Financial Econometrics Research Articles

A neural network enhanced volatility component model

Volatility prediction, a central issue in financial econometrics, attracts increasing attention in the data science literature as advances in computational methods enable us to develop models with great forecasting precision. In this paper, we draw upon both strands of the literature and develop a novel two-component volatility model. The realized volatility is decomposed by a nonparametric filter into long- and short-run components, which are modeled by an artificial neural network and an ARMA process, respectively. We use intraday data on four major exchange rates and a Chinese stock index to construct daily realized volatility and perform out-of-sample evaluation of volatility forecasts generated by our model and well-established alternatives. Empirical results show that our model outperforms alternative models across all statistical metrics and over different forecasting horizons. Furthermore, volatility forecasts from our model offer economic gain to a mean-variance utility investor with higher portfolio returns and Sharpe ratio.

On long memory origins and forecast horizons

AbstractMost long memory forecasting studies assume that long memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference operator and assess the performance of the autoregressive fractionally integrated moving average (ARFIMA) model when forecasting series with long memory generated by nonfractional models. We find that ARFIMA models dominate in forecast performance regardless of the long memory generating mechanism and forecast horizon. Nonetheless, forecasting uncertainty at the shortest forecast horizon could make short memory models provide suitable forecast performance, particularly for smaller degrees of memory. Additionally, we analyze the forecasting performance of the heterogeneous autoregressive (HAR) model, which imposes restrictions on high‐order AR models. We find that the structure imposed by the HAR model produces better short and medium horizon forecasts than unconstrained AR models of the same order. Our results have implications for, among others, climate econometrics and financial econometrics models dealing with long memory series at different forecast horizons.

Semiparametric estimation and inference on the fractal index of Gaussian and conditionally Gaussian time series data

This paper studies the properties of a particular estimator of the fractal index of a time series with a view to applications in financial econometrics and mathematical finance. We show how measurement noise (e.g., microstructure noise) in the observations will bias the estimator, potentially resulting in the econometrician erroneously finding evidence of fractal characteristics in a time series. We propose a new estimator which is robust to such noise and construct a formal hypothesis test for the presence of noise in the observations. A number of simulation exercises are carried out, providing guidance for implementation of the theory. Finally, the methods are illustrated on two empirical data sets; one of turbulent velocity flows and one of financial prices.

Technical change in U.S. industries

We use the normalized quadratic cost function, introduced by Diewert and Wales (1987), to measure and analyze the rate and biases of technical change at the sectoral level in eleven major U.S. industries — manufacturing, construction, mining, agriculture, finance, health, wholesale, transportation, education, hospitality, and utilities — using annual KLEM (capital, labor, energy, and intermediate materials) data from the World KLEMS database, over the period from 1947 to 2010. We extend the work in Feng and Serletis (2008), by taking a new approach to econometric modeling, merging the econometric approach to productivity measurement with recent state-of-the-art advances in financial econometrics. In particular, we relax the homoskedasticity assumption and instead assume that the covariance matrix of the errors of the flexible interrelated factor demand systems is time-varying. We also pay explicit attention to theoretical regularity, treating the curvature property as a maintained hypothesis, thus achieving superior modeling in the context of a parametric nonlinear factor demand system that captures certain important features of the data.

An Alpha-Stable Approach to Modelling Highly Speculative Assets and Cryptocurrencies

We investigate the behaviour of cryptocurrencies' return data. Using return data for bitcoin, ethereum and ripple which account for over 70% of the cyrptocurrency market, we demonstrate that α-stable distribution models highly speculative cryptocurrencies more robustly compared to other heavy tailed distributions that are used in financial econometrics. We find that the Maximum Likelihood Method proposed by DuMouchel (1971) produces estimates that fit the cryptocurrency return data much better than the quantile based approach of McCulloch (1986) and sample characteristic method by Koutrouvelis (1980). The empirical results show that the leptokurtic feature presented in cryptocurrency return data can be captured by an α-stable distribution. This papers covers predominant literature in cryptocurrencies and stable distributions.

Climate Risks and Financial Stability

Climate change has been recently recognised as a new source of risk for the financial system. Several financial supervisors with a financial stability mandate have recently recommended that investors and financial institutions need to assess their exposure to climate-related financial risks and conduct climate stress-tests. Nevertheless, they fall short of methodologies to do so. Indeed, the characteristics of climate risks (like deep uncertainty, non-linearities and endogeneity) challenge traditional approaches to macroeconomic and financial risk analysis. Embedding climate change in macroeconomic and financial analysis is fundamental for a comprehensive understanding of risks and opportunities in the era of the climate crisis. This Special Issue is devoted to the relations between climate risks and financial stability and represents the first comprehensive attempt to fill methodological gaps in this area and to shed light on the financial implications of climate change. It includes original contributions that use a range of methodologies, like network modelling, dynamic evolutionary macroeconomic modelling and financial econometrics, to analyse the impacts of climate-related financial risks, as well as of financial policies and instruments aiming at the low-carbon transition. The research insights of these contributions inform financial supervisors about the integration of climate change considerations in financial risk assessment.

