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First published: 11 April 2018 A large number of models have been developed in the literature to analyze and forecast changes in output dynamics. The objective of this paper was to compare the predictive ability of univariate and bivariate models, in terms of forecasting US gross national product (GNP) growth at different forecasting horizons, with the bivariate models containing information on a measure of economic uncertainty. Based on point and density forecast accuracy measures, as well as on equal predictive ability (EPA) and superior predictive ability (SPA) tests, we evaluate the relative forecasting performance of different model specifications over the quarterly period of 1919:Q2 until 2014:Q4. We find that the economic policy uncertainty (EPU) index should improve the accuracy of US GNP growth forecasts in bivariate models. We also find that the EPU exhibits similar forecasting ability to the term spread and outperforms other uncertainty measures such as the volatility index and geopolitical risk in predicting US recessions. While the Markov switching time-varying parameter vector autoregressive model yields the lowest values for the root mean squared error in most cases, we observe relatively low values for the log predictive density score, when using the Bayesian vector regression model with stochastic volatility. More importantly, our results highlight the importance of uncertainty in forecasting US GNP growth rates.

This paper analyzes the performance of the monthly economic policy uncertainty (EPU) index in predicting recessionary regimes of the (quarterly) U.S. GDP. In this regard, the authors apply a mixed-frequency Markov-switching vector autoregressive (MF-MSVAR) model, and compare its in-sample and out-of-sample forecasting performances to those of a Markov-switching vector autoregressive model (MS-VAR, where the EPU is averaged over the months to produce quarterly values) and a Markov-switching autoregressive (MS-AR) model. The results show that the MF-MS-VAR fits the different recession regimes, and provides out-of-sample forecasts of recession probabilities which are more accurate than those derived from the MS-VAR and MS-AR models. The results highlight the importance of using high-frequency values of the EPU, and not averaging them to obtain quarterly values, when forecasting recessionary regimes for the U.S. economy.

This paper uses the Markov-switching multifractal (MSM) model and generalized autoregressive conditional heteroscedasticity (GARCH)-type models to forecast oil price volatility over the time periods from January 02, 1875 to December 31, 1895 and from January 03, 1977 to March 24, 2014. Based on six different loss functions and by means of the superior predictive ability (SPA) test, we evaluate and compare their forecasting performance at short and long horizons. The empirical results indicate that none of our volatility models can uniformly outperform other models across all six different loss functions. However, the new MSM model comes out as the model that most often across forecasting horizons and subsamples cannot be outperformed by other models, with long memory GARCH-type models coming out second best.

This paper applies Markov-switching multifractal (MSM) processes to model and forecast carbon dioxide (CO2) emission price volatility, and compares their forecasting performance to the standard GARCH, fractionally integrated GARCH (FIGARCH) and the two-state Markov-switching GARCH (MS-GARCH) models via three loss functions (the mean squared error, the mean absolute error and the value-at-risk). We evaluate the performance of these models via the superior predictive ability test. We find that the forecasts based on the MSM model cannot be outperformed by its competitors under the vast majority of criteria and forecast horizons, while MS-GARCH mostly comes out as the least successful model. Applying various VaR backtesting procedures, we do, however, not find significant differences in the performance of the candidate models under this particular criterion. We also find that we cannot reject the null hypothesis of MSM forecasts encompassing those of GARCH-type models. In line with this result, optimally combined forecasts do indeed hardly improve upon the best single models in our sample.

