Chasing volatility: A persistent multiplicative error model with jumps

We provide new empirical evidence on volatility forecasting in relation to asymmetries present in the dynamics of both return and volatility processes. Leverage and volatility feedback effects of the S&P 500 price and volatility dynamics are examined using recently developed methodologies to detect jumps and to disentangle their size from continuous return and continuous volatility. Granted that jumps in both return and volatility are important components for generating the two effects, we find jumps in return can improve forecasts of volatility, while jumps in volatility improve volatility forecasts to a lesser extent. Moreover, disentangling jump and continuous variations into signed semivariances further improve the out-of-sample performance of volatility forecasting models, with negative jump semivariance being highly more informative then positive jump semivariance. The model proposed is able to capture many empirical stylized facts while still remaining parsimonious in terms of number of parameters to be estimated.

Long-term electricity load forecasting plays a vital role for utilities and planners in terms of grid development and expansion planning. An overestimate of long-term electricity load will result in substantial wasted investment on the construction of excess power facilities, while an underestimate of the future load will result in insufficient generation and inadequate demand. As a first of its kind, this research proposes the use of a multiplicative error model (MEM) in forecasting electricity load for the long-term horizon. MEM originates from the structure of autoregressive conditional heteroscedasticity (ARCH) model where conditional variance is dynamically parameterized and it multiplicatively interacts with an innovation term of time-series. Historical load data, as accessed from a United States (U.S.) regional transmission operator, and recession data, accessed from the National Bureau of Economic Research, are used in this study. The superiority of considering volatility is proven by out-of-sample forecast results as well as directional accuracy during the great economic recession of 2008. Historical volatility is used to account for implied volatility. To incorporate future volatility, backtesting of MEM is performed. Two performance indicators used to assess the proposed model are: (i) loss functions in terms of mean absolute percentage error and mean squared error (for both in-sample model fit and out-of-sample forecasts) and (ii) directional accuracy.

A multiplicative error model with time-varying parameters and an error term following a mixture of gamma distributions is introduced. The model is fitted to the daily realized volatility series of deutschemark/dollar and yen/dollar returns and is shown to capture the conditional distribution of these variables better than the commonly used autoregressive fractionally integrated moving average model. The forecasting performance of the new model is found to be, in general, superior to that of the set of volatility models recently considered by Andersen et al. (2003, Econometrica 71, 579--625) for the same data. Copyright 2006, Oxford University Press.

The Distribution of Uncertainty: Evidence from the VIX Options Market

Enriched environment enhances left-right asymmetry of the hippocampus

In the geodetic data processing field, most methods for dealing with inequality constraints model are based on additive random error (ARE) models, and there have been few studies on mixed additive and multiplicative random error (MAAMRE) models with inequality constraints. To address this problem, a MAAMRE model with inequality constraints is first established based on the definition of inequality constraint equations, and then, a corresponding parameter estimation algorithm is proposed based on the idea of an exhaustive search method. In addition, considering a MAAMRE model for an ill-posed problem, an iterative regularization solution for an ill-posed MAAMRE model is first derived, and then, a specific parameter estimation algorithm for an ill-posed MAAMRE model with inequality constraints is further proposed by applying the exhaustive search approach. Finally, the feasibility and advantages of the proposed algorithms are verified by global positioning system (GPS) elevation fitting model and digital terrain model (DTM) examples.Graphical

In this chapter, we present generalizations of the basic multiplicative error model as introduced in Chap. 5. Section 6.1 discusses a class of ACD models which can be presented in terms of a generalized polynomial random coefficient model according to Carrasco and Chen (2002). We illustrate various special cases, discuss the theoretical properties and show empirical illustrations. In Sect. 6.2, we consider regime-switching ACD models allowing for parameters which might change in dependence of observable or unobservable characteristics. We concentrate on threshold ACD models, smooth transition ACD models as well as Markov Switching ACD specifications. Section 6.3 focuses on ACD models accommodating long range dependence in the data. In this context, we discuss different possibilities to capture long memory.

Copula-Based Specification of Vector MEMs

A new variant of RealGARCH for volatility modeling

Big Data Approach to Realised Volatility Forecasting Using HAR Model Augmented With Limit Order Book and News

In this work, the two-point probability density function (PDF) for the velocity field of isotropic turbulence is modeled using the kappa distribution and the concept of superstatistics. The PDF consists of a symmetric and an anti-symmetric part, whose symmetry properties follow from the reflection symmetry of isotropic turbulence, and the associated non-trivial conditions are established. The symmetric part is modeled by the kappa distribution. The anti-symmetric part, constructed in the context of superstatistics, is a novel function whose simplest form (called “the minimal model”) is solely dictated by the symmetry conditions. We obtain that the ensemble of eddies of size up to a given length r has a temperature parameter given by the second order structure function and a kappa-index related to the second and the third order structure functions. The latter relationship depends on the inverse temperature parameter (gamma) distribution of the superstatistics and it is not specific to the minimal model. Comparison with data from direct numerical simulations (DNS) of turbulence shows that our model is applicable within the dissipation subrange of scales. Also, the derived PDF of the velocity gradient shows excellent agreement with the DNS in six orders of magnitude. Future developments, in the context of superstatistics, are also discussed.

