Inference about Realized Volatility using Infill Subsampling

We investigate the use of subsampling for conducting inference about the quadratic variation of a discretely observed diffusion process under an infill asymptotic scheme. We show that the usual subsampling method of Politis and Romano (1994) is inconsistent when applied to our inference question. Recently, a type of subsampling has been used to do an additive bias correction to obtain a consistent estimator of the quadratic variation of a diffusion process subject to measurement error, Zhang, Mykland, and Ait-Sahalia (2005). This subsampling scheme is also inconsistent when applied to the inference question above. This is due to a high correlation between estimators on different subsamples. We discuss an alternative approach that does not have this correlation problem; however, it has a vanishing bias only under smoothness assumptions on the volatility path. Finally, we propose a subsampling scheme that delivers consistent inference without any smoothness assumptions on the volatility path. This is a general method and can be potentially applied to conduct inference for quadratic variation in the presence of jumps and/or microstructure noise by subsampling appropriate consistent estimators.Realised Volatility, Semimartingale, Subsampling, Infill Asymptotic Scheme

Estimating Quadratic VariationConsistently in thePresence of Correlated MeasurementError

We propose an econometric model that captures the e¤ects of marketmicrostructure on a latent price process. In particular, we allow for correlationbetween the measurement error and the return process and we allow themeasurement error process to have a diurnal heteroskedasticity. Wepropose a modification of the TSRV estimator of quadratic variation. Weshow that this estimator is consistent, with a rate of convergence thatdepends on the size of the measurement error, but is no worse than n1=6.We investigate in simulation experiments the finite sample performance ofvarious proposed implementations.Endogenous noise, Market Microstructure, Realised Volatility,Semimartingale

Inference for nonparametric high-frequency estimators with an application to time variation in betas

We consider the problem of conducting inference on nonparametric high-frequency estimators without knowing their asymptotic variances. We prove that a multivariate subsampling method achieves this goal under general conditions that were not previously available in the literature. We suggest a procedure for a data-driven choice of the bandwidth parameters. Our simulation study indicates that the subsampling method is much more robust than the plug-in method based on the asymptotic expression for the variance. Importantly, the subsampling method reliably estimates the variability of the Two Scale estimator even when its parameters are chosen to minimize the finite sample Mean Squared Error; in contrast, the plugin estimator substantially underestimates the sampling uncertainty. By construction, the subsampling method delivers estimates of the variance-covariance matrices that are always positive semi-definite. We use the subsampling method to study the dynamics of financial betas of six stocks on the NYSE. We document significant variation in betas within year 2006, and find that tick data captures more variation in betas than the data sampled at moderate frequencies such as every five or twenty minutes. To capture this variation we estimate a simple dynamic model for betas. The variance estimation is also important for the correction of the errors-in-variables bias in such models. We find that the bias corrections are substantial, and that betas are more persistent than the naive estimators would lead one to believe

Cross-sectional dependence in idiosyncratic volatility

This paper introduces a framework for analysis of cross-sectional dependence in the idiosyncratic volatilities of assets using high frequency data. We first consider the estimation of standard measures of dependence in the idiosyncratic volatilities such as covariances and correlations. Next, we study an idiosyncratic volatility factor model, in which we decompose the co-movements in idiosyncratic volatilities into two parts: those related to factors such as the market volatility, and the residual co-movements. When using high frequency data, naive estimators of all of the above measures are biased due to the estimation errors in idiosyncratic volatility. We provide bias-corrected estimators and establish their asymptotic properties. We apply our estimators to high-frequency data on 27 individual stocks from nine different sectors, and document strong cross-sectional dependence in their idiosyncratic volatilities. We also find that on average 74% of this dependence can be explained by the market volatility

Challenges for Economic Growth of Regions in the Baltic Sea Region Case Study of Latvia

