Heteroskedasticity And Autocorrelation Consistent Research Articles

On the (In)efficiency of gold and bitcoin: impact of COVID-19

PurposeWe aim to examine the impact of COVID-19 on the efficiency of Gold and Bitcoin returns. In particular, our efficiency tests are based on the popular calendar anomaly, the turn-of-the-month (TOM) effect in these markets.Design/methodology/approachWe define the TOM days as the final trading day of a month and initial three trading days of the immediate next month. To understand the TOM effect, we estimate the typical Ordinary Least Squares (OLS) regression model using the Heteroskedasticity and Autocorrelation Consistent (HAC) standard errors and covariances.FindingsThough in the full sample, a positive and significant TOM effect is observed only for Bitcoin, during COVID period, the TOM effect appears in Gold returns and becomes stronger for Bitcoin, implying that the considered securities become inefficient during COVID period.Practical implicationsBased on these results, we create a trading strategy which is found to surpass the buy-and-hold strategy for both the full sample as well as the COVID period for Bitcoin while only during the COVID period for Gold. Our results provide useful implications for investors and policymakers as the Gold and Bitcoin markets can be timed by taking positions especially based on the behavior of the TOM effect.Originality/valueWe examine the TOM effect in the two important securities – Gold and Bitcoin. Though, a few studies have examined this anomaly in currency, equity and cryptocurrency markets, however, they have not considered the Gold market. Additionally, no study has examined the impact of COVID-19 on the TOM effect in these markets, and hence, market efficiency. We believe that our study is the first to examine the TOM effect in these markets simultaneously.

A Unified Frequency Domain Cross-Validatory Approach to HAC Standard Error Estimation

A unified frequency domain cross-validation (FDCV) method is proposed to obtain a heteroskedasticity and autocorrelation consistent (HAC) standard error. This method enables model/tuning parameter selection across both parametric and nonparametric spectral estimators simultaneously. The candidate class for this approach consists of restricted maximum likelihood-based (REML) autoregressive spectral estimators and lag-weights estimators with the Parzen kernel. Additionally, an efficient technique for computing the REML estimators of autoregressive models is provided. Through simulations, the reliability of the FDCV method is demonstrated, comparing favorably with popular HAC estimators such as Andrews-Monahan and Newey-West.

Exchange rate responses to macroeconomic announcement on the COVID-19 pandemic

This study examines the effects of macroeconomic announcements on the USD/IDR exchange rate before and during the COVID-19 pandemic, and the difference between the impact of positive and negative announcements on the exchange rate. To measure the macroeconomic announcement, a surprise component is used, that is the difference between actual data and market forecasts. The data in this research are daily time series from 1 January 2014 to 30 November 2020. The actual data and market forecasts for each indicator are obtained from Bloomberg. To test the exchange rate response to the macroeconomic announcement, the Ordinary Least Square (OLS) analysis method is used with heteroskedasticity and autocorrelation consistent (HAC). This study finds that during the COVID-19 pandemic, the USD/IDR exchange rate is more sensitive to the surprise component of the macroeconomic announcement compared to the period before the COVID-19 pandemic. This research also finds evidence that positive Indonesian news and negative US news have a significant effect on changes in the USD/IDR exchange rate.

COVID-19: Tail risk and predictive regressions.

The paper focuses on econometrically justified robust analysis of the effects of the COVID-19 pandemic on financial markets in different countries across the World. It provides the results of robust estimation and inference on predictive regressions for returns on major stock indexes in 23 countries in North and South America, Europe, and Asia incorporating the time series of reported infections and deaths from COVID-19. We also present a detailed study of persistence, heavy-tailedness and tail risk properties of the time series of the COVID-19 infections and death rates that motivate the necessity in applications of robust inference methods in the analysis. Econometrically justified analysis is based on heteroskedasticity and autocorrelation consistent (HAC) inference methods, recently developed robust t-statistic inference approaches and robust tail index estimation.

