Bayesian Forecasting for Financial Risk Management,Pre and Post the Global Financial Crisis

Value‐at‐risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models is compared, including standard, threshold nonlinear and Markov switching generalized autoregressive conditional heteroskedasticity (GARCH) specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student‐t, skewed‐t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia–Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models outperformed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre crisis, while at the 1% level during and post crisis, for a 1‐day horizon, models with skewed‐t errors ranked best, while integrated GARCH models were favoured at the 5% level; (iii) all models forecast VaR less accurately and anti‐conservatively post crisis. Copyright © 2011 John Wiley & Sons, Ltd.     

Forecasting the price of crude oil via convenience yield predictions

The paper develops an oil price forecasting technique which is based on the present value model of rational commodity pricing. The approach suggests shifting the forecasting problem to the marginal convenience yield, which can be derived from the cost‐of‐carry relationship. In a recursive out‐of‐sample analysis, forecast accuracy at horizons within one year is checked by the root mean squared error as well as the mean error and the frequency of a correct direction‐of‐change prediction. For all criteria employed, the proposed forecasting tool outperforms the approach of using futures prices as direct predictors of future spot prices. Vis‐à‐vis the random‐walk model, it does not significantly improve forecast accuracy but provides valuable statements on the direction of change. Copyright © 2007 John Wiley & Sons, Ltd.     

Predicting the Distribution of Stock Returns: Model Formulation,Statistical Evaluation,VaR Analysis and Economic Significance

A large literature has investigated predictability of the conditional mean of low‐frequency stock returns by macroeconomic and financial variables; however, little is known about predictability of the conditional distribution. We look at one‐step‐ahead out‐of‐sample predictability of the conditional distribution of monthly US stock returns in relation to the macroeconomic and financial environment. Our methodological approach is innovative: we consider several specifications for the conditional density and combinations schemes. Our results are as follows: the entire density is predicted under combination schemes as applied to univariate GARCH models with Gaussian innovations; the Bayesian winner in relation to GARCH‐skewed‐t models is informative about the 5% value at risk; the average realised utility of a mean–variance investor is maximised under the Bayesian winner as applied to GARCH models with symmetric Student t innovations. Our results have two implications: the best prediction model depends on the evaluation criterion; and combination schemes outperform individual models. Copyright © 2015 John Wiley & Sons, Ltd.     

On the Predictive Information of Futures' Prices: A Wavelet‐Based Assessment

While in speculative markets forward prices could be regarded as natural predictors for future spot rates, empirically, forward prices often fail to indicate ex ante the direction of price movements. In terms of forecasting, the random walk approximation of speculative prices has been established to provide ‘naive’ predictors that are most difficult to outperform by both purely backward‐looking time series models and more structural approaches processing information from forward markets. We empirically assess the implicit predictive content of forward prices by means of wavelet‐based prediction of two foreign exchange (FX) rates and the price of Brent oil quoted either in US dollars or euros. Essentially, wavelet‐based predictors are smoothed auxiliary (padded) time series quotes that are added to the sample information beyond the forecast origin. We compare wavelet predictors obtained from padding with constant prices (i.e. random walk predictors) and forward prices. For the case of FX markets, padding with forward prices is more effective than padding with constant prices, and, moreover, respective wavelet‐based predictors outperform purely backward‐looking time series approaches (ARIMA). For the case of Brent oil quoted in US dollars, wavelet‐based predictors do not signal predictive content of forward prices for future spot prices. Copyright © 2016 John Wiley & Sons, Ltd.     

Short‐term salmon price forecasting

This study establishes a benchmark for short‐term salmon price forecasting. The weekly spot price of Norwegian farmed Atlantic salmon is predicted 1–5 weeks ahead using data from 2007 to 2014. Sixteen alternative forecasting methods are considered, ranging from classical time series models to customized machine learning techniques to salmon futures prices. The best predictions are delivered by k‐nearest neighbors method for 1 week ahead; vector error correction model estimated using elastic net regularization for 2 and 3 weeks ahead; and futures prices for 4 and 5 weeks ahead. While the nominal gains in forecast accuracy over a naïve benchmark are small, the economic value of the forecasts is considerable. Using a simple trading strategy for timing the sales based on price forecasts could increase the net profit of a salmon farmer by around 7%.     

