Estimation of structural mean breaks for long-memory data sets

In long-memory data sets such as the realized volatilities of financial assets, a sequential test is developed for the detection of structural mean breaks. The long memory, if any, is adjusted by fitting an HAR (heterogeneous autoregressive) model to the data sets and taking the residuals. Our test consists of applying the sequential test of Bai and Perron [Estimating and testing linear models with multiple structural changes. Econometrica. 1998;66:47–78] to the residuals. The large-sample validity of the proposed test is investigated in terms of the consistency of the estimated number of breaks and the asymptotic null distribution of the proposed test. A finite-sample Monte-Carlo experiment reveals that the proposed test tends to produce an unbiased break time estimate, while the usual sequential test of Bai and Perron tends to produce biased break times in the case of long memory. The experiment also reveals that the proposed test has a more stable size than the Bai and Perron test. The proposed test is applied to two realized volatility data sets of the S&P index and the Korea won-US dollar exchange rate for the past 7 years and finds 2 or 3 breaks, while the Bai and Perron test finds 8 or more breaks.     

Testing and dating structural changes in copula-based dependence measures

This paper is concerned with testing and dating structural breaks in the dependence structure of multivariate time series. We consider a cumulative sum (CUSUM) type test for constant copula-based dependence measures, such as Spearman''s rank correlation and quantile dependencies. The asymptotic null distribution is not known in closed form and critical values are estimated by an i.i.d. bootstrap procedure. We analyze size and power properties in a simulation study under different dependence measure settings, such as skewed and fat-tailed distributions. To date breakpoints and to decide whether two estimated break locations belong to the same break event, we propose a pivot confidence interval procedure. Finally, we apply the test to the historical data of 10 large financial firms during the last financial crisis from 2002 to mid-2013.     

Sparse Change-point HAR Models for Realized Variance

Change-point time series specifications constitute flexible models that capture unknown structural changes by allowing for switches in the model parameters. Nevertheless most models suffer from an over-parametrization issue since typically only one latent state variable drives the switches in all parameters. This implies that all parameters have to change when a break happens. To gauge whether and where there are structural breaks in realized variance, we introduce the sparse change-point HAR model. The approach controls for model parsimony by limiting the number of parameters which evolve from one regime to another. Sparsity is achieved thanks to employing a nonstandard shrinkage prior distribution. We derive a Gibbs sampler for inferring the parameters of this process. Simulation studies illustrate the excellent performance of the sampler. Relying on this new framework, we study the stability of the HAR model using realized variance series of several major international indices between January 2000 and August 2015.     

Asymmetric Volatility Models with Structural Breaks

This article develops an asymmetric volatility model that takes into consideration the structural breaks in the volatility process. Break points and other parameters of the model are estimated using MCMC and Gibbs sampling techniques. Models with different number of break points are compared using the Bayes factor and BIC. We provide a formal test and hence a new procedure for Bayes factor computation to choose between models with different number of breaks. The procedure is illustrated using simulated as well as real data sets. The analysis shows an evidence to the fact that the financial crisis in the market from the first week of September 2008 has caused a significant break in the structure of the return series of two major NYSE indices viz., S & P 500 and Dow Jones. Analysis of the USD/EURO exchange rate data also shows an evidence of structural break around the same time.     

Realized Volatility and Long Memory: An Overview

The challenge of modeling, estimating, testing, and forecasting financial volatility is both intellectually worthwhile and also central to the successful analysis of financial returns and optimal investment strategies. In each of the three primary areas of volatility modeling, namely, conditional (or generalized autoregressive conditional heteroskedasticity) volatility, stochastic volatility and realized volatility (RV), numerous univariate volatility models of individual financial assets and multivariate volatility models of portfolios of assets have been established. This special issue has eleven innovative articles, eight of which are focused directly on RV and three on long memory, while two are concerned with both RV and long memory.     

Realized Volatility and Long Memory: An Overview

The challenge of modeling, estimating, testing, and forecasting financial volatility is both intellectually worthwhile and also central to the successful analysis of financial returns and optimal investment strategies. In each of the three primary areas of volatility modeling, namely, conditional (or generalized autoregressive conditional heteroskedasticity) volatility, stochastic volatility and realized volatility (RV), numerous univariate volatility models of individual financial assets and multivariate volatility models of portfolios of assets have been established. This special issue has eleven innovative articles, eight of which are focused directly on RV and three on long memory, while two are concerned with both RV and long memory.     

Comparison of the finite mixture of ARMA-GARCH,back propagation neural networks and support-vector machines in forecasting financial returns

The use of GARCH type models and computational-intelligence-based techniques for forecasting financial time series has been proved extremely successful in recent times. In this article, we apply the finite mixture of ARMA-GARCH model instead of AR or ARMA models to compare with the standard BP and SVM in forecasting financial time series (daily stock market index returns and exchange rate returns). We do not apply the pure GARCH model as the finite mixture of the ARMA-GARCH model outperforms the pure GARCH model. These models are evaluated on five performance metrics or criteria. Our experiment shows that the SVM model outperforms both the finite mixture of ARMA-GARCH and BP models in deviation performance criteria. In direction performance criteria, the finite mixture of ARMA-GARCH model performs better. The memory property of these forecasting techniques is also examined using the behavior of forecasted values vis-à-vis the original values. Only the SVM model shows long memory property in forecasting financial returns.     

