Out-of-sample prediction of Bitcoin realized volatility: Do other cryptocurrencies help?

Inspired by cross-market information flows among international stock markets, we incorporate external predictive information from other cryptocurrency markets to forecast the realized volatility (RV) of Bitcoin. To make the most of such external information, we employ six widely accepted approaches to construct predictive models based on multivariate information. Our results suggest that the scaled principal component analysis (SPCA) approach steadily improves the predictive ability of the prevailing heterogeneous autoregressive (HAR) benchmark model considering both the model confidence set (MCS) test and the Diebold–Mariano (DM) test based on three widely accepted loss functions. The forecasting performance is persistent to various robustness checks and extensions. Notably, a mean–variance investor can obtain steady positive economic gains if the investment portfolio is constructed on the basis of the forecasts from the HAR-SPCA model. The results of this study show that external predictive information is statistically and economically important in forecasting Bitcoin RV.     

Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models

In a data-rich environment, forecasting economic variables amounts to extracting and organizing useful information from a large number of predictors. So far, the dynamic factor model and its variants have been the most successful models for such exercises. In this paper, we investigate a category of LASSO-based approaches and evaluate their predictive abilities for forecasting twenty important macroeconomic variables. These alternative models can handle hundreds of data series simultaneously, and extract useful information for forecasting. We also show, both analytically and empirically, that combing forecasts from LASSO-based models with those from dynamic factor models can reduce the mean square forecast error (MSFE) further. Our three main findings can be summarized as follows. First, for most of the variables under investigation, all of the LASSO-based models outperform dynamic factor models in the out-of-sample forecast evaluations. Second, by extracting information and formulating predictors at economically meaningful block levels, the new methods greatly enhance the interpretability of the models. Third, once forecasts from a LASSO-based approach are combined with those from a dynamic factor model by forecast combination techniques, the combined forecasts are significantly better than either dynamic factor model forecasts or the naïve random walk benchmark.     

Economic indicators and stock market volatility in an emerging economy

By analyzing the daily realized volatility series calculated from intraday stock price observations, this study examines the direct causality between one-day-ahead aggregate stock market volatility and several economic and financial indicators in the Korean market, a leading emerging market. Using the predictive regression and superior predictive ability tests, we find that the model-free implied volatility index (VKOSPI) and stock market indicators both lead the daily market volatility. However, daily economic indicators provide no predictive information beyond that contained in historical volatility. Though in-sample causality does not guarantee a better out-of-sample forecasting performance, the VKOSPI and combinations of predictors exhibit significant predictive ability regardless of the time period. Our study verifies the information role of the VKOSPI as an indicator of daily market risk.     

Forecasting economic time series using targeted predictors

This paper studies two refinements to the method of factor forecasting. First, we consider the method of quadratic principal components that allows the link function between the predictors and the factors to be non-linear. Second, the factors used in the forecasting equation are estimated in a way to take into account that the goal is to forecast a specific series. This is accomplished by applying the method of principal components to ‘targeted predictors’ selected using hard and soft thresholding rules. Our three main findings can be summarized as follows. First, we find improvements at all forecast horizons over the current diffusion index forecasts by estimating the factors using fewer but informative predictors. Allowing for non-linearity often leads to additional gains. Second, forecasting the volatile one month ahead inflation warrants a high degree of targeting to screen out the noisy predictors. A handful of variables, notably relating to housing starts and interest rates, are found to have systematic predictive power for inflation at all horizons. Third, the targeted predictors selected by both soft and hard thresholding changes with the forecast horizon and the sample period. Holding the set of predictors fixed as is the current practice of factor forecasting is unnecessarily restrictive.     

