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1.
Ke. Zhu 《时间序列分析杂志》2013,34(2):230-237
This paper investigates the joint limiting distribution of the residual autocorrelation functions and the absolute residual autocorrelation functions of ARMA‐GARCH models. This leads a mixed portmanteau test for diagnostic checking of the ARMA‐GARCH model fitted by using the quasi‐maximum exponential likelihood estimation approach in Zhu and Ling (2011) . Simulation studies are carried out to examine our asymptotic theory, and assess the performance of this mixed test and other two portmanteau tests in Li and Li (2008) . A real example is given. 相似文献
2.
Zero crossing (ZC) statistic is the number of zero crossings observed in a time series. The expected value of the ZC specifies the first‐order autocorrelation of the processes. Hence, we can estimate the autocorrelation by using the ZC estimator. The asymptotic consistency and normality of the ZC estimator for scalar Gaussian processes are already discussed in 1980. In this article, first, we derive the joint asymptotic distribution of the ZC estimator for ellipsoidal processes. Next, we show the variance of the ZC estimator does not attain the Cramer–Rao lower bound (CRLB). However, it is shown that the ZC estimator has robustness when the process is contaminated by an outlier. In contrast with this, we observe that the quasi‐maximum likelihood estimator (QMLE) attains the CRLB. However, we can see that QMLE is sensitive for the outlier. 相似文献
3.
In this article, we consider the problem of testing for a copula parameter change based on the cusum test. We first handle this issue in i.i.d. samples and extend it to semiparametric copula ARMA‐GARCH models. We construct the cusum test based on pseudo maximum likelihood estimation of the copula parameter and derive its limiting null distribution. Simulation results are reported for illustration. 相似文献
4.
Jin Yu Fu;Jin Guan Lin;Guangying Liu;Hong Xia Hao; 《时间序列分析杂志》2024,45(4):613-638
This article introduces a novel approach that unifies two types of models: one is the continuous-time jump-diffusion used to model high-frequency market financial data, and the other is discrete-time GQARCH for modeling low-frequency financial data by embedding the discrete GQARCH structure with jumps in the instantaneous volatility process. This model is named GQARCH-Itô-Jumps model. Quasi-likelihood functions for the low-frequency GQARCH structure are developed for the parametric estimations. In the quasi-likelihood functions, for high-frequency financial data, the realized range-based estimations are adopted as the ‘observations’, rather than the realized return-based volatility estimators which entail the loss of intra-day information of the price movements. Meanwhile, the asymptotic properties are mainly established for the proposed estimators in the case of finite activity jumps. Moreover, simulation studies and some financial data are implemented to check the finite sample performance of the proposed methodology. 相似文献
5.
A two‐step approach for conditional value at risk estimation is considered. First, a generalized quasi‐maximum likelihood estimator is employed to estimate the volatility parameter, then the empirical quantile of the residuals serves to estimate the theoretical quantile of the innovations. When the instrumental density h of the generalized quasi‐maximum likelihood estimator is not the Gaussian density, both the estimations of the volatility and of the quantile are generally asymptotically biased. However, the two errors counterbalance and lead to a consistent estimator of the value at risk. We obtain the asymptotic behavior of this estimator and show how to choose optimally h. 相似文献
6.
Abstract. A conditionally heteroscedastic model, different from the more commonly used autoregressive moving average–generalized autoregressive conditionally heteroscedastic (ARMA‐GARCH) processes, is established and analysed here. The time‐dependent variance of innovations passing through an ARMA filter is conditioned on the lagged values of the generated process, rather than on the lagged innovations, and is defined to be asymptotically proportional to those past values. Designed this way, the model incorporates certain feedback from the modelled process, the innovation is no longer of GARCH type, and all moments of the modelled process are finite provided the same is true for the generating noise. The article gives the condition of stationarity, and proves consistency and asymptotic normality of the Gaussian quasi‐maximum likelihood estimator of the variance parameters, even though the estimated parameters of the linear filter contain an error. An analysis of six diurnal water discharge series observed along Rivers Danube and Tisza in Hungary demonstrates the usefulness of such a model. The effect of lagged river discharge turns out to be highly significant on the variance of innovations, and nonparametric estimation approves its approximate linearity. Simulations from the new model preserve well the probability distribution, the high quantiles, the tail behaviour and the high‐level clustering of the original series, further justifying model choice. 相似文献
7.