On- and offline detection of structural breaks in thermal spraying processes

We investigate and develop methods for structural break detection, considering time series from thermal spraying process monitoring. Since engineers induce technical malfunctions during the processes, the time series exhibit structural breaks at known time points, giving us valuable information to conduct the investigations. First, we consider a recently developed robust online (also real-time) filtering (i.e. smoothing) procedure that comprises a test for local linearity. This test rejects when jumps and trend changes are present, so that it can also be useful to detect such structural breaks online. Second, based on the filtering procedure we develop a robust method for the online detection of ongoing trends. We investigate these two methods as to the online detection of structural breaks by simulations and applications to the time series from the manipulated spraying processes. Third, we consider a recently developed fluctuation test for constant variances that can be applied offline, i.e. after the whole time series has been observed, to control the spraying results. Since this test is not reliable when jumps are present in the time series, we suggest data transformation based on filtering and demonstrate that this transformation makes the test applicable.     

Nonlinearity,Breaks, and Long-Range Dependence in Time-Series Models

We study the simultaneous occurrence of long memory and nonlinear effects, such as parameter changes and threshold effects, in time series models and apply our modeling framework to daily realized measures of integrated variance. We develop asymptotic theory for parameter estimation and propose two model-building procedures. The methodology is applied to stocks of the Dow Jones Industrial Average during the period 2000 to 2009. We find strong evidence of nonlinear effects in financial volatility. An out-of-sample analysis shows that modeling these effects can improve forecast performance. Supplementary materials for this article are available online.     

Integer autoregressive models with structural breaks

Even though integer-valued time series are common in practice, the methods for their analysis have been developed only in recent past. Several models for stationary processes with discrete marginal distributions have been proposed in the literature. Such processes assume the parameters of the model to remain constant throughout the time period. However, this need not be true in practice. In this paper, we introduce non-stationary integer-valued autoregressive (INAR) models with structural breaks to model a situation, where the parameters of the INAR process do not remain constant over time. Such models are useful while modelling count data time series with structural breaks. The Bayesian and Markov Chain Monte Carlo (MCMC) procedures for the estimation of the parameters and break points of such models are discussed. We illustrate the model and estimation procedure with the help of a simulation study. The proposed model is applied to the two real biometrical data sets.     

Nonparametric monitoring of financial time series by jump-preserving control charts

Since structural changes in a possibly transformed financial time series may contain important information for investors and analysts, we consider the following problem of sequential econometrics. For a given time series we aim at detecting the first change-point where a jump of size a occurs, i.e., the mean changes from, say, m ₀to m ₀+ a and returns to m ₀after a possibly short period s. To address this problem, we study a Shewhart-type control chart based on a sequential version of the sigma filter, which extends kernel smoothers by employing stochastic weights depending on the process history to detect jumps in the data more accurately than classical approaches. We study both theoretical properties and performance issues. Concerning the statistical properties, it is important to know whether the normed delay time of the considered control chart is bounded, at least asymptotically. Extending known results for linear statistics employing deterministic weighting schemes, we establish an upper bound which holds if the memory of the chart tends to infinity. The performance of the proposed control charts is studied by simulations. We confine ourselves to some special models which try to mimic important features of real time series. Our empirical results provide some evidence that jump-preserving weights are preferable under certain circumstances.     

A multivariate long-memory model with structural breaks

This paper introduces a multivariate long-memory model with structural breaks. In the proposed framework, the time series exhibits possibly fractional orders of integration which are allowed to be different in each subsample. The break date is endogenously determined using a procedure that minimizes the residual sum of squares (RSS). Monte Carlo experiments show that this method for detecting breaks performs well in large samples. As an illustration, we estimate a trivariate VAR including prices, employment and GDP in both the US and Mexico. For the subsample preceding the break, our findings are similar to those of earlier studies based on a standard VAR approach in both the countries, such that the variables exhibit integer degrees of integration. On the contrary, the series is found to be fractionally integrated after the break, with the fractional differencing parameters being higher than one in the case of Mexico.     

The Volatility of Realized Volatility

In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and predicting (daily) volatility. In this article, we show that the residuals of commonly used time-series models for realized volatility and logarithmic realized variance exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance for modeling and forecasting realized volatility. In an empirical application for S&P 500 index futures we show that allowing for time-varying volatility of realized volatility and logarithmic realized variance substantially improves the fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.     

The Volatility of Realized Volatility

In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and predicting (daily) volatility. In this article, we show that the residuals of commonly used time-series models for realized volatility and logarithmic realized variance exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance for modeling and forecasting realized volatility. In an empirical application for S&P 500 index futures we show that allowing for time-varying volatility of realized volatility and logarithmic realized variance substantially improves the fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.     