Forecasting crude oil price volatility

We use high-frequency intra-day realized volatility data to evaluate the relative forecasting performances of various models that are used commonly for forecasting the volatility of crude oil daily spot returns at multiple horizons. These models include the RiskMetrics, GARCH, asymmetric GARCH, fractional integrated GARCH and Markov switching GARCH models. We begin by implementing Carrasco, Hu, and Ploberger’s (2014) test for regime switching in the mean and variance of the GARCH(1, 1), and find overwhelming support for regime switching. We then perform a comprehensive out-of-sample forecasting performance evaluation using a battery of tests. We find that, under the MSE and QLIKE loss functions: (i) models with a Student’s t innovation are favored over those with a normal innovation; (ii) RiskMetrics and GARCH(1, 1) have good predictive accuracies at short forecast horizons, whereas EGARCH(1, 1) yields the most accurate forecasts at medium horizons; and (iii) the Markov switching GARCH shows a superior predictive accuracy at long horizons. These results are established by computing the equal predictive ability test of Diebold and Mariano (1995) and West (1996) and the model confidence set of Hansen, Lunde, and Nason (2011) over the entire evaluation sample. In addition, a comparison of the MSPE ratios computed using a rolling window suggests that the Markov switching GARCH model is better at predicting the volatility during periods of turmoil.     

Forecasting the Value-at-Risk of REITs using realized volatility jump models

This paper examines jump risk in the time series of Real Estate Investment Trusts (REITs). Using high-frequency index-level and firm-level data, the econometric model in this paper integrates jumps into the volatility forecast by estimating jump augmented Heterogeneous Autoregressive (HAR) models of realized volatility. To assess the information value of these specifications, their forecasting accuracies for generating one-step ahead daily Value-at-Risk are also compared with other VaR specifications, including those generated from historical returns, bootstrap technique, and severity loss distribution.     

Are low-frequency data really uninformative? A forecasting combination perspective

In this study, we investigate whether low-frequency data improve volatility forecasting when high-frequency data are available. To answer this question, we utilize four forecast combination strategies that combine low-frequency and high-frequency volatility models and employ a rolling window and a range of loss functions in the framework of the novel Model Confidence Set test. Out-of-sample results show that combination forecasts with GARCH-class models can achieve high forecast accuracy. However, the combination forecast methods appear not to significantly outperform individual high-frequency volatility models. Furthermore, we find that models that combine low-frequency and high-frequency volatility yield significantly better performance than other models and combination forecast strategies in both a statistical and economic sense.     

Quantiles as optimal point forecasts

Loss functions play a central role in the theory and practice of forecasting. If the loss function is quadratic, the mean of the predictive distribution is the unique optimal point predictor. If the loss is symmetric piecewise linear, any median is an optimal point forecast. Quantiles arise as optimal point forecasts under a general class of economically relevant loss functions, which nests the asymmetric piecewise linear loss, and which we refer to as generalized piecewise linear (GPL). The level of the quantile depends on a generic asymmetry parameter which reflects the possibly distinct costs of underprediction and overprediction. Conversely, a loss function for which quantiles are optimal point forecasts is necessarily GPL. We review characterizations of this type in the work of Thomson, Saerens and Komunjer, and relate to proper scoring rules, incentive-compatible compensation schemes and quantile regression. In the empirical part of the paper, the relevance of decision theoretic guidance in the transition from a predictive distribution to a point forecast is illustrated using the Bank of England’s density forecasts of United Kingdom inflation rates, and probabilistic predictions of wind energy resources in the Pacific Northwest.     

Robust optimization of forecast combinations

We develop a methodology for constructing robust combinations of time series forecast models which improve upon a given benchmark specification for all symmetric and convex loss functions. Under standard regularity conditions, the optimal forecast combination asymptotically almost surely dominates the benchmark, and also optimizes the chosen goal function. The optimum in a given sample can be found by solving a convex optimization problem. An application to the forecasting of changes in the S&P 500 volatility index shows that robust optimized combinations improve significantly upon the out-of-sample forecasting accuracy of both simple averaging and unrestricted optimization.     

Forecasting U.S. money growth using economic uncertainty measures and regularisation techniques

This paper examines the out-of-sample forecasting properties of six different economic uncertainty variables for the growth of the real M2 and real M4 Divisia money series for the U.S. using monthly data. The core contention is that information on economic uncertainty improves the forecasting accuracy. We estimate vector autoregressive models using the iterated rolling-window forecasting scheme, in combination with modern regularisation techniques from the field of machine learning. Applying the Hansen-Lunde-Nason model confidence set approach under two different loss functions reveals strong evidence that uncertainty variables that are related to financial markets, the state of the macroeconomy or economic policy provide additional informational content when forecasting monetary dynamics. The use of regularisation techniques improves the forecast accuracy substantially.     

