Optimal forecast intervals under asymmetric loss

An optimality criterion for forecast intervals under asymmetric loss functions is proposed. A loss optimal forecast interval is obtained by requiring that the expected loss, conditional on a future realization within the desired interval, be minimal. The main difficulty in the context of forecasting under asymmetric loss emerges when there is no knowledge about the distribution of the innovations. For solving this problem, an extension of estimation under the relevant loss function is suggested. In many cases, one also needs to account for the additional variability due to estimation of model parameters. Another solution, based on the bootstrap, works for both problems. Copyright © 2007 John Wiley & Sons, Ltd.     

Modeling and Forecasting Online Auction Prices: A Semiparametric Regression Analysis

Interest in online auctions has been growing in recent years. There is an extensive literature on this topic, whereas modeling online auction price process constitutes one of the most active research areas. Most of the research, however, only focuses on modeling price curves, ignoring the bidding process. In this paper, a semiparametric regression model is proposed to model the online auction process. This model captures two main features of online auction data: changing arrival rates of bidding processes and changing dynamics of prices. A new inference procedure using B‐splines is also established for parameter estimation. The proposed model is used to forecast the price of an online auction. The advantage of this proposed approach is that the price can be forecast dynamically and the prediction can be updated according to newly arriving information. The model is applied to Xbox data with satisfactory forecasting properties. Copyright © 2016 John Wiley & Sons, Ltd.     

Integrating time-series and end-use methods to forecast electricity sales

Two types of forecasting methods have been receiving increasing attention by electric utility forecasters. The first type, called end-use forecasting, is recognized as an approach which is well suited for forecasting during periods characterized by technological change. The method is straightforward. The stock levels of energy-consuming equipment are forecast, as well as the energy consumption characteristics of the equipment. The final forecast is the product of the stock and usage characteristics. This approach is well suited to forecasting long time periods when technological change, equipment depletion and replacement, and other structural changes are evident. For time periods of shorter duration, these factors are static and variations are more likely to result from shocks to the environment. The shocks influence the usage of the equipment. A second forecasting approach using time-series analysis has been demonstrated to be superior for these applications. This paper discusses the integration of the two methods into a unified system. The result is a time-series model whose parameter effects become dynamic in character. An example of the models being used at the Georgia Power Company is presented. It is demonstrated that a time-series model which incorporates end-use stock and usage information is superior—even in short-term forecasting situations—to a similar time-series model which excludes the information.     

Small sample properties of quarterly forecast errors

There are two basic approaches used in the comparative evaluation of forecasters: (1) Statistical tests of significance of differences in error measures, (2) Ordinal rankings of forecasters. To use the first approach of statistical tests, the forecast error data must satisfy the assumptions underlying those tests. This paper examines the validity of those assumptions by enquiring into the small sample properties of the forecast error data of quarterly forecasts of the U.S. economy.     

Forecasting energy prices: Quantile-based risk models

The goal of this paper is to use a new modelling approach to extract quantile-based oil and natural gas risk measures using quantile autoregressive distributed lag mixed-frequency data sampling (QADL-MIDAS) regression models. The analysis compares this model to a standard quantile auto-regression (QAR) model and shows that it delivers better quantile forecasts at the majority of forecasting horizons. The analysis also uses the QADL-MIDAS model to construct oil and natural gas prices risk measures proxying for uncertainty, third-moment dynamics, and the risk of extreme energy realizations. The results document that these risk measures are linked to the future evolution of energy prices, while they are linked to the future evolution of US economic growth.     

Predictive ability and economic gains from volatility forecast combinations

The availability of numerous modeling approaches for volatility forecasting leads to model uncertainty for both researchers and practitioners. A large number of studies provide evidence in favor of combination methods for forecasting a variety of financial variables, but most of them are implemented on returns forecasting and evaluate their performance based solely on statistical evaluation criteria. In this paper, we combine various volatility forecasts based on different combination schemes and evaluate their performance in forecasting the volatility of the S&P 500 index. We use an exhaustive variety of combination methods to forecast volatility, ranging from simple techniques to time-varying techniques based on the past performance of the single models and regression techniques. We then evaluate the forecasting performance of single and combination volatility forecasts based on both statistical and economic loss functions. The empirical analysis in this paper yields an important conclusion. Although combination forecasts based on more complex methods perform better than the simple combinations and single models, there is no dominant combination technique that outperforms the rest in both statistical and economic terms.     

