Improved autoregressive forecasts in the presence of non-normal errors

This paper is concerned with obtaining more accurate point forecasts in the presence of non-normal errors. Specifically, we apply the residual augmented least-squares (RALS) estimator to autoregressive models to utilize the additional moment restrictions embodied in non-normal errors. Monte Carlo experiments are performed to compare our RALS forecasts to forecasts based on the ordinary least-squares estimator and the least absolute deviations (LAD) estimator. We find that the RALS approach provides superior forecasts when the data are skewed. Compared to the LAD forecast, the RALS forecast has smaller mean squared prediction errors in the baseline case with normal errors.     

Improved multivariate prediction regions for Markov process models

This paper concerns the specification of multivariate prediction regions which may be useful in time series applications whenever we aim at considering not just one single forecast but a group of consecutive forecasts. We review a general result on improved multivariate prediction and we use it in order to calculate conditional prediction intervals for Markov process models so that the associated coverage probability turns out to be close to the target value. This improved solution is asymptotically superior to the estimative one, which is simpler but it may lead to unreliable predictive conclusions. An application to general autoregressive models is presented, focusing in particular on AR and ARCH models.     

Statistical models for short- and long-term forecasts of snow depth

Forecasting of future snow depths is useful for many applications like road safety, winter sport activities, avalanche risk assessment and hydrology. Motivated by the lack of statistical forecasts models for snow depth, in this paper we present a set of models to fill this gap. First, we present a model to do short-term forecasts when we assume that reliable weather forecasts of air temperature and precipitation are available. The covariates are included nonlinearly into the model following basic physical principles of snowfall, snow aging and melting. Due to the large set of observations with snow depth equal to zero, we use a zero-inflated gamma regression model, which is commonly used to similar applications like precipitation. We also do long-term forecasts of snow depth and much further than traditional weather forecasts for temperature and precipitation. The long-term forecasts are based on fitting models to historic time series of precipitation, temperature and snow depth. We fit the models to data from six locations in Norway with different climatic and vegetation properties. Forecasting five days into the future, the results showed that, given reliable weather forecasts of temperature and precipitation, the forecast errors in absolute value was between 3 and 7?cm for different locations in Norway. Forecasting three weeks into the future, the forecast errors were between 7 and 16?cm.     

Real-Time Forecasts of the Real Price of Oil

We construct a monthly real-time dataset consisting of vintages for 1991.1–2010.12 that is suitable for generating forecasts of the real price of oil from a variety of models. We document that revisions of the data typically represent news, and we introduce backcasting and nowcasting techniques to fill gaps in the real-time data. We show that real-time forecasts of the real price of oil can be more accurate than the no-change forecast at horizons up to 1 year. In some cases, real-time mean squared prediction error (MSPE) reductions may be as high as 25% 1 month ahead and 24% 3 months ahead. This result is in striking contrast to related results in the literature for asset prices. In particular, recursive vector autoregressive (VAR) forecasts based on global oil market variables tend to have lower MSPE at short horizons than forecasts based on oil futures prices, forecasts based on autoregressive (AR) and autoregressive moving average (ARMA) models, and the no-change forecast. In addition, these VAR models have consistently higher directional accuracy.     

Term structure forecasting in affine framework with time-varying volatility

This study extends the affine Nelson–Siegel model by introducing the time-varying volatility component in the observation equation of yield curve, modeled as a standard EGARCH process. The model is illustrated in state-space framework and empirically compared to the standard affine and dynamic Nelson–Siegel model in terms of in-sample fit and out-of-sample forecast accuracy. The affine based extended model that accounts for time-varying volatility outpaces the other models for fitting the yield curve and produces relatively more accurate 6- and 12-month ahead forecasts, while the standard affine model comes with more precise forecasts for the very short forecast horizons. The study concludes that the standard and affine Nelson–Siegel models have higher forecasting capability than their counterpart EGARCH based models for the short forecast horizons, i.e., 1 month. The EGARCH based extended models have excellent performance for the medium and longer forecast horizons.     