Forecasting crude oil market volatility using variable selection and common factor

This paper aims to improve the predictability of aggregate oil market volatility with a substantially large macroeconomic database, including 127 macro variables. To this end, we use machine learning from both the variable selection (VS) and common factor (i.e., dimension reduction) perspectives. We first use the lasso, elastic net (ENet), and two conventional supervised learning approaches based on the significance level of predictors’ regression coefficients and the incremental R-square to select useful predictors relevant to forecasting oil market volatility. We then rely on the principal component analysis (PCA) to extract a common factor from the selected predictors. Finally, we augment the autoregression (AR) benchmark model by including the supervised PCA common index. Our empirical results show that the supervised PCA regression model can successfully predict oil market volatility both in-sample and out-of-sample. Also, the recommended models can yield forecasting gains in both statistical and economic perspectives. We further shed light on the nature of VS over time. In particular, option-implied volatility is always the most powerful predictor.     

Adding dummy variables: A simple approach for improved volatility forecasting in electricity market

This study used dummy variables to measure the influence of day-of-the-week effects and structural breaks on volatility. Considering day-of-the-week effects, structural breaks, or both, we propose three classes of HAR models to forecast electricity volatility based on existing HAR models. The estimation results of the models showed that day-of-the-week effects only improve the fitting ability of HAR models for electricity volatility forecasting at the daily horizon, whereas structural breaks can improve the in-sample performance of HAR models when forecasting electricity volatility at daily, weekly, and monthly horizons. The out-of-sample analysis indicated that both day-of-the-week effects and structural breaks contain additional ex ante information for predicting electricity volatility, and in most cases, dummy variables used to measure structural breaks contain more out-of-sample predictive information than those used to measure day-of-the-week effects. The out-of-sample results were robust across three different methods. More importantly, we argue that adding dummy variables to measure day-of-the-week effects and structural breaks can improve the performance of most other existing HAR models for volatility forecasting in the electricity market.     

Trading and non-trading period realized market volatility: Does it matter for forecasting the volatility of US stocks?

We study the potential merits of using trading and non-trading period market volatilities to model and forecast the stock volatility over the next one to 22 days. We demonstrate the role of overnight volatility information by estimating heterogeneous autoregressive (HAR) model specifications with and without a trading period market risk factor using ten years of high-frequency data for the 431 constituents of the S&P 500 index. The stocks’ own overnight squared returns perform poorly across stocks and forecast horizons, as well as in the asset allocation exercise. In contrast, we find overwhelming evidence that the market-level volatility, proxied by S&P Mini futures, matters significantly for improving the model fit and volatility forecasting accuracy. The greatest model fit and forecast improvements are found for short-term forecast horizons of up to five trading days, and for the non-trading period market-level volatility. The documented increase in forecast accuracy is found to be associated with the stocks’ sensitivity to the market risk factor. Finally, we show that both the trading and non-trading period market realized volatilities are relevant in an asset allocation context, as they increase the average returns, Sharpe ratios and certainty equivalent returns of a mean–variance investor.     

The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange,stock, and bond markets

We study the forecasting of future realized volatility in the foreign exchange, stock, and bond markets from variables in our information set, including implied volatility backed out from option prices. Realized volatility is separated into its continuous and jump components, and the heterogeneous autoregressive (HAR) model is applied with implied volatility as an additional forecasting variable. A vector HAR (VecHAR) model for the resulting simultaneous system is introduced, controlling for possible endogeneity issues. We find that implied volatility contains incremental information about future volatility in all three markets, relative to past continuous and jump components, and it is an unbiased forecast in the foreign exchange and stock markets. Out-of-sample forecasting experiments confirm that implied volatility is important in forecasting future realized volatility components in all three markets. Perhaps surprisingly, the jump component is, to some extent, predictable, and options appear calibrated to incorporate information about future jumps in all three markets.     

Multivariate volatility forecasts for stock market indices

Volatility forecasts aim to measure future risk and they are key inputs for financial analysis. In this study, we forecast the realized variance as an observable measure of volatility for several major international stock market indices and accounted for the different predictive information present in jump, continuous, and option-implied variance components. We allowed for volatility spillovers in different stock markets by using a multivariate modeling approach. We used heterogeneous autoregressive (HAR)-type models to obtain the forecasts. Based an out-of-sample forecast study, we show that: (i) including option-implied variances in the HAR model substantially improves the forecast accuracy, (ii) lasso-based lag selection methods do not outperform the parsimonious day-week-month lag structure of the HAR model, and (iii) cross-market spillover effects embedded in the multivariate HAR model have long-term forecasting power.     