Forecasting in long horizons using smoothed direct forecast

This paper constructs a forecast method that obtains long‐horizon forecasts with improved performance through modification of the direct forecast approach. Direct forecasts are more robust to model misspecification compared to iterated forecasts, which makes them preferable in long horizons. However, direct forecast estimates tend to have jagged shapes across horizons. Our forecast method aims to “smooth out” erratic estimates across horizons while maintaining the robust aspect of direct forecasts through ridge regression, which is a restricted regression on the first differences of regression coefficients. The forecasts are compared to the conventional iterated and direct forecasts in two empirical applications: real oil prices and US macroeconomic series. In both applications, our method shows improvement over direct forecasts.     

Consistent forecast intervals when the forecast-period exogenous variables are stochastic

Derivation of prediction intervals in the k-variable regression model is problematic when future-period values of exogenous variables are not known with certainty. Even in the most favourable case when the forecasts of the exogenous variables are jointly normal, the distribution of the forecast error is non-normal, and thus traditional asymptotic normal theory does not apply. This paper presents an alternative bootstrap method. In contrast to the traditional predictor of the future value of the endogenous variable, which is known to be inconsistent, the bootstrap predictor converges weakly to the true value. Monte Carlo results show that the bootstrap prediction intervals can achieve approximately nominal coverage.     

Using the yield curve to forecast economic growth

This paper finds the yield curve to have a well-performing ability to forecast the real gross domestic product growth in the USA, compared to professional forecasters and time series models. Past studies have different arguments concerning growth lags, structural breaks, and ultimately the ability of the yield curve to forecast economic growth. This paper finds such results to be dependent on the estimation and forecasting techniques employed. By allowing various interest rates to act as explanatory variables and various window sizes for the out-of-sample forecasts, significant forecasts from many window sizes can be found. These seemingly good forecasts may face issues, including persistent forecasting errors. However, by using statistical learning algorithms, such issues can be cured to some extent. The overall result suggests, by scientifically deciding the window sizes, interest rate data, and learning algorithms, many outperforming forecasts can be produced for all lags from one quarter to 3 years, although some may be worse than the others due to the irreducible noise of the data.     

Evaluating volatility and interval forecasts

A widely used approach to evaluating volatility forecasts uses a regression framework which measures the bias and variance of the forecast. We show that the associated test for bias is inappropriate before introducing a more suitable procedure which is based on the test for bias in a conditional mean forecast. Although volatility has been the most common measure of the variability in a financial time series, in many situations confidence interval forecasts are required. We consider the evaluation of interval forecasts and present a regression‐based procedure which uses quantile regression to assess quantile estimator bias and variance. We use exchange rate data to illustrate the proposal by evaluating seven quantile estimators, one of which is a new non‐parametric autoregressive conditional heteroscedasticity quantile estimator. The empirical analysis shows that the new evaluation procedure provides useful insight into the quality of quantile estimators. Copyright © 1999 John Wiley & Sons, Ltd.     

Bootstrapping forecast intervals: An application to AR(p) models

Forecast intervals typically depend upon an assumption of normal forecast errors due to lack of information concerning the distribution of the forecast. This article applies the bootstrap to the problem of estimating forecast intervals for an AR(p) model. Box-Jenkins intervals are compared to intervals produced from a naive bootstrap and a bias-correction bootstrap. Substantial differences between the three methods are found. Bootstrapping an AR(p) model requires use of the backward residuals which typically are not i.i.d. and hence inappropriate for bootstrap resampling. A recently developed method of obtaining i.i.d. backward residuals is employed and was found to affect the bootstrap prediction intervals.     

