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155
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 2290 (31 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 185 (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 63 (2 self)
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Keywords: ARCH(∞), FIGARCH, hyperbolic lag, near epoch dependence.
Testing for NonLinearity in Daily Sterling Exchange Rates
 Applied Financial Economics
, 1996
"... A number of tests for nonlinear dependence in time series are presented and implemented on a set of 10 daily sterling exchange rates covering the entire postBretton Ð Woods era until the present day. Irrefutable evidence of nonlinearity is shown in many of the series, but most of this dependence ..."
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Cited by 32 (1 self)
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A number of tests for nonlinear dependence in time series are presented and implemented on a set of 10 daily sterling exchange rates covering the entire postBretton Ð Woods era until the present day. Irrefutable evidence of nonlinearity is shown in many of the series, but most of this dependence can apparently be explained by reference to the GARCH family of models. It is suggested that the literature in this area has reached an impasse, with the presence of ARCH e ects clearly demonstrated in a large number of papers, but with the tests for nonlinearity which are currently available being unable to classify any additional nonlinear structure. Testing for nonlinear dependence has become an important area of research in ® nancial econometrics because of its profound implications for model adequacy, market e ciency, and predictability. If we ® nd evidence of nonlinearity
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 27 (7 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.
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 25 (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.
Testing for ARCH in the presence of additive outliers
 Journal of Applied Econometrics
, 1999
"... 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 aected ..."
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Cited by 24 (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 aected 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 diculty detecting genuine GARCH eects. 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 eects may be due to only a small number of outliers and, conversely, that genuine GARCH eects can be masked by outliers.
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 17 (5 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.
Generating scheme for long memory process : Regimes, Aggregation and linearity
 Journal of Econometrics
"... 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 16 (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. 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 ( 12, 1) and (0, 1 2) respectively. 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. 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. 1
doi:10.1111/j.14679892.2006.00519.x EFFECTS OF OUTLIERS ON THE IDENTIFICATION AND ESTIMATION OF GARCH MODELS 1
"... First Version received Abstract. This paper analyses how outliers affect the identification of conditional heteroscedasticity and the estimation of generalized autoregressive conditionally heteroscedastic (GARCH) models. First, we derive the asymptotic biases of the sample autocorrelations of square ..."
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Cited by 15 (4 self)
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First Version received Abstract. This paper analyses how outliers affect the identification of conditional heteroscedasticity and the estimation of generalized autoregressive conditionally heteroscedastic (GARCH) models. First, we derive the asymptotic biases of the sample autocorrelations of squared observations generated by stationary processes and show that the properties of some conditional homoscedasticity tests can be distorted. Second, we obtain the asymptotic and finite sample biases of the oridnary least square (OLS) estimator of ARCH(p) models. The finite sample results are extended to generalized least square (GLS), maximum likelihood (ML) and quasimaximum likelihood (QML) estimators of ARCH(p) and GARCH(1,1) models. Finally, we show that the estimated asymptotic standard deviations are biased estimates of the sample standard deviations.