Rounding Errors and Volatility Estimation

• HAR models are used to forecast Realized Volatility (RV) for a portfolio of stocks. • Low-, medium-, and high-frequency components of RV are isolated using wavelet decomposition. • Low-frequency volatility forecasts improve utility and reduce portfolio turnover. • Benefits are robust to direct forecasts of portfolio weights and jump robust RV. • Results stress the distinction between statistical and practical performance metrics in volatility forecasting. This study proposes a wavelet-based approach to forecasting Realized Volatility (RV) and evaluates its economic value within a volatility-timing framework. We apply wavelet decomposition to separate short-, medium-, and long-term components and generate forecasts using Heterogeneous Autoregressive (HAR) models. Forecasts based on the low-frequency component consistently lead to better portfolio outcomes, reducing turnover and enhancing investor utility without increasing risk. These results hold even when portfolio weights are forecast directly after being constructed from RV, or when jump-robust volatility estimates are used. The results highlight the importance of aligning forecast evaluation with practical investment objectives. Forecasts delivering the greatest welfare gains may not minimize conventional statistical loss functions.

Intraday volatility predictability in china gold futures market: The case of last half-hour realized volatility forecasting

Modelling and forecasting noisy realized volatility

Volatility forecasting is important both theoretically and in practice, varying by forecasting methods and financial markets. In this article, we explore this topic in the Taiwanese markets, using the encompassing regression models. We use the volatility of the Taiwan Stock Index (TAIEX) and its futures in the encompassing regression model to respectively make asynchronous forecasts of realized volatility (RV) and implied volatility (IV). Besides trading frequency, we find that transaction matching time is a key factor for obtaining steady RV values. Also, we find that the TAIEX index RV has a long memory. Moreover, we discover that, to obtain a stationary RV with a stable, long memory parameter, the optimal sampling intervals for the intraday return were nine (9) and thirty (30) minutes. In addition, we uncover that the spot volatility is more predictive of RV than the futures volatility. In the forecasting of IV, the volatility of futures has more information content, which can help improve overall forecast performance, especially when employing the ARFIMA+Jump model in the non-bear market and the ARFIMA+Jump/Leverage model in the bear market. The empirical result implies that the underlying asset of the TAIEX options (TXO) is approximately the index futures rather than the spot index, owing mainly to the demands for hedging and arbitrage from the TXO holders.

ABSTRACTThis article applies two measures to assess spillovers across markets: the Diebold and Yilmaz’s (2012) spillover index and the Hafner and Herwartz’s (2006) analysis of multivariate GARCH models using volatility impulse response analysis. We use two sets of data, daily realized volatility (RV) estimates taken from the Oxford-Man RV library, for the S&P500 and the FTSE, plus 10 years of daily returns series for the New York Stock Exchange Index and the FTSE 100 index. Both data sets capture both the global Financial Crisis (GFC) and the subsequent European Sovereign Debt Crisis (ESDC). The spillover index captures the transmission of volatility to and from markets, plus net spillovers. The Volatility Impulse Responses (VIRF) have to be calibrated to conditional volatility estimated at a particular point in time. We explore the impact of three different shocks, the onset of the GFC, the height of the GFC, and the impact of the ESDC. Our modelling includes leverage and asymmetric effects applying a multivariate GARCH model, and further analysis using both BEKK and diagonal BEKK (DBEKK) models. We find the impact of negative shocks is larger, but shorter in duration, in this case a difference between 3 and 6 months.

This research investigates the role of trading volume and data frequency in volatility forecasting by evaluating the performance of Generalized Autoregressive Conditional Heteroskedasticity Mixed‐Data Sampling (GARCH‐MIDAS), traditional GARCH, and intraday GARCH models. We take trading volume as the proxy for information flow and examine whether the Sequential Information Arrival Hypothesis (SIAH) is supported in the China stock market. The contributions of this study are as follows. (1) We provide a more consistent comparison to evaluate the forecasting ability of the MIDAS approach. (2) We extend the literature on the forecasting performance of trading volume to the GARCH‐MIDAS approach. (3) We present clear evidence to support that forecasting ability strongly relies upon data frequency. The empirical results show that: (1) GARCH‐MIDAS is not able to beat the traditional GARCH method when both are estimated by the same predictor sampled at different frequencies; (2) there is a positive relation between trading volume and volatility, but no clear evidence appears that SIAH holds in the China stock market; and (3) high‐frequency data are highly recommended for daily realized volatility (RV) forecasting, whereas intraday GARCH could significantly outperform traditional GARCH and GARCH‐MIDAS in volatility forecasting.

Operative Use of Eddy Covariance Measurements: Are High Frequency Data Indispensable?

A Lagrangian multiplier test for market microstructure noise with applications to sampling interval determination for realized volatilities

Which sentiment index is more informative to forecast stock market volatility? Evidence from China

Market microstructure theory highlights two important empirical predictions about how financial asset prices evolve over time, which are: (1) trades convey information that contributes to security price movements; and (2) intensified trading activity increases price volatility. This thesis provides three essays that develop new empirical models for high frequency returns, volatility, trading volumes and trade durations in order to test these two empirical predictions. Our newly proposed models show strong support for these theoretically implied predictions and provide additional insights into the interdependence amongst returns, volatility, volumes, and trade durations.

Properties of range-based volatility estimators

Volatility forecasts crucial to many financial applications usually assume implicitly that the frequency of the data should match the forecast horizon; portfolio managers typically rely on risk models estimated using monthly data to produce monthly volatility forecasts, for example. For longer–term forecasts, this practice has two drawbacks: Volatility estimates can be based on stale data; and return events occurring within long sampling intervals are obscured, confounding estimation. Monthly volatility risk measures constructed using higher–frequency data seem to be more robust than those using low–frequency data. Microstructure effects can explain the differences in estimates.

Dynamic Copula Models and High Frequency Data

Estimation of realized volatility of cryptocurrencies using CEEMDAN-RF-LSTM

Consistent High-Precision Volatility from High-Frequency Data