Yipeng ZhuangDong LiPhilip L. H. YuWai Keung Li...
599-622页
查看更多>>摘要：There has been growing interest in extending the popular threshold time series models to include a buffer zone for regime transition. However, almost all attention has been on buffered autoregressive models. Note that the classical moving average (MA) model plays an equally important role as the autoregressive model in classical time series analysis. It is therefore natural to extend our investigation to the buffered MA (BMA) model. We focus on the first‐order BMA model while extending to more general MA model should be direct in principle. The proposed model shares the piecewise linear structure of the threshold model, but has a more flexible regime switching mechanism. Its probabilistic structure is studied to some extent. A nonlinear least squares estimation procedure is proposed. Under some standard regularity conditions, the estimator is strongly consistent and the estimator of the coefficients is asymptotically normal when the parameter of the boundary of the buffer zone is known. A portmanteau goodness‐of‐fit test is derived. Simulation results and empirical examples are carried out and lend further support to the usefulness of the BMA model and the asymptotic results.
查看更多>>摘要：We introduce a new methodology to conduct simultaneous inference of the non‐parametric component in partially linear time series regression models where the non‐parametric part is a multi‐variate unknown function. In particular, we construct a simultaneous confidence region (SCR) for the multi‐variate function by extending the high‐dimensional Gaussian approximation to dependent processes with continuous index sets. Our results allow for a more general dependence structure compared to previous works and are widely applicable to a variety of linear and non‐linear autoregressive processes. We demonstrate the validity of our proposed methodology by examining the finite‐sample performance in the simulation study. Finally, an application in time series, the forward premium regression, is presented, where we construct the SCR for the foreign exchange risk premium from the exchange rate and macroeconomic data.
查看更多>>摘要：The memory parameter is usually assumed to be constant in traditional long memory time series. We relax this restriction by considering the memory a time‐varying function that depends on a finite number of parameters. A time‐varying Local Whittle estimator of these parameters, and hence of the memory function, is proposed. Its consistency and asymptotic normality are shown for locally stationary and locally non‐stationary long memory processes, where the spectral behaviour is restricted only at frequencies close to the origin. Its good finite sample performance is shown in a Monte Carlo exercise and in two empirical applications, highlighting its benefits over the fully parametric Whittle estimator proposed by Palma and Olea (2010). Standard inference techniques for the constancy of the memory are also proposed based on this estimator.
查看更多>>摘要：The problem of estimating the spectral density matrix f(w) of a multi‐variate time series is revisited with special focus on the frequencies w=0 and w=π. Recognizing that the entries of the spectral density matrix at these two boundary points are real‐valued, we propose a new estimator constructed from a local polynomial regression of the real portion of the multi‐variate periodogram. The case w=0 is of particular importance, since f(0) is associated with the large‐sample covariance matrix of the sample mean; hence, estimating f(0) is crucial to conduct any sort of statistical inference on the mean. We explore the properties of the local polynomial estimator through theory and simulations, and discuss an application to inflation and unemployment.
查看更多>>摘要：In this article, we derive (local) orthogonality graphs for the popular continuous‐time state space models, including in particular multivariate continuous‐time ARMA (MCARMA) processes. In these (local) orthogonality graphs, vertices represent the components of the process, directed edges between the vertices indicate causal influences and undirected edges indicate contemporaneous correlations between the component processes. We present sufficient criteria for state space models to satisfy the assumptions of Fasen‐Hartmann and Schenk (2024a) so that the (local) orthogonality graphs are well‐defined and various Markov properties hold. Both directed and undirected edges in these graphs are characterised by orthogonal projections on well‐defined linear spaces. To compute these orthogonal projections, we use the unique controller canonical form of a state space model, which exists under mild assumptions, to recover the input process from the output process. We are then able to derive some alternative representations of the output process and its highest derivative. Finally, we apply these representations to calculate the necessary orthogonal projections, which culminate in the characterisations of the edges in the (local) orthogonality graph. These characterisations are given by the parameters of the controller canonical form and the covariance matrix of the driving Lévy process.
查看更多>>摘要：We provide a new estimation method for conditional moment models via the martingale difference divergence (MDD). Our MDD‐based estimation method is formed in the framework of a continuum of unconditional moment restrictions. Unlike the existing estimation methods in this framework, the MDD‐based estimation method adopts a non‐integrable weighting function, which could capture more information from unconditional moment restrictions than the integrable weighting function to enhance the estimation efficiency. Due to the nature of shift‐invariance in MDD, our MDD‐based estimation method can not identify the intercept parameters. To overcome this identification issue, we further provide a two‐step estimation procedure for the model with intercept parameters. Under regularity conditions, we establish the asymptotics of the proposed estimators, which are not only easy‐to‐implement with expectation‐based asymptotic variances, but also applicable to time series data with an unspecified form of conditional heteroskedasticity. Finally, we illustrate the usefulness of the proposed estimators by simulations and two real examples.
查看更多>>摘要：We in this article propose a novel non‐parametric estimator for the volatility function within a broad context that encompasses nonlinear time series models as a special case. The new estimator, built on the mode value, is designed to complement existing mean volatility measures to reveal distinct data features. We demonstrate that the suggested modal volatility estimator can be obtained asymptotically as well as if the conditional mean regression function were known, assuming observations are from a strictly stationary and absolutely regular process. Under mild regularity conditions, we establish that the asymptotic distributions of the resulting estimator align with those derived from independent observations, albeit with a slower convergence rate compared to non‐parametric mean regression. The theory and practice of bandwidth selection are discussed. Moreover, we put forward a variance reduction technique for the modal volatility estimator to attain asymptotic relative efficiency while maintaining the asymptotic bias unchanged. We numerically solve the modal regression model with the use of a modified modal‐expectation‐maximization algorithm. Monte Carlo simulations are conducted to assess the finite sample performance of the developed estimation procedure. Two real data analyses are presented to further illustrate the newly proposed model in practical applications. To potentially enhance the accuracy of the bias term, we in the end discuss the extension of the method to local exponential modal estimation. We showcase that the suggested exponential modal volatility estimator shares the same asymptotic variance as the non‐parametric modal volatility estimator but may exhibit a smaller bias.
查看更多>>摘要：We obtain a novel analytic expression of the likelihood for a stationary inverse gamma stochastic volatility (SV) model. This allows us to obtain the maximum likelihood estimator for this nonlinear non‐Gaussian state space model. Further, we obtain both the filtering and smoothing distributions for the inverse volatilities as mixtures of gammas, and therefore, we can provide the smoothed estimates of the volatility. We show that by integrating out the volatilities the model that we obtain has the resemblance of a GARCH in the sense that the formulas are similar, which simplifies computations significantly. The model allows for fat tails in the observed data. We provide empirical applications using exchange rates data for seven currencies and quarterly inflation data for four countries. We find that the empirical fit of our proposed model is overall better than alternative models for four countries currency data and for two countries inflation data.
查看更多>>摘要：This note presents insights on the Jordan structure of a matrix which are derived from an extension of the I(1) and I(2) conditions in Johansen (1996). It is first observed that these conditions not only characterize, as it is well known, the size (1 or 2) of the largest Jordan block in the Jordan form of the companion matrix but more generally the geometric multiplicities, the algebraic multiplicities and the whole Jordan structure for eigenvalues of index 1 or 2. In the context of the Granger representation theorem, this means that the Johansen rank conditions do more than determine the order of integration of the process. It is then shown that an extension of these conditions leads to the characterization of the Jordan structure of any matrix.
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Wiley