Forecast Evaluation in the Presence of Unobserved Volatility

A number of volatility forecasting studies have led to the perception that the ARCH- and Stochastic Volatility-type models provide poor out-of-sample forecasts of volatility. This is primarily based on the use of traditional forecast evaluation criteria concerning the accuracy and the unbiasedness of forecasts. In this paper we provide an analytical assessment of volatility forecasting performance. We use the volatility and log volatility framework to prove how the inherent noise in the approximation of the true- and unobservable-volatility by the squared return, results in a misleading forecast evaluation, inflating the observed mean squared forecast error and invalidating the Diebold-Mariano statistic. We analytically characterize this noise and explicitly quantify its effects assuming normal errors. We extend our results using more general error structures such as the Compound Normal and the Gram-Charlier classes of distributions. We argue that evaluation problems are likely to be exacerbated by non-normality of the shocks and that non-linear and utility-based criteria can be more suitable for the evaluation of volatility forecasts.     

Time series forecasting with neural networks: a comparative study using the air line data

This case-study fits a variety of neural network (NN) models to the well-known air line data and compares the resulting forecasts with those obtained from the Box–Jenkins and Holt–Winters methods. Many potential problems in fitting NN models were revealed such as the possibility that the fitting routine may not converge or may converge to a local minimum. Moreover it was found that an NN model which fits well may give poor out-of-sample forecasts. Thus we think it is unwise to apply NN models blindly in 'black box' mode as has sometimes been suggested. Rather, the wise analyst needs to use traditional modelling skills to select a good NN model, e.g. to select appropriate lagged variables as the 'inputs'. The Bayesian information criterion is preferred to Akaike's information criterion for comparing different models. Methods of examining the response surface implied by an NN model are examined and compared with the results of alternative nonparametric procedures using generalized additive models and projection pursuit regression. The latter imposes less structure on the model and is arguably easier to understand.     

FORECASTING VOLATILITY IN THE PRESENCE OF MODEL INSTABILITY

Recent advances in financial econometrics have allowed for the construction of efficient ex post measures of daily volatility. This paper investigates the importance of instability in models of realised volatility and their corresponding forecasts. Testing for model instability is conducted with a subsampling method. We show that removing structurally unstable data of a short duration has a negligible impact on the accuracy of conditional mean forecasts of volatility. In contrast, it does provide a substantial improvement in a model's forecast density of volatility. In addition, the forecasting performance improves, often dramatically, when we evaluate models on structurally stable data.     

Forecasting interest rates volatilities by GARCH (1,1) and stochastic volatility models

In this paper, we compare the forecast ability of GARCH(1,1) and stochastic volatility models for interest rates. The stochastic volatility is estimated using Markov chain Monte Carlo methods. The comparison is based on daily data from 1994 to 1996 for the ten year swap rates for Deutsch Mark, Japanese Yen, and Pound Sterling. Various forecast horizons are considered. It turns out that forecasts based on stochastic volatility models are in most cases superiour to those obtained by GARCH(1,1) models.     

Forecast Evaluation in the Presence of Unobserved Volatility

Abstract

A number of volatility forecasting studies have led to the perception that the ARCH- and Stochastic Volatility-type models provide poor out-of-sample forecasts of volatility. This is primarily based on the use of traditional forecast evaluation criteria concerning the accuracy and the unbiasedness of forecasts. In this paper we provide an analytical assessment of volatility forecasting performance. We use the volatility and log volatility framework to prove how the inherent noise in the approximation of the true- and unobservable-volatility by the squared return, results in a misleading forecast evaluation, inflating the observed mean squared forecast error and invalidating the Diebold–Mariano statistic. We analytically characterize this noise and explicitly quantify its effects assuming normal errors. We extend our results using more general error structures such as the Compound Normal and the Gram–Charlier classes of distributions. We argue that evaluation problems are likely to be exacerbated by non-normality of the shocks and that non-linear and utility-based criteria can be more suitable for the evaluation of volatility forecasts.     