We put forward a new method to construct jump‐robust estimators of integrated volatility, namely realized information variation (RIV) and realized information power variation (RIPV). The ‘information’ here refers to the difference between two‐grid of ranges in high‐frequency intervals, which preserves continuous variation and eliminates jump variation asymptotically. We show that such kind of estimators have several superior statistical properties, i.e., the estimators are generally more efficient with sufficiently using the opening, high, low, closing (OHLC) data in high‐frequency intervals, and have faster jump convergence rate due to a new type of construction. For example, the RIV is much more efficient than the estimators that only use closing prices or ranges, and the RIPV has faster jump convergence rate at Op(1/n), while the other (multi)power‐based estimators are usually . We also extend our results to integrated quarticity and higher‐order variation estimation, and then propose the corresponding jump testing method. Simulation studies provide extensive evidence on the finite sample properties of our estimators and tests, comparing with alternative prevalent methods. Empirical results further demonstrate the practical relevance and advantages of our method. 相似文献
8.
A CARMA(p,q) process Y is a strictly stationary solution Y of the pth‐order formal stochastic differential equation a(D)Yt = b(D)DLt, where L is a two‐sided Lévy process, a(z) and b(z) are polynomials of degrees p and q respectively, with p > q, and D denotes differentiation with respect to t. Since estimation of the coefficients of a(z) and b(z) is frequently based on observations of the Δ‐sampled sequence , for some Δ > 0, it is crucial to understand the relation between Y and YΔ. If then YΔ is an ARMA sequence with coefficients depending on those of Y and the crucial problems for estimation are the determination of the coefficients of YΔ from those of Y (the sampling problem) and the determination of the coefficients of Y from those of YΔ (the embedding problem). In this article we consider both questions and use the results to determine the asymptotic distribution, as n→∞, with Δ fixed, of , where is the quasi‐maximum‐likelihood estimator of the vector of coefficients of a(z) and b(z), based on n consecutive observations of YΔ. 相似文献
9.
Recently, to account for low-frequency market dynamics, several volatility models, employing high-frequency financial data, have been developed. However, in financial markets, we often observe that financial volatility processes depend on economic states, so they have a state heterogeneous structure. In this article, to study state heterogeneous market dynamics based on high-frequency data, we introduce a novel volatility model based on a continuous Itô diffusion process whose intraday instantaneous volatility process evolves depending on the exogenous state variable, as well as its integrated volatility. We call it the state heterogeneous GARCH-Itô (SG-Itô) model. We suggest a quasi-likelihood estimation procedure with the realized volatility proxy and establish its asymptotic behaviors. Moreover, to test the low-frequency state heterogeneity, we develop a Wald test-type hypothesis testing procedure. The results of empirical studies suggest the existence of leverage, investor attention, market illiquidity, stock market comovement, and post-holiday effect in S&P 500 index volatility. 相似文献
10.
This article first studies the non‐stationarity of the first‐order double AR model, which is defined by the random recurrence equation , where γ0 > 0, α0 ≥ 0, and {ηt}is a sequence of i.i.d. symmetric random variables. It is shown that the double AR(1) model is explosive under the condition . Based on this, it is shown that the quasi‐maximum likelihood estimator of (φ0,α0) is consistent and asymptotically normal so that the unit root problem does not exist in the double AR(1) model. Simulation studies are carried out to assess the performance of the quasi‐maximum likelihood estimator in finite samples. 相似文献
11.
Regularity conditions are given for the consistency of the Poisson quasi‐maximum likelihood estimator of the conditional mean parameter of a count time series model. The asymptotic distribution of the estimator is studied when the parameter belongs to the interior of the parameter space and when it lies at the boundary. Tests for the significance of the parameters and for constant conditional mean are deduced. Applications to specific integer‐valued autoregressive (INAR) and integer‐valued generalized autoregressive conditional heteroscedasticity (INGARCH) models are considered. Numerical illustrations, Monte Carlo simulations and real data series are provided. 相似文献
12.
We discuss parametric quasi‐maximum likelihood estimation for quadratic autoregressive conditional heteroskedasticity (ARCH) process with long memory introduced in Doukhan emphet al. (2016) and Grublyt? and ?karnulis (2016) with conditional variance involving the square of inhomogeneous linear combination of observable sequence with square summable weights. The aforementioned model extends the quadratic ARCH model of Sentana ( 1995 ) and the linear ARCH model of Robinson ( 1991 ) to the case of strictly positive conditional variance. We prove consistency and asymptotic normality of the corresponding quasi‐maximum likelihood estimates, including the estimate of long memory parameter 0 < d < 1/2. A simulation study of empirical mean‐squared error is included. 相似文献
13.