The Baltic Sea region is one of the most socially, economically and technologically developed regions in the world. The region has a high GDP level, limited social inequality in a global context, leading positions in Doing Business and Global Competitiveness indeces. Meanwhile, the region is experiencing rapid aging of society and depopulation of the territories, the region internally has large differences in the development of human capital and productivity rates. The eastern part of the region is expressively dependent on one supplier's power resources; it is experiencing the largest fall as a result of the global economic crisis; and has high unemployment and poverty rates. One of the most prosperous and sustainable macro-regions in the world is facing high challenges in development of balanced and sustainable socio-economic structure inside it. The report analyzes which factors have promoted or hampered the growth of the regions (at NUTS3 level) of Baltic countries; and what areas of development play a crucial role for further growth. Therefore perspective policy intervention areas for promotion of the region's sustainable economic growth are analysed, - implementation of integrated development planning practice; exploration of advantages of modern regional governance practice; strengthening of business and innovation capacity at the regional level. By using the approach and methodology developed by OECD in the analysis of regional growth factors, calculations have been made about the comparative rates of the 3 Baltic countries - Estonia, Latvia and Lithuania. For the basis of the analysis, 6 indicators were used describing GDP growth, productivity, employment and population. The comparative growth speeds of the regions were analyzed over a period of several years. Results of the analysis clearly demonstrate the impact left by the global economic crisis on the economy of the regions. It also demonstrates failures of the selected and enforced government's regional policy based on subsidies to support development of infrastructure in the lagging regions of Latvia. The tendencies indicate specific policy implications. The best results may be achieved by combining different possibilities existing in the regions and by using modern and innovative management tools

Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error

We propose an econometric model that captures the effects of market microstructure on a latent price process. In particular, we allow for correlation between the measurement error and the return process and we allow the measurement error process to have a diurnal heteroskedasticity. We propose a modification of the TSRV estimator of quadratic variation. We show that this estimator is consistent, with a rate of convergence that depends on the size of the measurement error, but is no worse than n−1/6. We investigate in simulation experiments the finite sample performance of various proposed implementations

"Good death" - the circumstances in which it would be best for a person to die. The representative survey of Latvian population

The paper analyses the opinions of Latvian residents about the desired/best conditions for person’s death. Our intention was to use the concept of “good death” as it has been described in academic literature on the end of life to describe what circumstances of dying are preferred in Latvian population. A nationally representative survey of Latvian permanent residents (n = 1012) was conducted in October 2020. The obtained answers are analysed in different demographic groups, as well as in connection with other respondents’ perceptions and values. The results of the study show that the possibility of dying in pain and suffering is a major concern for the majority of Latvian society, and a large percentage of people would like to leave their lives in sleep or sudden death. The results of the study also show people’s desire to be in their homes at the time of death, to die in the presence of relatives. The survey shows a statistically significant relationship between people’s perceptions of the desired/best conditions in which to die - “good death” and a range of demographic and social factors. The data of the study carried out provide new information on people’s perceptions of death, highlighting differences in different socio-demographic groups.publishersversionPeer reviewe

Nonparametric estimation of the leverage effect: a trade-off between robustness and efficiency

We consider two new approaches to nonparametric estimation of the leverage effect. The first approach uses stock prices alone. The second approach uses the data on stock prices as well as a certain volatility instrument, such as the CBOE volatility index (VIX) or the Black-Scholes implied volatility. The theoretical justification for the instrument-based estimator relies on a certain invariance property, which can be exploited when high frequency data is available. The price-only estimator is more robust since it is valid under weaker assumptions. However, in the presence of a valid volatility instrument, the price-only estimator is inefficient as the instrument-based estimator has a faster rate of convergence. We consider two empirical applications, in which we study the relationship between the leverage effect and the debt-to-equity ratio, credit risk, and illiquidity

Essays on estimation and inference for volatility with high frequency data.

Volatility is a measure of risk, and as such it is crucial for finance. But volatility is not observable, which is why estimation and inference for it are important. Large high frequency data sets have the potential to increase the precision of volatility estimates. However, this data is also known to be contaminated by market microstructure frictions, such as bid-ask spread, which pose a challenge to estimation of volatility. The first chapter, joint with Oliver Linton, proposes an econometric model that captures the effects of market microstructure on a latent price process. In particular, this model allows for correlation between the measurement error and the return process and allows the measurement error process to have diurnal heteroskedasticity. A modification of the TSRV estimator of quadratic variation is proposed and asymptotic distribution derived. Financial econometrics continues to make progress in developing more robust and efficient estimators of volatility. But for some estimators, the asymptotic variance is hard to derive or may take a complicated form and be difficult to estimate. To tackle these problems, the second chapter develops an automated method of inference that does not rely on the exact form of the asymptotic variance. The need for a new approach is motivated by the failure of traditional bootstrap and subsampling variance estimators with high frequency data, which is explained in the paper. The main contribution is to propose a novel way of conducting inference for an important general class of estimators that includes many estimators of integrated volatility. A subsampling scheme is introduced that consistently estimates the asymptotic variance for an estimator, thereby facilitating inference and the construction of valid confidence intervals. The third chapter shows how the multivariate version of the subsampling method of Chapter 2 can be used to study the question of time variability in equity betas