Fractionally integrated GARCH model with tempered stable distribution: a simulation study

With the growing availability of high-frequency data, long memory has become a popular topic in finance research. Fractionally Integrated GARCH (FIGARCH) model is a standard approach to study the long memory of financial volatility. The original specification of FIGARCH model is developed using Normal distribution, which cannot accommodate fat-tailed properties commonly existing in financial time series. Traditionally, the Student-t distribution and General Error Distribution (GED) are used instead to solve that problem. However, a recent study points out that the Student-t lacks stability. Instead, the Stable distribution is introduced. The issue of this distribution is that its second moment does not exist. To overcome this new problem, the tempered stable distribution, which retains most attractive characteristics of the Stable distribution and has defined moments, is a natural candidate. In this paper, we describe the estimation procedure of the FIGARCH model with tempered stable distribution and conduct a series of simulation studies to demonstrate that it consistently outperforms FIGARCH models with the Normal, Student-t and GED distributions. An empirical evidence of the S&P 500 hourly return is also provided with robust results. Therefore, we argue that the tempered stable distribution could be a widely useful tool for modelling the high-frequency financial volatility in general contexts with a FIGARCH-type specification.     

Wavelet semi-parametric inference for long memory in volatility in the presence of a trend

Risk of investing in a financial asset is quantified by functionals of squared returns. Discrete time stochastic volatility (SV) models impose a convenient and practically relevant time series dependence structure on the log-squared returns. Different long-term risk characteristics are postulated by short-memory SV and long-memory SV models. It is therefore important to test which of these two alternatives is suitable for a specific asset. Most standard tests are confounded by deterministic trends. This paper introduces a new, wavelet-based, test of the null hypothesis of short versus long memory in volatility which is robust to deterministic trends. In finite samples, the test performs better than currently available tests which are based on the Fourier transform.     

我国通货膨胀结构突变及不确定性检验

 我们利用GARCH (1, 1) 模型对我国通货膨胀率动态过程中的结构转变点进行了样本内及样本外检验,进而对通货膨胀不确定性进行测度。研究发现,我国通货膨胀率序列在1983年1月至2008年5月之间存在一个显著的结构转变,结构转变点发生在1996年1月,这与我国在1996年成功实现经济“软着陆”的事实相一致。基于两个基准模型和五个比较模型在不同预测水平下对样本外数据进行预测所得结果表明,五个比较模型在大多数情况下能够获得小于两个基准模型的均值损失。此外,我们使用多个模型进行联合预测,发现联合预测的结果具有一定的代表性。     

Continuous Time Wishart Process for Stochastic Risk

Risks are usually represented and measured by volatility-covolatility matrices. Wishart processes are models for a dynamic analysis of multivariate risk and describe the evolution of stochastic volatility-covolatility matrices, constrained to be symmetric positive definite. The autoregressive Wishart process (WAR) is the multivariate extension of the Cox, Ingersoll, Ross (CIR) process introduced for scalar stochastic volatility. As a CIR process it allows for closed-form solutions for a number of financial problems, such as term structure of T-bonds and corporate bonds, derivative pricing in a multivariate stochastic volatility model, and the structural model for credit risk. Moreover, the Wishart dynamics are very flexible and are serious competitors for less structural multivariate ARCH models.     

Bayesian inference of multiple structural change models with asymmetric GARCH errors

Structural change in any time series is practically unavoidable, and thus correctly detecting breakpoints plays a pivotal role in statistical modelling. This research considers segmented autoregressive models with exogenous variables and asymmetric GARCH errors, GJR-GARCH and exponential-GARCH specifications, which utilize the leverage phenomenon to demonstrate asymmetry in response to positive and negative shocks. The proposed models incorporate skew Student-t distribution and prove the advantages of the fat-tailed skew Student-t distribution versus other distributions when structural changes appear in financial time series. We employ Bayesian Markov Chain Monte Carlo methods in order to make inferences about the locations of structural change points and model parameters and utilize deviance information criterion to determine the optimal number of breakpoints via a sequential approach. Our models can accurately detect the number and locations of structural change points in simulation studies. For real data analysis, we examine the impacts of daily gold returns and VIX on S&P 500 returns during 2007–2019. The proposed methods are able to integrate structural changes through the model parameters and to capture the variability of a financial market more efficiently.

     

Continuous Time Wishart Process for Stochastic Risk

Risks are usually represented and measured by volatility–covolatility matrices. Wishart processes are models for a dynamic analysis of multivariate risk and describe the evolution of stochastic volatility–covolatility matrices, constrained to be symmetric positive definite. The autoregressive Wishart process (WAR) is the multivariate extension of the Cox, Ingersoll, Ross (CIR) process introduced for scalar stochastic volatility. As a CIR process it allows for closed-form solutions for a number of financial problems, such as term structure of T-bonds and corporate bonds, derivative pricing in a multivariate stochastic volatility model, and the structural model for credit risk. Moreover, the Wishart dynamics are very flexible and are serious competitors for less structural multivariate ARCH models.