This thesis covers the application of multifractal processes in modeling financial time series. It aims to demonstrate the capacity and the robustness of the multifractal processes to better model return volatility and ultra high frequency financial data than both the generalized autoregressive conditional heteroscedasticity (GARCH)-type and autoregressive conditional duration (ACD) models currently used in research and practice. The thesis is comprised of four main parts that particularize the different procedures and the main findings. In the first part of the thesis we first delineate the genesis of multifractal (MF) measures and processes and how one can construct a simple MF measure. We outline the generic properties of the MF processes, mention how they motivate financial time series models, and present the different tools developed for the estimation of the MF models and the forecasting of return volatilities and some empirical results. Second, we give a short overview of both autoregressive conditional duration (ACD) models and Markov switching multifractal duration (MSMD) models. We start with some theoretical microstructure literature that motivate both models. We present ACD and MSMD models and their subsequent extensions. Finally, we cite the different diagnostic tests developed in the literature for assessing their adequacy and provide some prominent empirical studies. The second part deals with the application the Markov-switching multifractal (MSM) model and generalized autoregressive conditional heteroscedasticity (GARCH) type models in forecasting crude oil price volatility. Based on six different loss functions and by means of the superior predictive ability (SPA) test of Hansen (2005) we evaluate and compare their forecasting performance at short- and long-horizons. The results give evidence that none of our volatility models can outperform other models across all six different loss functions. However, the long memory GARCH-type models and the MSM model seem to be more appropriate in terms of fitting and forecasting oil price volatility. We also found that forecast combinations of long memory GARCH-type models and the MSM lead to an improvement in forecasting crude oil price volatility. The third and longest part of the thesis compares the predictive ability of the Markov switching multifractal duration (MSMD) model recently introduced by Chen et al. (2013) to those of the standard ACD (cf. Engle and Russell, 1998), Log-ACD (cf. Bauwens and Giot, 2000), and fractionally integrated ACD (FIACD) (cf. Jasiak, 1998) models. We assume that innovations in the ACD and Log-ACD models follow Weibull, Burr, generalized gamma and Lognormal distributions. For FIACD we only consider the case where the innovation is standard exponentially distributed. We assess the forecasting performance of the models using density forecasts evaluation methodologies proposed by Diebold et al. (1998) and the likelihood ratio test of Berkowitz (2001). We complement these methodologies with Kolmogorov-Smirnov and Anderson-Darling distances (cf. Rachev and Mittnik, 2000). Empirically, results are quite nice and speak for the MSMD model. In fact, the MSMD model can better capture the long memory and the fat tails observed in trade and price duration data, and therefore, outperforms both the FIACD, ACD and Log-ACD models. We also found that certain distributional assumptions for the innovations strongly enhance the forecasting performance of the ACD and Log-ACD models. In line with the last result, we want to know to what extent different distributional assumptions for the innovation in the MSMD model may influence the model’s forecasting performance. So, we assume that the innovation in the MSMD model follows generalized gamma or Burr distribution. To compare and select the model that provides better fit to the empirical data (trade, price and volume durations) we make use of the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the likelihood ratio test. Surprisingly, both distributional assumptions for the innovation do not much affect the predictive ability of the model. It seems that the ability of the MSMD model to fit financial duration data largely stems from the multifractal processes. Third, we generalize the univariate MSMD model to a bivariate one. The bivariate MSMD model is substantially an adaptation of the bivariate Markov switching multifractal (MSM) process proposed by Calvet et al. (2006) to high frequency financial data. We apply the bivariate MSMD model to analyze the co-movement between the bid-ask spreads of different stocks. The results indicate that bid-ask spreads of sector-specific or cross-sector stocks may be simultaneously affected by arrival of information in the market. Fourth, we apply the standard MSMD and the generalized gamma ACD (GGACD) models to forecast irregularly spaced intra-day value-at-risk (ISIVaR) in a semi-parametric framework. We assess the performance of both models to produce accurate irregularly spaced intra-day VaR via the generalized moments method (GMM) duration-based test developed by Candelon et al. (2011). The results show that the MSMD model outperforms the GGACD model and can be used in practice to manage market risk. The last part summarizes the main findings of the thesis and presents some outlooks for future research.

This chapter provides an overview over the recently developed so called multifractal (MF) approach for modeling and forecasting volatility. We outline the genesis of this approach from similar models of turbulent flows in statistical physics and provide details on different specifications of multifractal time series models in finance, available methods for their estimation, and the current state of their empirical applications.