Rate-optimal estimation of the Blumenthal–Getoor index of a Lévy process

The Blumenthal–Getoor (BG) index characterizes the jump measure of an infinitely active Lévy process. It determines sample path properties and affects the behavior of various econometric procedures. If the process contains a diffusion term, existing estimators of the BG index based on high-frequency observations achieve rates of convergence which are suboptimal by a polynomial factor. In this paper, a novel estimator for the BG index and the successive BG indices is presented, attaining the optimal rate of convergence. If an additional proportionality factor needs to be inferred, the proposed estimator is rate-optimal up to logarithmic factors. Furthermore, our method yields a new efficient volatility estimator which accounts for jumps of infinite variation. All parameters are estimated jointly by the generalized method of moments. A simulation study compares the finite sample behavior of the proposed estimators with competing methods from the financial econometrics literature.

A comparison of realised measures for daily REIT volatility

ABSTRACTRecent advances in financial econometrics have led to the development of a variety of estimators of asset volatility using frequently sampled price data, known as ‘realised measures’. These estimators rely on different assumptions and take many different functional forms. In this paper, we aim to examine the accuracy of these estimators in the measurement of daily volatility of REIT returns. We consider a wide range of commonly used realised measures and apply them to several major global REIT markets. Our findings suggest that there is no single estimator which can perform the best for all markets under study. The best-performing estimator varies across markets. We obtain our results by considering the accuracy of both volatility estimation and forecast and by using multiple robust evaluation metrics.

Editorial for the Special Issue on Financial Econometrics

Financial econometrics has developed into a very fruitful and vibrant research area in the last two decades [...]

A new methodology for assessing the energy use-environmental degradation nexus.

The international community is more than ever before worrying about the unremitting global warming and climate change and the responsibility of extensive energy use for that situation. This article contributes to the existing literature by examining whether energy consumption predicts CO2 emissions during the past 50 years in the five most polluting nations in the world. To do this, we have been using the recently developed predictability test of Westerlund and Narayan (Journal of Banking and Finance, 36, 2632-2640, 2012, Journal of Financial Econometrics, 13, 342-375, 2015). We take thereby into account the problem of endogeneity and persistence in the explanatory variable. Likewise, this test has the advantage of treating the problem of heteroscedasticity. Using several predictive evaluation measures and assuming the historical average as a benchmark, we find that the basic model of the predictability test of Westerlund and Narayan (2012, 2015) surpasses the benchmark model. These findings reveal that primary energy consumption predicts CO2 emissions in the world and all countries, for different forecast horizons. Further, the in-sample evidence of predictability has been supported by the out-of-sample analysis.

Editorial for the special issue on financial econometrics

Editorial for the special issue on financial econometrics

The economic value of using CAW-type models to forecast covariance matrix

Purpose The purpose of this paper is twofold: to improve the traditional conditional autoregressive Wishart (CAW) and heterogeneous autoregressive (HAR)-CAW model to account for heterogeneous leverage effect and to adjust the high-frequency volatility. The other is to confirm whether CAW-type models that have statistical advantages have economic advantages. Design/methodology/approach Based on the high-frequency data, this study proposed a new model to describe the volatility process according to the heterogeneous market hypothesis. Thus, the authors acquire needed and credible high-frequency data. Findings By designing two mean-variance frameworks and considering several economic performance measures, the authors find that compared with five other models based on daily data, CAW-type models, especially LHAR-CAW and HAR-CAW, indeed generate the substantial economic values, and matrix adjustment method significantly improves the three CAW-type performances. Research limitations/implications The findings in this study suggest that from the aspect of economics, LHAR-CAW model can more accurately built the dynamic process of return rates and covariance matrix, respectively, and the matrix adjustment can reduce bias of realized volatility as covariance matrix estimator of return rates, and greatly improves the performance of unadjusted CAW-type models. Practical implications Compared with traditional low-frequency models, investors should allocate assets according to the LHAR-CAW model so as to get more economic values. Originality/value This study proposes LHAR-CAW model with the matrix adjustment, to account for heterogeneous leverage effect and empirically show their economic advantage. The new model and the new bias adjustment approach are pioneering and promote the evolution of financial econometrics based on high-frequency data.

Event Studies and Outlier Returns: Symptoms, Consequences and Treatment

This paper makes specifics contributions in the methodology of event studies. First, it develops a financial econometrics framework for understanding, measuring and testing the impact of outlier returns on the estimated parameters of stock return models. Second, it presents a maximum likelihood robust estimation method that enables the decomposition of a firm’s stock returns into regular and outlier returns for the purpose of computing robust or outlier resistant CAR statistics. Third, it presents analytical results on how outliers in the estimation sample affect OLS-CAR statistics. Results based on extensive Monte Carlo and actual data simulations, depict that outliers in the estimation sample affect adversely and significantly the performance of the OLS-CAR statistics in event studies. Outliers, however, do not impair the forecasting ability of the robust-CAR statistics introduced in this paper.