Masanobu Taniguchi 《时间序列分析杂志》1984,5(1):37-51
Abstract. In this paper, we discuss the validity of the multivariate Edgeworth expansion of distribution functions of statistics which need not be standardized sums of independent and identically distributed vectors. We apply this result to statistics of time series. In particular, we shall give the asymptotic expansion of the distribution of the maximum likelihood estimator of a parameter of a circular autoregresive moving average process. 相似文献
14.
Abstract. In this article, we investigate an optimal property of the maximum likelihood estimator of Gaussian locally stationary processes by the second-order approximation. In the case where the model is correctly specified, it is shown that appropriate modifications of the maximum likelihood estimator for Gaussian locally stationary processes is second-order asymptotically efficient. We also discuss second-order robustness properties. 相似文献
15.
Autoregressive conditional heteroskedasticity (ARCH)() models nest a wide range of ARCH and generalized ARCH models including models with long memory in volatility. Existing work assumes the existence of second moments. However, the fractionally integrated generalized ARCH model, one version of a long memory in volatility model, does not have finite second moments and rarely satisfies the moment conditions of the existing literature. This article weakens the moment assumptions of a general ARCH( ) class of models and develops the theory for consistency and asymptotic normality of the quasi‐maximum likelihood estimator. 相似文献
16.
This article considers GARCH(1,1) models in which the time‐varying coefficients are functions of the realizations of an exogenous stochastic process. Time series generated by this model are in general nonstationary. Necessary and sufficient conditions are given for the existence of nonexplosive solutions, and for the existence of moments of these solutions. The asymptotic properties of the quasi‐maximum likelihood estimator are derived under mild assumptions. 相似文献
17.
Abstract. Maximum likelihood estimation for stationary autoregressive processes when the signal is subject to a moving-average sampling error is discussed. A modified maximum likelihood estimator is proposed. An algorithm for computing derivatives of the modified likelihood is suggested. Maximum likelihood estimators of the parameter vector are shown to be strongly consistent and to have a multivariate normal limiting distribution. A Monte Carlo simulation shows that the modified maximum likelihood estimator performs better than other available estimators. US current labour force data are analysed as an example. 相似文献
18.
This article derives the consistency and asymptotic distribution of the bias corrected least squares estimators (LSEs) of the regression parameters in linear regression models when covariates have measurement error (ME) and errors and covariates form mutually independent long memory moving average processes. In the structural ME linear regression model, the nature of the asymptotic distribution of suitably standardized bias corrected LSEs depends on the range of the values of where d X ,d u , and d ε are the LM parameters of the covariate, ME and regression error processes respectively. This limiting distribution is Gaussian when and non‐Gaussian in the case . In the former case some consistent estimators of the asymptotic variances of these estimators and a log(n)‐consistent estimator of an underlying LM parameter are also provided. They are useful in the construction of the large sample confidence intervals for regression parameters. The article also discusses the asymptotic distribution of these estimators in some functional ME linear regression models, where the unobservable covariate is non‐random. In these models, the limiting distribution of the bias corrected LSEs is always a Gaussian distribution determined by the range of the values of d ε ? d u . 相似文献
19.
The article reviews methods of inference for single and multiple change‐points in time series, when data are of retrospective (off‐line) type. The inferential methods reviewed for a single change‐point in time series include likelihood, Bayes, Bayes‐type and some relevant non‐parametric methods. Inference for multiple change‐points requires methods that can handle large data sets and can be implemented efficiently for estimating the number of change‐points as well as their locations. Our review in this important area focuses on some of the recent advances in this direction. Greater emphasis is placed on multivariate data while reviewing inferential methods for a single change‐point in time series. Throughout the article, more attention is paid to estimation of unknown change‐point(s) in time series, and this is especially true in the case of multiple change‐points. Some specific data sets for which change‐point modelling has been carried out in the literature are provided as illustrative examples under both single and multiple change‐point scenarios. 相似文献
20.
William Charky Kengne 《时间序列分析杂志》2012,33(3):503-518
We consider a process belonging to a large class of causal models including AR(∞), ARCH(∞), TARCH(∞),… processes. We assume that the model depends on a parameter and consider the problem of testing for change in the parameter. Two statistics and are constructed using quasi‐likelihood estimator of the parameter. Under the null hypothesis that there is no change, it is shown that each of these two statistics weakly converges to the supremum of the sum of the squares of independent Brownian bridges. Under the alternative of a change in the parameter, we show that the test statistic diverges to infinity. Some simulation results for AR(1), ARCH(1), GARCH(1,1) and TARCH(1) models are reported to show the applicability and the performance of our procedure with comparisons to some other approaches. 相似文献