economics
- 1985

This paper tests the martingale hypothesis for daily data from the Deutschmark/US dollar futures and spot foreign exchange markets. Time-varying volatility of daily price changes is modelled as… Expand

A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices

- Economics
- 1973

S. Bochner's concept of a subordinate stochastic process is proposed as a model for speculative price series. A general class of finite-variance distributions for price changes is described, and a… Expand

Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation

- Economics
- 1982

Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional… Expand

Models of Stock Returns—A Comparison

- Economics
- 1984

In this paper a discrete mixture of normal distributions is proposed to explain the observed significant kurtosis (fat tails) and significant positive skewness in the distribution of daily rates of… Expand

The statistical properties of daily foreign exchange rates: 1974–1983

- Economics
- 1988

Abstract This paper examines the statistical properties of daily rates of change of five foreign currencies from 1974 to 1983. The main purpose is to discriminate between two competing explanations… Expand

The Distribution of Share Price Changes

- Economics
- 1972

This paper presents both theoretical and empirical evidence about a probability distribution which describes the behavior of share price changes. Osborne's Brownian motion theory of share price… Expand

Empirical Properties of Foreign Exchange Rates

- Economics
- 1978

This paper investigates the behavior of foreign exchange rates. Empirical tests indicate that the distribution of the underlying stochastic process for foreign exchange rate changes was stable… Expand