Exchange rates and oil prices: A multivariate stochastic volatility analysis

This paper uses the multivariate stochastic volatility (MSV) and the multivariate GARCH (MGARCH) models to investigate the volatility interactions between the oil market and the foreign exchange (FX) market, in an attempt to extract information intertwined in the two for better volatility forecast. Our analysis takes into account structural breaks in the data. We find that when the markets are relatively calm (before the 2008 crisis), both oil and FX markets respond to shocks simultaneously and therefore no interaction is detected in daily data. However, during turbulent time, there is bi-directional volatility interaction between the two. In other words, innovations that hit one market also have some impact on the other at a later date and thus using such a dependence significantly improves the forecasting power of volatility models. The MSV models outperform others in fitting the data and forecasting exchange rate volatility. However, the MGARCH models do better job in forecasting oil volatility.     

The impact of sentiment and attention measures on stock market volatility

We analyze the impact of sentiment and attention variables on the stock market volatility by using a novel and extensive dataset that combines social media, news articles, information consumption, and search engine data. We apply a state-of-the-art sentiment classification technique in order to investigate the question of whether sentiment and attention measures contain additional predictive power for realized volatility when controlling for a wide range of economic and financial predictors. Using a penalized regression framework, we identify the most relevant variables to be investors’ attention, as measured by the number of Google searches on financial keywords (e.g. “financial market” and “stock market”), and the daily volume of company-specific short messages posted on StockTwits. In addition, our study shows that attention and sentiment variables are able to improve volatility forecasts significantly, although the magnitudes of the improvements are relatively small from an economic point of view.     

Volatility forecasting in the Bitcoin market: A new proposed measure based on the VS-ACARR approach

This paper proposes a new volatility-spillover-asymmetric conditional autoregressive range (VS-ACARR) approach that takes into account the intraday information, the volatility spillover from crude oil as well as the volatility asymmetry (leverage effect) to model/forecast Bitcoin volatility (price range). An empirical application to Bitcoin and crude oil (WTI) price ranges shows the existence of strong volatility spillover from crude oil to the Bitcoin market and a weak leverage effect in the Bitcoin market. The VS-ACARR model yields higher forecasting accuracy than the GARCH, CARR, and VS-CARR models regarding out-of-sample forecast performance, suggesting that accounting for the volatility spillover and asymmetry can significantly improve the forecasting accuracy of Bitcoin volatility. The superior forecast performance of the VS-ACARR model is robust to alternative out-of-sample forecast windows. Our findings highlight the importance of accommodating intraday information, spillover from crude oil, and volatility asymmetry in forecasting Bitcoin volatility.     

Volatility forecasting in European government bond markets

In this paper we examine the predictive power of the heterogeneous autoregressive (HAR) model for the return volatility of major European government bond markets. The results from HAR-type volatility forecasting models show that past short- and medium-term volatility are significant predictors of the term structure of the intraday volatility of European bonds with maturities ranging from 1 year up to 30 years. When we decompose bond market volatility into its continuous and discontinuous (jump) component, we find that the jump component is a significant predictor. Moreover, we show that feedback from past short-term volatility to forecasts of future volatility is stronger in the days that precede monetary policy announcements.     

Forecasting national activity using lots of international predictors: An application to New Zealand

We assess the marginal predictive content of a large international dataset for forecasting GDP in New Zealand, an archetypal small open economy. We apply “data-rich” factor and shrinkage methods to efficiently handle hundreds of predictor series from many countries. The methods covered are principal components, targeted predictors, weighted principal components, partial least squares, elastic net and ridge regression. We find that exploiting a large international dataset can improve forecasts relative to data-rich approaches based on a large national dataset only, and also relative to more traditional approaches based on small datasets. This is in spite of New Zealand’s business and consumer confidence and expectations data capturing a substantial proportion of the predictive information in the international data. The largest forecasting accuracy gains from including international predictors are at longer forecast horizons. The forecasting performance achievable with the data-rich methods differs widely, with shrinkage methods and partial least squares performing best in handling the international data.