We adopt Tobit Regressions to examine the hedging behavior of the listed firms in Taiwan during 2005-2009. With the concern of bankruptcy and risk-shifting motivation of the firm, the risk-shifting, risk management, and risk-return-trade-off hypotheses are then reviewed and tested. The results show that return volatility is significantly negative to hedge ratio for distressed firms, controlling for the selection biases, time period of catastrophe (i.e., the Financial Crisis started from 2008), and the model sensitivity to different definitions of financial distress. It strongly supports the risk-shifting phenomenon for distressed firms. Significant negative relationship between hedge ratio and return volatility for non-distress group can also be observed in most tests, apart from some models for the Heckman tests for controlling selection biases. These findings partly support the risk-return-trade-off hypothesis. For the firms being in-between extreme distress levels, the return volatility is positive to hedge ratio, showing a weak support to risk management hypothesis. Our empirical results clarify the impacts of financial distress, return volatility, and their interaction term on corporate hedging behavior.

This dissertation is composed of three loosely related chapters, all of which are empirical.In Chapter 1, I examine whether expectations are formed in a systematically different manner during periods of low volatility versus periods of high volatility. I achieve this by measuring non-linearities in relationship between the SP 500 and the VIX across different market regimes. Three distinct market regimes are identified through a Markov Process, allowing for the capture of non-constant behavior in the relationship between contemporaneous price changes and future volatility expectations. The results indicate that the effect of the underlying asset on the supply and demand dynamics of its derivative is strongest during periods of low volatility and weakest during periods of high volatility. The decrease in magnitude of the SP 500 coefficient as the market switches from low volatility to high, suggests that information scarcity (low volatility) makes additional data (price changes) more impactful. Measures to limit market volatility may make market participant prone to expect changes in the state of the system. The purpose of Chapter 2 is to draw inference from the tail behavior of financial market price volatility in order to compare and contrast volatility expectations with volatility realizations. In doing so, I discuss the implications of slowly decaying tails as they relate to systems susceptible to unpredictable and consequential events. In such cases where fat tails are identified, typical values such as the average and variance, do not properly characterize the risk and unpredictability of the dynamic process under study. Prior research has identified asset prices and asset volatility as being drawn from a power law distribution. This paper aims to quantitatively confirm this characterization, specifically for market volatility. Further, this paper identifies whether or not volatility expectations exhibit similar power law characteristics. Goodness of fit and log likelihood tests indicate that most realized volatility series are plausibly drawn from a power- law distribution. However, none of the studied implied volatility series show evidence of power-law behavior, suggesting that risk premia may exist for lower levels of volatility but does not scale proportionally to the more extreme crisis events. That is, risk premia does not scale proportionally as values move farther into the tail. In Chapter 3, co-authored with Minh Pham, we investigate how economic uncertainty, specifically stock market uncertainty, correlates to individuals' life-satisfaction. Using expected price volatility (VIX) as our anticipatory indicator and life-satisfaction as our measure of utility, our hypothesis is built on the Anticipatory Utility framework, which suggests that people also derive utility from their beliefs. After accounting for associations with the unemployment rate and stock ownership, we find a positive relationship between the VIX and low self-reported life- satisfaction. This analysis captures the contemporaneous effects of future beliefs and indicates that economic sentiment about the future plays an important role in individuals' feelings about the present. This work was inspired by a desire to understand the economic crises that redirect and ultimately redefine our socioeconomic lives, as individuals and as nations. I began my economic studies during one of the most profound crises in recent history, the global financial crisis of the late 2000s. Here again in 2021, as my studies conclude, economies grapple with another, albeit different crisis. Both the Covid-19 pandemic and the subprime financial crisis highlight a salient fact; we never really know when, why, or from where such extreme events arrive. But they do, and do so more frequently than we like or predict. Each of the chapters presented in this dissertation seek to understand the ways in which we anticipate and interact with a characteristic marker of economic and financial crises, uncertainty.

Chapter 6 - Superstatistics: Superposition of Maxwell–Boltzmann Distributions

This article analyzes the business cycle in Japan by applying Markov switching (MS) models to the monthly data on the coincident indicator of composite index (CI) during the period of 1985/01-2012/12 calculated by Economic and Social Research Institute (ESRI), Cabinet Office, the Government of Japan. It is shown that the impact of the financial crisis in 2008 and the Tohoku earthquake in 2011 on this index is so large that the simple MS model with normal error and constant volatility cannot detect the business cycle turning points properly. The MS model is extended by incorporating Student's t-error and stochastic volatility (SV), and a Bayesian method via Markov chain Monte Carlo is developed for the analysis of the extended models. It is also shown that the MS model provides the estimates of the business cycle turning points close to those published by ESRI once t-error or SV is introduced. Bayesian model comparison based on marginal likelihood provides evidence that the MS model with both t-error and SV fits the data best.