Forecasting Interest Rates and Yield Spreads: The Informational Content of Implied Futures Yields and Best-fitting Forward Rate Models

Forecasts of interest rates for different maturities are essential for forecasts of asset prices. The growth of derivatives markets coupled with the development of complex theories of the term structure of interest rates have provided forecasters with a rich array of variables for predicting interest rates and yield spreads. This paper extends previous work on forecasting future interest rates and yield spreads using market data for T-bills, T-Notes, and Treasury Bond spot and futures contracts. The information conveyed in technical models that use market data is also assessed, using a recent innovation in interest rate modelling, the maximum smoothness approach. Forecasts from this model are compared with predicted yields and yield spreads derived from futures prices as well as with those of the random walk model. The results show some evidence of market segmentation, with more arbitrage evident for nearby maturities. Market participants appear to show a greater degree of consensus on short-term interest rates than on longer-term interest rates. There is some indication that forecasts from the futures markets are marginally better than those provided by those of the maximum-smoothness approach, consistent with the informational advantages of futures markets. Finally, futures and maximum-smoothness market forecasts are shown to outperform those of the random walk model.© 1997 John Wiley & Sons, Ltd.     

Step-ahead spot price densities using daily synchronously reported prices and wind forecasts

This paper uses non-linear methodologies to follow the synchronously reported relationship between the Nordic/Baltic electric daily spot auction prices and geographical relevant wind forecasts in MWh from early 2013 to 2020. It is a well-known market (auctions) microstructure fact that the daily wind forecasts are information available to the market before the daily auction bid deadline at 11 a.m. The main objective is therefore to establish conditional and marginal step ahead spot price density forecast using a stochastic representation of the lagged, synchronously reported and stationary spot price and wind forecast movements. Using an upward expansion path applying the Schwarz (Bayesian information criterion [BIC]) criterion and a battery of residual test statistics, an optimal maximum likelihood process density is suggested. The optimal specification reports a significant negative covariance between the daily price and wind forecast movements. Conditional on bivariate lags from the SNP information and using the known market information for wind forecast movements at t₁, the paper establishes one-step-ahead bivariate and marginal day-ahead spot price movement densities. The result shows that wind forecasts significantly influence the synchronously reported spot price densities (means and volatilities). The paper reports day-ahead bivariate and marginal densities for spot price movements conditional on several very plausible price and wind forecast movements. The paper suggests day-ahead spot price predictions from conditional and synchronously reported wind forecasts movements. The information should increase market participants spot market insight and consequently make spot price predictions more accurate and the confidence interval considerably narrower.     

Conditional predictability of daily exchange rates

At what forecast horizon is one time series more predictable than another? This paper applies the Diebold–Kilian conditional predictability measure to assess the out‐of‐sample performance of three alternative models of daily GBP/USD and DEM/USD exchange rate returns. Predictability is defined as a non‐linear statistic of a model's relative expected losses at short and long forecast horizons, allowing flexible choice of both the estimation procedure and loss function. The long horizon is set to 2 weeks and one month ahead and forecasts evaluated according to MSE loss. Bootstrap methodology is used to estimate the data's conditional predictability using GARCH models. This is then compared to predictability under a random walk and a model using the prediction bias in uncovered interest parity (UIP). We find that both exchange rates are less predictable using GARCH than using a random walk, but they are more predictable using UIP than a random walk. Predictability using GARCH is relatively higher for the 2‐weeks‐than for the 1‐month long forecast horizon. Comparing the results using a random walk to that using UIP reveals ‘pockets’ of predictability, that is, particular short horizons for which predictability using the random walk exceeds that using UIP, or vice versa. Overall, GBP/USD returns appear more predictable than DEM/USD returns at short horizons. Copyright © 2002 John Wiley & Sons, Ltd.     

Stock market volatility and the forecasting performance of stock index futures

This study attempts to apply the general equilibrium model of stock index futures with both stochastic market volatility and stochastic interest rates to the TAIFEX and the SGX Taiwan stock index futures data, and compares the predictive power of the cost of carry and the general equilibrium models. This study also represents the first attempt to investigate which of the five volatility estimators can enhance the forecasting performance of the general equilibrium model. Additionally, the impact of the up‐tick rule and other various explanatory factors on mispricing is also tested using a regression framework. Overall, the general equilibrium model outperforms the cost of carry model in forecasting prices of the TAIFEX and the SGX futures. This finding indicates that in the higher volatility of the Taiwan stock market incorporating stochastic market volatility into the pricing model helps in predicting the prices of these two futures. Furthermore, the comparison results of different volatility estimators support the conclusion that the power EWMA and the GARCH(1,1) estimators can enhance the forecasting performance of the general equilibrium model compared to the other estimators. Additionally, the relaxation of the up‐tick rule helps reduce the degree of mispricing. Copyright © 2008 John Wiley & Sons, Ltd.     

