Volatility forecasting of financial time series using wavelet based exponential generalized autoregressive conditional heteroscedasticity model

Abstract

An improved forecasting model by merging two different computational models in predicting future volatility was proposed. The model integrates wavelet and EGARCH model where the pre-processing activity based on wavelet transform is performed with de-noising technique to eliminate noise in observed signal. The denoised signal is then feed into EGARCH model to forecast the volatility. The predictive capability of the proposed model is compared with the existing EGARCH model. The results show that the hybrid model has increased the accuracy of forecasting future volatility.     

A Markov Model of Switching-Regime ARCH

In this article I present a new approach to model more realistically the variability of financial time series. I develop a Markov-ARCH model that incorporates the features of both Hamilton's switching-regime model and Engle's autoregressive conditional heteroscedasticity (ARCH) model to examine the issue of volatility persistence in the monthly excess returns of the three-month treasury bill. The issue can be resolved by taking into account occasional shifts in the asymptotic variance of the Markov-ARCH process that cause the spurious persistence of the volatility process. I identify two periods during which there is a regime shift, the 1974:2–1974:8 period associated with the oil shock and the 1979:9–1982:8 period associated with the Federal Reserve's policy change. The variance approached asymptotically in these two episodes is more than 10 times as high as the asymptotic variance for the remainder of the sample. I conclude that regime shifts have a greater impact on the properties of the data, and I cannot reject the null hypothesis of no ARCH effects within the regimes. As a consequence of the striking findings in this article, previous empirical results that adopt an ARCH approach in modeling monthly or lower frequency interest-rate dynamics are rendered questionable.     

中国农产品价格波动特征的实证研究——基于广义误差分布的ARCH类模型

近年来农产品价格波动频繁,结构特征明显,主要是因为受到生猪、棉花、大豆、胶脂果实类林产品和稻谷等农作物价格波动的影响.利用广义误差分布的ARCH类模型对主要农产品价格波动特征进行分析,结果表明:棉花价格没有显著的异方差效应;生猪、大豆和稻谷的价格波动具有显著的集聚性,但其市场并没有表现出高风险高回报的特征;稻谷价格波动具有显著的非对称性,但大豆和生猪的价格波动没有显著的非对称性.基于GED的ARCH类模型提高了模型的拟合效果,可以更好地分析中国主要农产品价格波动特征.     

Parameter Estimation Robust to Low-Frequency Contamination

We provide methods to robustly estimate the parameters of stationary ergodic short-memory time series models in the potential presence of additive low-frequency contamination. The types of contamination covered include level shifts (changes in mean) and monotone or smooth time trends, both of which have been shown to bias parameter estimates toward regions of persistence in a variety of contexts. The estimators presented here minimize trimmed frequency domain quasi-maximum likelihood (FDQML) objective functions without requiring specification of the low-frequency contaminating component. When proper sample size-dependent trimmings are used, the FDQML estimators are consistent and asymptotically normal, asymptotically eliminating the presence of any spurious persistence. These asymptotic results also hold in the absence of additive low-frequency contamination, enabling the practitioner to robustly estimate model parameters without prior knowledge of whether contamination is present. Popular time series models that fit into the framework of this article include autoregressive moving average (ARMA), stochastic volatility, generalized autoregressive conditional heteroscedasticity (GARCH), and autoregressive conditional heteroscedasticity (ARCH) models. We explore the finite sample properties of the trimmed FDQML estimators of the parameters of some of these models, providing practical guidance on trimming choice. Empirical estimation results suggest that a large portion of the apparent persistence in certain volatility time series may indeed be spurious. Supplementary materials for this article are available online.     

The Effects of Structural Breaks in ARCH and GARCH Parameters on Persistence of GARCH Models

We show that persistence of conditional volatility in large samples could be exaggerated by the existence of structural breaks in the ARCH and GARCH parameters. Our results suggest that extreme persistence frequently observed in index volatility does not necessarily indicate the same level of persistence over the sample period.     

Conditional correlation in asset return and GARCH intensity model

In an asset return series, there is a conditional asymmetric dependence between current return and past volatility depending on the current return’s sign. To take into account the conditional asymmetry, we introduce new models for asset return dynamics in which frequencies of the up and down movements of asset price have conditionally independent Poisson distributions with stochastic intensities. The intensities are assumed to be stochastic recurrence equations of the GARCH type to capture the volatility clustering and the leverage effect. We provide an important linkage between our model and existing GARCH, explain how to apply maximum likelihood estimation to determine the parameters in the intensity model and show empirical results with the S&P 500 index return series.     