High-Dimensional Granger Causality Tests with an Application to VIX and News

Abstract We study Granger causality testing for high-dimensional time series using regularized regressions. To perform proper inference, we rely on heteroskedasticity and autocorrelation consistent (HAC) estimation of the asymptotic variance and develop the inferential theory in the high-dimensional setting. To recognize the time-series data structures, we focus on the sparse-group LASSO (sg-LASSO) estimator, which includes the LASSO and the group LASSO as special cases. We establish the debiased central limit theorem for low-dimensional groups of regression coefficients and study the HAC estimator of the long-run variance based on the sg-LASSO residuals. This leads to valid time-series inference for individual regression coefficients as well as groups, including Granger causality tests. The treatment relies on a new Fuk–Nagaev inequality for a class of τ-mixing processes with heavier than Gaussian tails, which is of independent interest. In an empirical application, we study the Granger causal relationship between the VIX and financial news.

Predictability of cryptocurrency returns: evidence from robust tests

Abstract The paper provides a comparative empirical study of predictability of cryptocurrency returns and prices using econometrically justified robust inference methods. We present robust econometric analysis of predictive regressions incorporating factors, which were suggested by Liu, Y., & Tsyvinski, A. (2018). Risks and returns of cryptocurrency. NBER working paper no. 24877; Liu, Y., & Tsyvinski, A. (2021). Risks and returns of cryptocurrency. The Review of Financial Studies, 34(6), 2689–2727, as useful predictors for cryptocurrency returns, including cryptocurrency momentum, stock market factors, acceptance of Bitcoin, and Google trends measure of investors’ attention. Due to inherent heterogeneity and dependence properties of returns and other time series in financial and crypto markets, we provide the analysis of the predictive regressions using both heteroskedasticity and autocorrelation consistent (HAC) standard-errors and also the recently developed t t -statistic robust inference approaches, Ibragimov, R., & Müller, U. K. (2010). t-statistic based correlation and heterogeneity robust inference. Journal of Business and Economic Statistics, 28, 453–468; Ibragimov, R., & Müller, U. K. (2016). Inference with few heterogeneous clusters. Review of Economics and Statistics, 98, 83–96. We provide comparisons of robust predictive regression estimates between different cryptocurrencies and their corresponding risk and factor exposures. In general, the number of significant factors decreases as we use more robust t-tests, and the t-statistic robust inference approaches appear to perform better than the t-tests based on HAC standard errors in terms of pointing out interpretable economic conclusions. The results in this paper emphasize the importance of the use of robust inference approaches in the analysis of economic and financial data affected by the problems of heterogeneity and dependence.

Robust inference under time‐varying volatility: A real‐time evaluation of professional forecasters

SummaryIn many forecast evaluation applications, standard tests as well as tests allowing for time‐variation in relative forecast ability build on heteroskedasticity‐and‐autocorrelation consistent (HAC) covariance estimators. Yet, the finite‐sample performance of these asymptotics is often poor. “Fixed‐ ” asymptotics, used to account for long‐run variance estimation, improve finite‐sample performance under homoskedasticity, but lose asymptotic pivotality under time‐varying volatility. Moreover, loss of pivotality due to time‐varying volatility is found in the standard HAC framework in certain cases as well. We prove a wild bootstrap implementation to restore asymptotically pivotal inference for the above and new CUSUM‐ and Cramér‐von Mises‐based tests in a fairly general setup, allowing for estimation uncertainty from either a rolling window or a recursive approach when fixed‐ asymptotics are adopted to achieve good finite‐sample performance. We then investigate the (time‐varying) performance of professional forecasters relative to naive no‐change and model‐based predictions in real‐time. We exploit the Survey of Professional Forecasters (SPF) database and analyze nowcasts and forecasts at different horizons for output and inflation. We find that not accounting for time‐varying volatility seriously affects outcomes of tests for equal forecast ability: wild bootstrap inference typically yields convincing evidence for advantages of the SPF, while tests using non‐robust critical values provide remarkably less. Moreover, we find significant evidence for time‐variation of relative forecast ability, the advantages of the SPF weakening considerably after the “Great Moderation.”

Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models

We develop a theory of evolutionary spectra for heteroskedasticity and autocorrelation robust (HAR) inference when the data may not satisfy second-order stationarity. Nonstationarity is a common feature of economic time series which may arise either from parameter variation or model misspecification. In such a context, the theories that support HAR inference are either not applicable or do not provide accurate approximations. HAR tests standardized by existing long-run variance estimators then may display size distortions and little or no power. This issue can be more severe for methods that use long bandwidths (i.e., fixed-b HAR tests). We introduce a class of nonstationary processes that have a time-varying spectral representation which evolves continuously except at a finite number of time points. We present an extension of the classical heteroskedasticity and autocorrelation consistent (HAC) estimators that applies two smoothing procedures. One is over the lagged autocovariances, akin to classical HAC estimators, and the other is over time. The latter element is important to flexibly account for nonstationarity. We name them double kernel HAC (DK-HAC) estimators. We show the consistency of the estimators and obtain an optimal DK-HAC estimator under the mean squared error (MSE) criterion. Overall, HAR tests standardized by the proposed DK-HAC estimators are competitive with fixed-b HAR tests, when the latter work well, with regards to size control even when there is strong dependence. Notably, in those empirically relevant situations in which previous HAR tests are undersized and have little or no power, the DK-HAC estimator leads to tests that have good size and power.

The Economics of Blockchain-Based Virtual Worlds: A Hedonic Regression Model for Virtual Land

Virtual worlds have become increasingly more important, and are being used for a large variety of recreational and business activities. Various companies have opened virtual offices and brand ambassador spaces, and the recent surge in online interactions has further increased the interest in these social platforms. In this paper, we analyze the first large-scale virtual world that has been built on a public blockchain network. We compile a comprehensive data set that allows us to study the economics of blockchain-based virtual property. We then use this data set to estimate hedonic regression models for virtual land and employ a semi-parametric Mixed Geographically Weighted Regression (MGWR) model that allows for spatially flexible coefficients. In particular, we expect the central business district (CBD) gradient and the street distance coefficients to vary across the virtual world. Conversely, we consider the coefficients of binary variables to be more meaningful in a global context. For inference purposes, we employ spatial robust heteroskedasticity and autocorrelation consistent (HAC) standard errors. We find evidence that prices of virtual land parcels are primarily driven by factors that are of particular importance in business applications. Land parcels in close proximity to popular landmarks, such as the city center, main streets, plazas and commercially-driven districts, as well as parcels with easily memorable address-like features were claimed at substantially higher prices. We used different model specifications and conducted various robustness checks, including a separate estimation for price segments and investor-specific effects. All specifications have led to similar results and support the evidence from our MGWR model.

The volatility of bank stock prices and macroeconomic fundamentals in the Pakistani context: an application of GARCH and EGARCH models

Research Background: The banking sector plays a crucial role in the world?s economic development. This research paper evaluates the volatility spillover, symmetric, and asymmetric effects between the macroeconomic fundamentals, i.e., market risks, interest rates, exchange rates, and bank stock returns, for the listed banks of Pakistan.
 Purpose of the article: The main purpose of this study is to examine the volatility of Pakistani banking stock returns due to the influence of market risk, interest rates, and exchange rates. Pakistan is selected for the study because the volatility of its banking stock returns is strongly influential in achieving sustainable economic development.
 Methods: By applying the OLS with the Heteroskedasticity and Autocorrelation Consistent (HAC) covariance matrix, the GARCH (1, 2), and the EGARCH (1, 1), analysis is conducted for the period from January 1, 2009 to December 31, 2019 using samples of 13 listed banks.
 Findings & Value added: The ARCH parameter is significant in the OLS with the HAC covariance matrix estimation, which is a clear indication of the existence of heteroskedasticity in the squared residuals and the inaccuracy of the OLS with the HAC covariance matrix. The results of the OLS with the HAC covariance matrix suggest using the GARCH model family to accurately measure the volatility of bank stock prices. The results of the mean equation in the GARCH (1, 2) and EGARCH (1, 1) indicate the positive significance of market risk and the low significance of interest and exchange rates, confirming that market returns strongly affect the sensitivity of bank stock returns compared to interest and exchange rates. It should be noted that the ARCH (?) and GARCH (?) parameters of the variance equation fulfill the non-negative conditions of the GARCH model. Furthermore, the leverage parameter (?) is found to be positively significant for all banks, and volatility is found to be influenced by positive shocks compared to negative shocks. Conclusively, it can be stated that market returns determine the dynamics of the conditional returns of bank stocks. Nevertheless, the interest and exchange rate volatilities determine the conditional bank stock returns? volatility.