Predicting opening spot prices using extended futures trading

Previous studies found that extended futures trading contains useful information in explaining subsequent overnight spot returns. This study therefore compares the performance of using the extended trading of the TAIFEX (Taiwan Futures Exchange) index futures and single‐stock futures to predict their opening underlying spot prices. Furthermore, according to the efficient market hypothesis, the share price fully reflects all the information available and should adjust to new information instantaneously. However, several studies have demonstrated that short‐sales restrictions delay the speed of price adjustment to negative information. The relevant question is whether short‐selling restrictions also slow down the speed at which the opening spot price adjusts to the new information revealed through extended futures trading, and thus reducing the price prediction function of extended futures trading. The empirical results find that using the opening futures price and the prediction method proposed in this study can more accurately predict the opening spot price on the same day. Furthermore, the performance of using the extended trading of index futures to predict the opening spot index price is superior to that of using the extended trading of single‐stock futures to predict the opening stock price. Finally, as found in previous studies, short‐selling restrictions also slow down the speed of stock price adjustment to the new information revealed through extended futures trading. Thus both the up‐tick rule and the short‐selling bans (especially the latter) negatively affect the price forecasting performance of extended futures trading.     

Forecasting Stock Returns: Do Commodity Prices Help?

This paper examines the relationship between stock prices and commodity prices and whether this can be used to forecast stock returns. As both prices are linked to expected future economic performance they should exhibit a long‐run relationship. Moreover, changes in sentiment towards commodity investing may affect the nature of the response to disequilibrium. Results support cointegration between stock and commodity prices, while Bai–Perron tests identify breaks in the forecast regression. Forecasts are computed using a standard fixed (static) in‐sample/out‐of‐sample approach and by both recursive and rolling regressions, which incorporate the effects of changing forecast parameter values. A range of model specifications and forecast metrics are used. The historical mean model outperforms the forecast models in both the static and recursive approaches. However, in the rolling forecasts, those models that incorporate information from the long‐run stock price/commodity price relationship outperform both the historical mean and other forecast models. Of note, the historical mean still performs relatively well compared to standard forecast models that include the dividend yield and short‐term interest rates but not the stock/commodity price ratio. Copyright © 2014 John Wiley & Sons, Ltd.     

Predicting crypto‐currencies using sparse non‐Gaussian state space models

In this paper we forecast daily returns of crypto‐currencies using a wide variety of different econometric models. To capture salient features commonly observed in financial time series like rapid changes in the conditional variance, non‐normality of the measurement errors and sharply increasing trends, we develop a time‐varying parameter VAR with t‐distributed measurement errors and stochastic volatility. To control for overparametrization, we rely on the Bayesian literature on shrinkage priors, which enables us to shrink coefficients associated with irrelevant predictors and/or perform model specification in a flexible manner. Using around one year of daily data, we perform a real‐time forecasting exercise and investigate whether any of the proposed models is able to outperform the naive random walk benchmark. To assess the economic relevance of the forecasting gains produced by the proposed models we, moreover, run a simple trading exercise.     

Prediction of α‐stable GARCH and ARMA‐GARCH‐M models

The best prediction of generalized autoregressive conditional heteroskedasticity (GARCH) models with α‐stable innovations, α‐stable power‐GARCH models and autoregressive moving average (ARMA) models with GARCH in mean effects (ARMA‐GARCH‐M) are proposed. We present a sufficient condition for stationarity of α‐stable GARCH models. The prediction methods are easy to implement in practice. The proposed prediction methods are applied for predicting future values of the daily SP500 stock market and wind speed data.     

Modeling and forecasting realized volatility in German–Austrian continuous intraday electricity prices

This paper uses high‐frequency continuous intraday electricity price data from the EPEX market to estimate and forecast realized volatility. Three different jump tests are used to break down the variation into jump and continuous components using quadratic variation theory. Several heterogeneous autoregressive models are then estimated for the logarithmic and standard deviation transformations. Generalized autoregressive conditional heteroskedasticity (GARCH) structures are included in the error terms of the models when evidence of conditional heteroskedasticity is found. Model selection is based on various out‐of‐sample criteria. Results show that decomposition of realized volatility is important for forecasting and that the decision whether to include GARCH‐type innovations might depend on the transformation selected. Finally, results are sensitive to the jump test used in the case of the standard deviation transformation.     

An outlier robust GARCH model and forecasting volatility of exchange rate returns

Since volatility is perceived as an explicit measure of risk, financial economists have long been concerned with accurate measures and forecasts of future volatility and, undoubtedly, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model has been widely used for doing so. It appears, however, from some empirical studies that the GARCH model tends to provide poor volatility forecasts in the presence of additive outliers. To overcome the forecasting limitation, this paper proposes a robust GARCH model (RGARCH) using least absolute deviation estimation and introduces a valuable estimation method from a practical point of view. Extensive Monte Carlo experiments substantiate our conjectures. As the magnitude of the outliers increases, the one‐step‐ahead forecasting performance of the RGARCH model has a more significant improvement in two forecast evaluation criteria over both the standard GARCH and random walk models. Strong evidence in favour of the RGARCH model over other competitive models is based on empirical application. By using a sample of two daily exchange rate series, we find that the out‐of‐sample volatility forecasts of the RGARCH model are apparently superior to those of other competitive models. Copyright © 2002 John Wiley & Sons, Ltd.     

