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56
Generalized Autoregressive Conditional Heteroskedasticity
 JOURNAL OF ECONOMETRICS
, 1986
"... A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametri ..."
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Cited by 1023 (18 self)
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A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.
Chaos and Nonlinear Dynamics: Application to Financial Markets
 Journal of Finance
, 1991
"... After the stock market crash of October 19, 1987, interest in nonlinear dynamics, especially deterministic chaotic dynamics, has increased in both the financial press and the academic literature. This has come about because the frequency of large moves in stock markets is greater than would be expec ..."
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Cited by 106 (3 self)
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After the stock market crash of October 19, 1987, interest in nonlinear dynamics, especially deterministic chaotic dynamics, has increased in both the financial press and the academic literature. This has come about because the frequency of large moves in stock markets is greater than would be expected
Moment and memory properties of linear conditional heteroscedasticity models
, 2001
"... Keywords: ARCH(∞), FIGARCH, hyperbolic lag, near epoch dependence. ..."
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Cited by 22 (2 self)
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Keywords: ARCH(∞), FIGARCH, hyperbolic lag, near epoch dependence.
Detecting Nonlinearity in Data with Long Coherence Times
, 1992
"... this article, we will describe (yet) another source of difficulty that arises in the analysis of time series data. The particular problem of detecting nonlinear structure  either by comparison of the data to linear surrogate data, or by comparing linear and nonlinear predictors  is seen to be ..."
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Cited by 20 (2 self)
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this article, we will describe (yet) another source of difficulty that arises in the analysis of time series data. The particular problem of detecting nonlinear structure  either by comparison of the data to linear surrogate data, or by comparing linear and nonlinear predictors  is seen to be complicated when the data exhibits long coherence times. In this section we define some terms and discuss linear modeling of time series. Section 2 describes the method of surrogate data, and compares two approaches to generating surrogate data. We find that both have difficulties trying to mimic data with long coherence time. We illustrate these problems with real and computergenerated time series in Section 3, including the time series E.dat from the the SFI competition. In the last section, we discuss what it is about the analysis or the data that is problematic.
Don't Bleach Chaotic Data
, 1993
"... this paper, that observation is extended. Even when the bleaching is constrained to relatively low order (by the Akaike criterion, for instance), and even for tasks other than detecting nonlinear structure, we find that the effect of bleaching on chaotic data can be detrimental. On the other hand, b ..."
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Cited by 11 (1 self)
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this paper, that observation is extended. Even when the bleaching is constrained to relatively low order (by the Akaike criterion, for instance), and even for tasks other than detecting nonlinear structure, we find that the effect of bleaching on chaotic data can be detrimental. On the other hand, bleaching
Modelling multivariate volatilities via conditionally uncorrelated components
 Journal of the Royal Statistical Society, Series B
, 2008
"... We propose to model multivariate volatility processes based on the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrixvalued processes. It is flexible in the sense that we may fit each CUC with any appropriate univariate volatil ..."
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Cited by 10 (2 self)
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We propose to model multivariate volatility processes based on the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrixvalued processes. It is flexible in the sense that we may fit each CUC with any appropriate univariate volatility model. Computationally it splits one highdimensional optimization problem into several lowerdimensional subproblems. Consistency for the estimated CUCs has been established. A bootstrap test is proposed for testing the existence of CUCs. The proposed methodology is illustrated with both simulated and real data sets. Key words: dimension reduction, extended GARCH(1,1), financial returns, multivariate volatility, portfolio volatility, time series. Partially supported by an EPSRC research grant and by NSF grant DMS0355179.
352� “Forecasting inflation with thick models and neural networks” by
, 2004
"... In 2004 all publications will carry a motif taken from the €100 banknote. This paper can be downloaded without charge from ..."
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Cited by 9 (0 self)
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In 2004 all publications will carry a motif taken from the €100 banknote. This paper can be downloaded without charge from
Testing for ARCH in the Presence of Additive Outliers
, 1996
"... In this paper we investigate the properties of the Lagrange Multiplier (LM) test for autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) in the presence of additive outliers (AO's). We show analytically that both the asymptotic size and power are adversely affected if A ..."
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Cited by 9 (0 self)
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In this paper we investigate the properties of the Lagrange Multiplier (LM) test for autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) in the presence of additive outliers (AO's). We show analytically that both the asymptotic size and power are adversely affected if AO's are neglected: the test rejects the null hypothesis of homoskedasticity too often when it is in fact true, while the test has difficulty detecting genuine GARCH effects. Several Monte Carlo experiments show that these phenomena occur in small samples as well. We design and implement a robust test, which has better size and power properties than the conventional test in the presence of AO's. Applications to the French industrial production series and weekly returns of the Spanish peseta/US dollar exchange rate reveal that, sometimes, apparent GARCH effects may be due to only a small number of outliers and, conversely, that genuine GARCH effects can be masked by outliers. Keywords: Genera...
A Model of Fractional Cointegration, and Tests Cointegration Using the Bootstrap
 Journal of Econometrics
, 2001
"... The paper proposes a framework for modelling cointegration in fractionally integrated processes, and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap. In these procedures, ARFIMA models are fitted to the data, and the estimates used to simu ..."
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Cited by 9 (5 self)
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The paper proposes a framework for modelling cointegration in fractionally integrated processes, and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap. In these procedures, ARFIMA models are fitted to the data, and the estimates used to simulate the null hypothesis of noncointegration in a vector autoregressive modelling framework. The simulations are used to estimate pvalues for alternative regressionbased test statistics, including the F goodnessoffit statistic, the DurbinWatson statistic and estimates of the residual d. The bootstrap distributions are economical to compute, being conditioned on the actual sample values of all but the dependent variable in the regression. The procedures are easily adapted to test stronger null hypotheses, such as statistical independence. The tests are not in general asymptotically pivotal, but implemented by the bootstrap, are shown to be consistent against alternatives with both stationary and nonstationary cointegrating residuals. As an example, the tests are applied to the series for UK consumption and disposable income. The power properties of the tests are studied by simulations of artificial cointegrating relationships based on the sample data. The F test performs better in these experiments than the residualbased tests, although the DurbinWatson in turn dominates the test based on the residual d.
Generating Schemes for Long Memory Processes: Regimes, Aggregation and Linearity
, 2004
"... This paper analyses a class of nonlinear time series models exhibiting long memory. These processes exhibit short memory fluctuations around a local mean (regime) which switches randomly such that the durations of the regimes follow a power law. We show that if a large number of independent copies o ..."
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Cited by 8 (1 self)
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This paper analyses a class of nonlinear time series models exhibiting long memory. These processes exhibit short memory fluctuations around a local mean (regime) which switches randomly such that the durations of the regimes follow a power law. We show that if a large number of independent copies of such a process are aggregated, the resulting processes are Gaussian, have a linear representation, and converge after normalisation to fractional Brownian motion. Alternatively, an aggregation scheme with Gaussian common components can yield the same result. However, a nonaggregated regime process is shown to converge to a Levy motion with infinite variance, suitably normalised, emphasising the fact that time aggregation alone fails to yield a FCLT. Two cases arise, a stationary case in which the partial sums of the process converge, and a nonstationary case in which the process itself converges, the Hurst coefficient falling in the ranges (1/2, 1) and (0, 1/2) respectively. We comment on the relevance of our results to the interpretation of the long memory phenomenon, and also report some simulations aimed to throw light on the problem of discriminating between the models in practice.