Beta Measurement and Forecasting with High Frequency Returns

Analysis with high frequency returns has become a core part of modern financial econometrics. Particularly in the measurement and forecasting of variance, covariance, correlation and Capital Asset Pricing Model (CAPM) beta. This paper studies CAPM beta measurement and forecasting with high frequency returns and evaluates trade-offs between bias and variability from different approaches. Our main finding is that the increasing of the return sampling frequency to a suitably high level with the inclusion of a lead and lag in the beta estimation, can result in substantial improvements in the bias and variability trade-off, relative to standard realized beta estimators with returns over a range of sampling frequencies.

Empirical performance of GARCH, GARCH-M, GJR-GARCH and log-GARCH models for returns volatility

Volatility plays an important role in the field of financial econometrics as one of the risk indicators. Many various models address the problem of modeling the volatilities of financial asset returns. This study provides a new empirical performance comparison of the four different GARCH-type models, namely GARCH, GARCH-M, GJR-GARCH, and log-GARCH models based on simulated data and real data such as the DJIA, S&P 500, and S&P CNX Nifty indices on a daily period from January 2000 to December 2017. We also investigate the estimation results obtained using Solver’Excel and verify those results against the results obtained using a Markov chain Monte Carlo method. The simulation study showed that the GARCH model is outperformed by other models. Meanwhile, the empirical study provides evidence that the GJR-GARCH model provides the best fitting, followed by the GARCH-M, GARCH, and log-GARCH models. Furthermore, this study recommends the use of Excel’s Solver in practice when the parameter estimates for GARCH-type model do not close to zero.

No arbitrage and lead–lag relationships

The existence of time-lagged cross-correlations between the returns of a pair of assets, which is known as the lead–lag relationship, is a well-known stylized fact in financial econometrics. Recently some continuous-time models have been proposed to take account of the lead–lag relationship. Such a model does not follow a semimartingale as long as the lead–lag relationship is present, so it admits an arbitrage without market frictions. In this paper we show that they are free of arbitrage if we take account of market frictions such as the presence of minimal waiting time on subsequent transactions or transaction costs.

Testing Market Efficiency with Nonlinear Methods: Evidence from Borsa Istanbul

Market efficiency has been analyzed through many studies using different linear methods. However, studies on financial econometrics reveal that financial time series exhibit nonlinear patterns because of various reasons. This paper examines market efficiency at Borsa Istanbul using a smooth transition autoregressive (STAR) type nonlinear model. I develop nonlinear ARCH and STAR models, a linear AR model and random walk model for 10 years’ weekly data and then out-of-sample forecast next 12 weeks’ return. Comparing forecast performance powers, I find that the STAR model outperforms random walk, that is Borsa Istanbul returns are predictable at the given period. The results show that the shareholders may earn abnormal return and identify the direction of the return change for the next week with at least 66% accuracy. Contrary to the linear level studies, these findings show that the Borsa Istanbul is not weak form efficient at nonlinear level within the studied period.

Gaussian approximation of maxima of Wiener functionals and its application to high-frequency data

This paper establishes an upper bound for the Kolmogorov distance between the maximum of a high-dimensional vector of smooth Wiener functionals and the maximum of a Gaussian random vector. As a special case, we show that the maximum of multiple Wiener–Itô integrals with common orders is well approximated by its Gaussian analog in terms of the Kolmogorov distance if their covariance matrices are close to each other and the maximum of the fourth cumulants of the multiple Wiener–Itô integrals is close to zero. This may be viewed as a new kind of fourth moment phenomenon, which has attracted considerable attention in the recent studies of probability. This type of Gaussian approximation result has many potential applications to statistics. To illustrate this point, we present two statistical applications in high-frequency financial econometrics: One is the hypothesis testing problem for the absence of lead-lag effects and the other is the construction of uniform confidence bands for spot volatility.

Comment on: Price Discovery in High Resolution

Abstract This note is a summary of my discussion of Joel Hasbrouck’s keynote paper at the 2018 Society for Financial Econometrics conference.

Fixed and Long Time Span Jump Tests: New Monte Carlo and Empirical Evidence

Numerous tests designed to detect realized jumps over a fixed time span have been proposed and extensively studied in the financial econometrics literature. These tests differ from “long time span tests” that detect jumps by examining the magnitude of the jump intensity parameter in the data generating process, and which are consistent. In this paper, long span jump tests are compared and contrasted with a variety of fixed span jump tests in a series of Monte Carlo experiments. It is found that both the long time span tests of Corradi et al. (2018) and the fixed span tests of Aït-Sahalia and Jacod (2009) exhibit reasonably good finite sample properties, for time spans both short and long. Various other tests suffer from finite sample distortions, both under sequential testing and under long time spans. The latter finding is new, and confirms the “pitfall” discussed in Huang and Tauchen (2005), of using asymptotic approximations associated with finite time span tests in order to study long time spans of data. An empirical analysis is carried out to investigate the implications of these findings, and “time-span robust” tests indicate that the prevalence of jumps is not as universal as might be expected.