On the invertibility of EGARCH(p,q)

Of the two most widely estimated univariate asymmetric conditional volatility models, the exponential GARCH (or EGARCH) specification is said to be able to capture asymmetry, which refers to the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which refers to the negative correlation between the returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-)maximum likelihood estimator (QMLE) of the EGARCH(p, q) parameters are not available under general conditions, but only for special cases under highly restrictive and unverifiable sufficient conditions, such as EGARCH(1,0) or EGARCH(1,1), and possibly only under simulation. A limitation in the development of asymptotic properties of the QMLE for the EGARCH(p, q) model is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this article that the EGARCH(p, q) model can be derived from a stochastic process, for which sufficient invertibility conditions can be stated simply and explicitly when the parameters respect a simple condition.¹¹Using the notation introduced in part 2, this refers to the cases where α ≥ |γ| or α ≤ ? |γ|. The first inequality is generally assumed in the literature related to the invertibility of EGARCH. This article provides (in the Appendix) an argument for the possible lack of invertibility when these conditions are not met. This will be useful in reinterpreting the existing properties of the QMLE of the EGARCH(p, q) parameters.     

基于AR—EGARCH的空气温度预测模型

天气衍生产品定价极其复杂,其中与温度相关的产品是目前研究热点,其定价核心在于温度变量的精确预测。传统AR-GARCH温度预测模型难以描述温度变量波动率的非对称性。基于此,构建了AR—EGARCH温度预测模型,它能够描述波动率的非对称性,更好地反映温度变化过程。对中国东部南北线六个较发达的城市进行实证研究,结果表明：六个城市的温度变化具有明显的非对称性,AR—EGARCH模型无论是拟合还是预测效果都较传统的AR-GARCH模型更优。     

股票市场波动预测的ARCH族模型选择

文章基于单步向前预测法,寻找对不同ARCH族波动预测模型进行选择的方法和评判标准,并以上证指数为例,根据有关评判标准,寻找适合我国股市的ARCH波动预测模型。     

GARCH-type forecasting models for volatility of stock market and MCS test

The prediction of time-changing volatility is an important task in the modeling of financial data. In the paper, a comprehensive analysis of the mean return and conditional variance of SSE380 index is performed to use GARCH, EGARCH and TGARCH models with Normal innovation and Student's t innovation. Conducting a bootstrap simulation study which shows the Model Confidence Set (MCS) captures the superior models across a range of significance levels. The experimental results show that, under various loss functions, the GARCH using Student's t innovation model is the best model for volatility predictions of SSE380 among the six models.     

Indirect estimation of randomized generalized autoregressive conditional heteroskedastic models

The class of generalized autoregressive conditional heteroskedastic (GARCH) models can be used to describe the volatility with less parameters than autoregressive conditional heteroskedastic (ARCH)-type models, their distributions are heavy-tailed, with time-dependent conditional variance, and are able to model clustering of volatility. Despite all these facts, the way that GARCH models are built imposes limits on the heaviness of the tails of their unconditional distribution. The class of randomized generalized autoregressive conditional heteroskedastic (R-GARCH) models includes the ARCH and GARCH models allowing the use of stable innovations. Estimation methods and empirical analysis of R-GARCH models are the focus of this work. We present the indirect inference method to estimate the R-GARCH models, some simulations and an empirical application.     

Kernel estimates of the mean and the volatility functions in a nonlinear autoregressive model with ARCH errors

In this paper, we deal with the nonparametric kernel estimation of the regression and volatility functions pertaining to nonlinear autoregressive model with ARCH errors. Under stationarity and ergodicity, we establish the strong uniform consistency and asymptotic normality of the estimators. Our results hold without any mixing condition and do not require the existence of marginal densities. Furthermore, rates of convergence are obtained.     

Term structure forecasting in affine framework with time-varying volatility

This study extends the affine Nelson–Siegel model by introducing the time-varying volatility component in the observation equation of yield curve, modeled as a standard EGARCH process. The model is illustrated in state-space framework and empirically compared to the standard affine and dynamic Nelson–Siegel model in terms of in-sample fit and out-of-sample forecast accuracy. The affine based extended model that accounts for time-varying volatility outpaces the other models for fitting the yield curve and produces relatively more accurate 6- and 12-month ahead forecasts, while the standard affine model comes with more precise forecasts for the very short forecast horizons. The study concludes that the standard and affine Nelson–Siegel models have higher forecasting capability than their counterpart EGARCH based models for the short forecast horizons, i.e., 1 month. The EGARCH based extended models have excellent performance for the medium and longer forecast horizons.     