Spatial HAC Estimator: Analysis of Convergence of European Regions

This paper applies a nonparametric heteroskedasticity and autocorrelation consistent (HAC) estimator of error terms in the context of the spatial autoregressive model of GDP per capita convergence of European regions at NUTS 2 level. By introducing the spatial dimension, it looks at how the equilibrium distribution of GDP per capita of EU regions evolves both in time and space dimensions. Results demonstrate that the global spatial spillovers of growth rates make an important contribution to the process of convergence by reinforcing the economic growth of neighboring regions. Results are even more pronounced when the convergence in wage per worker is considered. The choice of kernel functions does not significantly affect the estimation of the variance-covariance matrix, while the choice of the bandwidth parameter is quite important. Finally, results are sensitive to the weighting matrix specification, and further research is needed to give a more rigorous justification for the selection of the weighting matrix.

Limit theorems for network dependent random variables

This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following (Doukhan and Louhichi, 1999), we measure the strength of dependence by covariances of nonlinearly transformed variables. We provide a law of large numbers and central limit theorem for network dependent variables. We also provide a method of calculating standard errors robust to general forms of network dependence. For that purpose, we rely on a network heteroskedasticity and autocorrelation consistent (HAC) variance estimator, and show its consistency. The results rely on conditions characterized by tradeoffs between the rate of decay of dependence across a network and network’s denseness. Our approach can accommodate data generated by network formation models, random fields on graphs, conditional dependency graphs, and large functional-causal systems of equations.

Uniform nonparametric inference for time series

This paper provides the first result for the uniform inference based on nonparametric series estimators in a general time-series setting. We develop a strong approximation theory for sample averages of mixingales with dimensions growing with the sample size. We use this result to justify the asymptotic validity of a uniform confidence band for series estimators and show that it can also be used to conduct nonparametric specification test for conditional moment restrictions. New results on the validity of heteroskedasticity and autocorrelation consistent (HAC) estimators with increasing dimension are established for making feasible inference. An empirical application on the unemployment volatility puzzle for the search and matching model is provided as an illustration.

Using HAC Estimators for Intervention Analysis

The purpose of this article is to present an alternative method for intervention analysis of time series data that is simpler to use than the traditional method of fitting an explanatory Autoregressive Integrated Moving Average (ARIMA) model. Time series regression analysis is commonly used to test the effect of an event on a time series. An econometric modeling method, which uses a heteroskedasticity and autocorrelation consistent (HAC) estimator of the covariance matrix instead of fitting an ARIMA model, is proposed as an alternative. The method of parametric bootstrap is used to compare the two approaches for intervention analysis. The results of this study suggest that the time series regression method and the HAC method give very similar results for intervention analysis, and hence the proposed HAC method should be used for intervention analysis, instead of the more complicated method of ARIMA modeling. The alternative method presented here is expected to be very helpful in gaming and hospitality research.

Inference for High-Dimensional Regressions With Heteroskedasticity and Auto-correlation

We study Granger causality testing for high-dimensional time series using regularized regressions. To perform proper inference, we rely on heteroskedasticity and autocorrelation consistent (HAC) estimation of the asymptotic variance and develop the inferential theory in the high-dimensional setting. To recognize the time series data structures we focus on the sparse-group LASSO estimator, which includes the LASSO and the group LASSO as special cases. We establish the debiased central limit theorem for low dimensional groups of regression coefficients and study the HAC estimator of the long-run variance based on the sparse-group LASSO residuals. This leads to valid time series inference for individual regression coefficients as well as groups, including Granger causality tests. The treatment relies on a new Fuk-Nagaev inequality for a class of $\tau$-mixing processes with heavier than Gaussian tails, which is of independent interest. In an empirical application, we study the Granger causal relationship between the VIX and financial news.

HAR Testing for Spurious Regression in Trend

The usual t test, the t test based on heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators, and the heteroskedasticity and autocorrelation robust (HAR) test are three statistics that are widely used in applied econometric work. The use of these significance tests in trend regression is of particular interest given the potential for spurious relationships in trend formulations. Following a longstanding tradition in the spurious regression literature, this paper investigates the asymptotic and finite sample properties of these test statistics in several spurious regression contexts, including regression of stochastic trends on time polynomials and regressions among independent random walks. Concordant with existing theory (Phillips 1986, 1998; Sun 2004, 2014b) the usual t test and HAC standardized test fail to control size as the sample size n → ∞ in these spurious formulations, whereas HAR tests converge to well-defined limit distributions in each case and therefore have the capacity to be consistent and control size. However, it is shown that when the number of trend regressors K → ∞ , all three statistics, including the HAR test, diverge and fail to control size as n → ∞ . These findings are relevant to high-dimensional nonstationary time series regressions where machine learning methods may be employed.