基于深度学习LSTM神经网络的全球股票指数预测研究

作为深度学习技术的经典模型之一，长短期记忆（LSTM）神经网络在挖掘序列数据长期依赖关系中极具优势。基于深度神经网络优化技术，本文构造了一个深层LSTM神经网络并将其应用于全球30个股票指数三种不同期限的预测研究，结果发现：①LSTM神经网络具有很强的泛化能力，对全部指数不同期限的预测效果均很稳定；②LSTM神经网络具有优秀的预测精度，相比三种对照模型（SVR，MLP和ARIMA），其对全部指数的平均预测精度在不同期限上均有提升；③LSTM神经网络能够有效控制误差波动，其对全部指数的平均预测稳定度相比三种对照模型在不同期限上亦均有提高。鉴于LSTM神经网络在预测精度和稳定度两方面的优势，其未来在金融预测中将有广阔的应用前景。     

SEMIFAR forecasts, with applications to foreign exchange rates

SEMIFAR models introduced in Beran (1997. Estimating trends, long-range dependence and nonstationarity, preprint) provide a semiparametric modelling framework that enables the data analyst to separate deterministic and stochastic trends as well as short- and long-memory components in an observed time series. A correct distinction between these components, and in particular, the decision which of the components may be present in the data have an important impact on forecasts. In this paper, forecasts and forecast intervals for SEMIFAR models are obtained. The forecasts are based on an extrapolation of the nonparametric trend function and optimal forecasts of the stochastic component. In the data analytical part of the paper, the proposed method is applied to foreign exchange rates from Europe and Asia.     

Using large data sets to forecast sectoral employment

We use several models using classical and Bayesian methods to forecast employment for eight sectors of the US economy. In addition to using standard vector-autoregressive and Bayesian vector autoregressive models, we also augment these models to include the information content of 143 additional monthly series in some models. Several approaches exist for incorporating information from a large number of series. We consider two multivariate approaches—extracting common factors (principal components) and Bayesian shrinkage. After extracting the common factors, we use Bayesian factor-augmented vector autoregressive and vector error-correction models, as well as Bayesian shrinkage in a large-scale Bayesian vector autoregressive models. For an in-sample period of January 1972 to December 1989 and an out-of-sample period of January 1990 to March 2010, we compare the forecast performance of the alternative models. More specifically, we perform ex-post and ex-ante out-of-sample forecasts from January 1990 through March 2009 and from April 2009 through March 2010, respectively. We find that factor augmented models, especially error-correction versions, generally prove the best in out-of-sample forecast performance, implying that in addition to macroeconomic variables, incorporating long-run relationships along with short-run dynamics play an important role in forecasting employment. Forecast combination models, however, based on the simple average forecasts of the various models used, outperform the best performing individual models for six of the eight sectoral employment series.     

General partially linear additive transformation model with right-censored data

We propose a class of general partially linear additive transformation models (GPLATM) with right-censored survival data in this work. The class of models are flexible enough to cover many commonly used parametric and nonparametric survival analysis models as its special cases. Based on the B spline interpolation technique, we estimate the unknown regression parameters and functions by the maximum marginal likelihood estimation method. One important feature of the estimation procedure is that it does not need the baseline and censoring cumulative density distributions. Some numerical studies illustrate that this procedure can work very well for the moderate sample size.     

Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, and estimate the copula using Bayesian methods. We examine the forecasting performance of the model for four U.S. macroeconomic variables between 1975:Q1 and 2011:Q2 using quarterly real-time data. We find that the point and density forecasts from the copula model are competitive with those from a Bayesian VAR. During the recent recession the forecast densities exhibit substantial asymmetry, avoiding some of the pitfalls of the symmetric forecast densities from the Bayesian VAR. We show that the asymmetries in the predictive distributions of GDP growth and inflation are similar to those found in the probabilistic forecasts from the Survey of Professional Forecasters. Last, we find that unlike the linear VAR model, our fitted Gaussian copula models exhibit nonlinear dependencies between some macroeconomic variables. This article has online supplementary material.     