Foreign exchange market prediction with multiple classifiers

Foreign exchange market prediction is attractive and challenging. According to the efficient market and random walk hypotheses, market prices should follow a random walk pattern and thus should not be predictable with more than about 50% accuracy. In this article, we investigate the predictability of foreign exchange spot rates of the US dollar against the British pound to show that not all periods are equally random. We used the Hurst exponent to select a period with great predictability. Parameters for generating training patterns were determined heuristically by auto‐mutual information and false nearest‐neighbor methods. Some inductive machine‐learning classifiers—artificial neural network, decision tree, k‐nearest neighbor, and naïve Bayesian classifier—were then trained with these generated patterns. Through appropriate collaboration of these models, we achieved a prediction accuracy of up to 67%. Copyright © 2009 John Wiley & Sons, Ltd.     

Lead-lag relationship between spot index and futures price of the nikkei stock average

This paper examines the lead-lag relationship between the spot index and futures price of the Nikkei Stock Average. Using daily data in the post-crash period we investigate the interaction between the spot and futures series through the error correction model. Two versions of error correction models are considered, depending on the postulated long-run equilibrium relationship. It is found that lagged changes in the futures price affect the short-term adjustment in the spot index, but not vice versa. Forecasting models for the spot index are also constructed using the univariate time series approach and the vector autoregressive method. For the post-sample forecast comparison the error correction models produce the best results. The vector autoregressive method performs better than the martingale model, while the univariate time series method gives the poorest forecasts.     

Why do regime‐switching models forecast so badly?

Most non‐linear techniques give good in‐sample fits to exchange rate data but are usually outperformed by random walks or random walks with drift when used for out‐of‐sample forecasting. In the case of regime‐switching models it is possible to understand why forecasts based on the true model can have higher mean squared error than those of a random walk or random walk with drift. In this paper we provide some analytical results for the case of a simple switching model, the segmented trend model. It requires only a small misclassification, when forecasting which regime the world will be in, to lose any advantage from knowing the correct model specification. To illustrate this we discuss some results for the DM/dollar exchange rate. We conjecture that the forecasting result is more general and describes limitations to the use of switching models for forecasting. This result has two implications. First, it questions the leading role of the random walk hypothesis for the spot exchange rate. Second, it suggests that the mean square error is not an appropriate way to evaluate forecast performance for non‐linear models. Copyright © 1999 John Wiley & Sons, Ltd.     

The Role of High‐Frequency Intra‐daily Data,Daily Range and Implied Volatility in Multi‐period Value‐at‐Risk Forecasting

This paper assesses the informational content of alternative realized volatility estimators, daily range and implied volatility in multi‐period out‐of‐sample Value‐at‐Risk (VaR) predictions. We use the recently proposed Realized GARCH model combined with the skewed Student's t distribution for the innovations process and a Monte Carlo simulation approach in order to produce the multi‐period VaR estimates. Our empirical findings, based on the S&P 500 stock index, indicate that almost all realized and implied volatility measures can produce statistically and regulatory precise VaR forecasts across forecasting horizons, with the implied volatility being especially accurate in monthly VaR forecasts. The daily range produces inferior forecasting results in terms of regulatory accuracy and Basel II compliance. However, robust realized volatility measures, which are immune against microstructure noise bias or price jumps, generate superior VaR estimates in terms of capital efficiency, as they minimize the opportunity cost of capital and the Basel II regulatory capital. Copyright © 2013 John Wiley & Sons, Ltd.     

Forecasting volatility with outliers in GARCH models

In this paper, we detect and correct abnormal returns in 17 French stocks returns and the French index CAC40 from additive‐outlier detection method in GARCH models developed by Franses and Ghijsels (1999) and extended to innovative outliers by Charles and Darné (2005). We study the effects of outlying observations on several popular econometric tests. Moreover, we show that the parameters of the equation governing the volatility dynamics are biased when we do not take into account additive and innovative outliers. Finally, we show that the volatility forecast is better when the data are cleaned of outliers for several step‐ahead forecasts (short, medium‐ and long‐term) even if we consider a GARCH‐t process. Copyright © 2008 John Wiley & Sons, Ltd.