Inference on Difference-in-Differences average treatment effects: A fixed-[formula omitted] approach

This paper provides an analysis of the standard errors proposed by Driscoll and Kraay (1998) (DK) in linear Difference-in-Differences (DD) models with fixed effects and individual-specific time trends. The analysis is accomplished within the fixed-b asymptotic framework developed by Kiefer and Vogelsang (2005) for heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimator based tests. For both the fixed-N, large-T, and large-N, large-T cases, it is shown that fixed-b asymptotic distributions of test statistics constructed using the DD estimator and the DK standard errors are different from the results found by Kiefer and Vogelsang (2005) and Vogelsang (2012). The newly derived fixed-b asymptotic distributions depend on the date of policy change, individual-specific trend functions as well as the choice of kernel and bandwidth. Monte Carlo simulations illustrate the performance of the fixed-b approximations in practice.

A Robust Approach to Heteroskedasticity, Error Serial Correlation and Slope Heterogeneity for Large Linear Panel Data Models with Interactive Effects

In this paper, we propose a robust approach against heteroskedasticity, error serial correlation and slope heterogeneity for large linear panel data models. First, we establish the asymptotic validity of the Wald test based on the widely used panel heteroskedasticity and autocorrelation consistent (HAC) variance estimator of the pooled estimator under random coefficient models. Then, we show that a similar result holds with the proposed bias-corrected Bai's (2009) estimator for models with unobserved interactive effects. Our new theoretical result justifies the use of the same slope estimator and the variance estimator, both for slope homogeneous and heterogeneous models. This robust approach can significantly reduce the model selection uncertainty for applied researchers. In addition, we propose a novel test for the correlation and dependence of the random coefficient with covariates. The test is of great importance, since the widely used estimators and/or its variance estimators can become inconsistent when the variation of coefficients depends on covariates, in general. The finite sample evidence supports the usefulness and reliability of our approach.

Inference with Dependent Data in Accounting and Finance Applications

ABSTRACTWe review developments in conducting inference for model parameters in the presence of intertemporal and cross‐sectional dependence with an emphasis on panel data applications. We review the use of heteroskedasticity and autocorrelation consistent (HAC) standard error estimators, which include the standard clustered and multiway clustered estimators, and discuss alternative sample‐splitting inference procedures, such as the Fama–Macbeth procedure, within this context. We outline pros and cons of the different procedures. We then illustrate the properties of the discussed procedures within a simulation experiment designed to mimic the type of firm‐level panel data that might be encountered in accounting and finance applications. Our conclusion, based on theoretical properties and simulation performance, is that sample‐splitting procedures with suitably chosen splits are the most likely to deliver robust inferential statements with approximately correct coverage properties in the types of large, heterogeneous panels many researchers are likely to face.

GMM Long-Run Variance Estimation via VAR Averaging

This paper examines the heteroskedasticity and autocorrelation consistent (HAC) estimation of the long-run variance (LRV) matrix of a random vector process in a GMM estimation framework via vector autoregression (VAR) model averaging. By combining a VAR representation of GMM moments and VAR model averaging techniques, we present two new averaging-VAR-based LRV estimators: One constructs the LRV estimator based on the data-dependent weighted VAR residuals, and the other additionally combines with prewhitened kernel estimators in the spirit of Andrews and Monahan (1992). Our former proposal does not suffer from problems involving the choices of a truncation lag (bandwidth) or VAR lag length that are inherent in existing methods; the latter can be viewed as employing the VAR averaging strategy for prewhitening purposes. Theoretical justifications of the proposed methods rely on new consistency results for the averaging least-squares estimation of VAR coefficients and for the proposed LRV estimators. In extensive simulation experiments, our new averaging-VAR-based LRV estimators perform well in finite samples by offering more inference accuracy relative to existing competing estimators, with the improvement particularly prominent when combining VAR averaging with prewhitened kernel estimators. We empirically test the forward rate unbiasedness hypothesis to illustrate the utility of our methodology.