Quantile smoothing in financial time series

Various parametric models have been designed to analyze volatility in time series of financial market data. For maximum likelihood estimation these parametric methods require the assumption of a known conditional distribution. In this paper we examine the conditional distribution of daily DAX returns with the help of nonparametric methods. We use kernel estimators for conditional quantiles resulting from a kernel estimation of conditional distributions. This work was financially supported by the Deutsche Forschungsgemeinschaft     

A multivariate volatility vine copula model

This article proposes a dynamic framework for modeling and forecasting of realized covariance matrices using vine copulas to allow for more flexible dependencies between assets. Our model automatically guarantees positive definiteness of the forecast through the use of a Cholesky decomposition of the realized covariance matrix. We explicitly account for long-memory behavior by using fractionally integrated autoregressive moving average (ARFIMA) and heterogeneous autoregressive (HAR) models for the individual elements of the decomposition. Furthermore, our model incorporates non-Gaussian innovations and GARCH effects, accounting for volatility clustering and unconditional kurtosis. The dependence structure between assets is studied using vine copula constructions, which allow for nonlinearity and asymmetry without suffering from an inflexible tail behavior or symmetry restrictions as in conventional multivariate models. Further, the copulas have a direct impact on the point forecasts of the realized covariances matrices, due to being computed as a nonlinear transformation of the forecasts for the Cholesky matrix. Beside studying in-sample properties, we assess the usefulness of our method in a one-day-ahead forecasting framework, comparing recent types of models for the realized covariance matrix based on a model confidence set approach. Additionally, we find that in Value-at-Risk (VaR) forecasting, vine models require less capital requirements due to smoother and more accurate forecasts.     

Robust bootstrap densities for dynamic conditional correlations: implications for portfolio selection and Value-at-Risk

ABSTRACT

Many financial decisions such as portfolio allocation, risk management, option pricing and hedge strategies are based on the forecast of the conditional variances, covariances and correlations of financial returns. Although the decisions depend on the forecasts covariance matrix little is known about effects of outliers on the uncertainty associated with these forecasts. In this paper we analyse these effects on the context of dynamic conditional correlation models when the uncertainty is measured using bootstrap methods. We also propose a bootstrap procedure to obtain forecast densities for return, volatilities, conditional correlation and Value-at-Risk that is robust to outliers. The results are illustrated with simulated and real data.     

Bootstrapping an Econometric Model: Some Empirical Results

The bootstrap, like the jackknife, is a technique for estimating standard errors. The idea is to use Monte Carlo simulation, based on a nonparametric estimate of the underlying error distribution. The bootstrap will be applied to an econometric model describing the demand for capital, labor, energy, and materials. The model is fitted by three-stage least squares. In sharp contrast with previous results, the coefficient estimates and the estimated standard errors perform very well. However, the model's forecasts show serious bias and large random errors, significantly understated by the conventional standard error of forecast.     

Forecasting the spot price of gold:combined forecast approaches versus a composite forecast approach

The fluctuation of the gold price has significant impact on the economic and social aspects of a society. In the literature, most authors have employed fundamental analysis approach in forecast model building. The basic principle underlying this approach is that it is the supply and the demand which simultaneously determines the gold price. However, due to the lack of data of quantity supplied and quantity demanded, simultaneous econometric approach seems unsuccessful. In this paper, combined and composite time series forecasting techniques are proposed. The effects of various economic factors towards spot price of gold are also examined. Among the combined forecasting models, it seems that the odds-matrix method of assigning weights provides the most accurate forecasts of spot price of gold. For the economic factors considered, the futures price of gold and and the exchange rate seem to be most informative in forecasting the spot price of gold.