Generalized EGARCH Random Effect Models Application to Financial Time Series

In this article, we propose a simple alternative model to analyze the volatility of the financial time series. In the applications, the performance of this model is compared with the performance of the GARCH type models. Using GARCH, EGARCH, and the proposed models, we analyze the time series of the Bovespa and Dow Jones Industrial Average indexes. In the applications we can see that the proposed models have good performance compared with the usual GARCH type model.     

开放式基金收益的EGARCH模型及其非对称性研究

通过对极少被研究的中国股票型、债券型和混合型开放式基金收益率的波动性进行了GARCH和EGARCH模型分析，结果表明：大部分基金存在非对称效应，并且由于基金条件波动序列的非平稳性，信息冲击曲线具有多样化特征，这为非平稳非线性模型的研究提供了新的方向；通过构建基金类型指数，对开放式基金整体波动性的研究发现，中国开放式基金收益率的波动存在ARCH效应，但不具有非对称性效应。     

A Stochastic Volatility Model With Conditional Skewness

We develop a discrete-time affine stochastic volatility model with time-varying conditional skewness (SVS). Importantly, we disentangle the dynamics of conditional volatility and conditional skewness in a coherent way. Our approach allows current asset returns to be asymmetric conditional on current factors and past information, which we term contemporaneous asymmetry. Conditional skewness is an explicit combination of the conditional leverage effect and contemporaneous asymmetry. We derive analytical formulas for various return moments that are used for generalized method of moments (GMM) estimation. Applying our approach to S&P500 index daily returns and option data, we show that one- and two-factor SVS models provide a better fit for both the historical and the risk-neutral distribution of returns, compared to existing affine generalized autoregressive conditional heteroscedasticity (GARCH), and stochastic volatility with jumps (SVJ) models. Our results are not due to an overparameterization of the model: the one-factor SVS models have the same number of parameters as their one-factor GARCH competitors and less than the SVJ benchmark.     

Finite nonparametric grach model for foreign exchange volatility

GARCH model has been commonly used to describe the volatility of foreign exchange returns, which typically depends on returns many lags before, While the GARCH model provides a simple geometric decaying structure for persistence in time, it restricts tiie impact of variables to Quadratic functions. A finite nonparametric GARCH model is proposed that allows the variables' impact to be a smooth function of any form. A direct local polynomial estimation method for this finite GARCH model is proposed based on results on proportional additive model, and is applied to the German Mark (DEM)/US Dollar (USD) daily returns data. Estimators uf both the decaying rate and the impact function are obtained. Diagnostics show satisfactory out-of-sampie prediction based on the proposed model, which helps to better understand the dynamics of foreign exchange volatility.     

A New Approach to Volatility Modeling: The Factorial Hidden Markov Volatility Model

A new process—the factorial hidden Markov volatility (FHMV) model—is proposed to model financial returns or realized variances. Its dynamics are driven by a latent volatility process specified as a product of three components: a Markov chain controlling volatility persistence, an independent discrete process capable of generating jumps in the volatility, and a predictable (data-driven) process capturing the leverage effect. An economic interpretation is attached to each one of these components. Moreover, the Markov chain and jump components allow volatility to switch abruptly between thousands of states, and the transition matrix of the model is structured to generate a high degree of volatility persistence. An empirical study on six financial time series shows that the FHMV process compares favorably to state-of-the-art volatility models in terms of in-sample fit and out-of-sample forecasting performance over time horizons ranging from 1 to 100 days. Supplementary materials for this article are available online.     

ARCH类模型在风险价值测度中的应用

将ARCH类模型用于计算风险价值，会在很大程度上提高风险价值测度的精度。通过理论分析和实证分析都表明，利用ARCH类模型计算金融资产的风险价值，可以体现其收益率的分布状态和波动性的影响作用，适应风险价值计算的需要，能够提高风险价值的计算精度。     

Do daily retail gasoline prices adjust asymmetrically?

This paper analyses adjustments in the Dutch retail gasoline prices. We estimate an error correction model on changes in the daily retail price for gasoline (taxes excluded) for the period 1996–2004, taking care of volatility clustering by estimating an EGARCH model. It turns out that the volatility process is asymmetrical: a positive shock to the retail price has a greater effect on the variance of the retail price than a negative shock. We conclude that the retail price and the spot price do not drift apart in the long run. However, there is a faster reaction to upward changes in spot prices than to downward changes in spot prices in the short run. This asymmetry starts 3 days after the change in the spot price and lasts for 4 days.