Bootstrap prediction intervals for autoregressive models of unknown or infinite lag order

Recent studies on bootstrap prediction intervals for autoregressive (AR) model provide simulation findings when the lag order is known. In practical applications, however, the AR lag order is unknown or can even be infinite. This paper is concerned with prediction intervals for AR models of unknown or infinite lag order. Akaike's information criterion is used to estimate (approximate) the unknown (infinite) AR lag order. Small‐sample properties of bootstrap and asymptotic prediction intervals are compared under both normal and non‐normal innovations. Bootstrap prediction intervals are constructed based on the percentile and percentile‐t methods, using the standard bootstrap as well as the bootstrap‐after‐bootstrap. It is found that bootstrap‐after‐bootstrap prediction intervals show small‐sample properties substantially better than other alternatives, especially when the sample size is small and the model has a unit root or near‐unit root. Copyright © 2002 John Wiley & Sons, Ltd.     

Judgemental revision of sales forecasts: Effectiveness of forecast selection

When managers make revisions to sales forecasts initially generated by a rational quantitative model it is important that the particular forecasts selected for adjustment are those which would benefit most from the adjustment process (i.e. realize high errors). This study reports an empirical investigation on this issue, spanning six quarterly forecasting periods and incorporating forecasting data on over 850 products. The results show that the errors of the forecasts chosen for revision are, in general, higher than those which were not chosen. In addition, it is shown that managesrs tend to revise forecasts which are initially low, hence possibily introducing some degree of bias into the overall forecasts.     

Adaptive modelling and forecasting of offshore wind power fluctuations with Markov‐switching autoregressive models

Wind power production data at temporal resolutions of a few minutes exhibit successive periods with fluctuations of various dynamic nature and magnitude, which cannot be explained (so far) by the evolution of some explanatory variable. Our proposal is to capture this regime‐switching behaviour with an approach relying on Markov‐switching autoregressive (MSAR) models. An appropriate parameterization of the model coefficients is introduced, along with an adaptive estimation method allowing accommodation of long‐term variations in the process characteristics. The objective criterion to be recursively optimized is based on penalized maximum likelihood, with exponential forgetting of past observations. MSAR models are then employed for one‐step‐ahead point forecasting of 10 min resolution time series of wind power at two large offshore wind farms. They are favourably compared against persistence and autoregressive models. It is finally shown that the main interest of MSAR models lies in their ability to generate interval/density forecasts of significantly higher skill. Copyright © 2010 John Wiley & Sons, Ltd.     

On long memory origins and forecast horizons

Most long memory forecasting studies assume that long memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference operator and assess the performance of the autoregressive fractionally integrated moving average (ARFIMA) model when forecasting series with long memory generated by nonfractional models. We find that ARFIMA models dominate in forecast performance regardless of the long memory generating mechanism and forecast horizon. Nonetheless, forecasting uncertainty at the shortest forecast horizon could make short memory models provide suitable forecast performance, particularly for smaller degrees of memory. Additionally, we analyze the forecasting performance of the heterogeneous autoregressive (HAR) model, which imposes restrictions on high-order AR models. We find that the structure imposed by the HAR model produces better short and medium horizon forecasts than unconstrained AR models of the same order. Our results have implications for, among others, climate econometrics and financial econometrics models dealing with long memory series at different forecast horizons.     

Model uncertainty and forecast accuracy

In time-series analysis, a model is rarely pre-specified but rather is typically formulated in an iterative, interactive way using the given time-series data. Unfortunately the properties of the fitted model, and the forecasts from it, are generally calculated as if the model were known in the first place. This is theoretically incorrect, as least squares theory, for example, does not apply when the same data are used to formulates and fit a model. Ignoring prior model selection leads to biases, not only in estimates of model parameters but also in the subsequent construction of prediction intervals. The latter are typically too narrow, partly because they do not allow for model uncertainty. Empirical results also suggest that more complicated models tend to give a better fit but poorer ex-ante forecasts. The reasons behind these phenomena are reviewed. When comparing different forecasting models, the BIC is preferred to the AIC for identifying a model on the basis of within-sample fit, but out-of-sample forecasting accuracy provides the real test. Alternative approaches to forecasting, which avoid conditioning on a single model, include Bayesian model averaging and using a forecasting method which is not model-based but which is designed to be adaptable and robust.     

Forecast intervals of net migration: the case of the Netherlands

This study addresses problems concerning the forecasting of net migration in the preparation of population forecasts. "As the width of forecast intervals for migration in single years differs strongly from that of an interval for average migration during the forecast period, it is important that the forecaster indicates which type of interval is presented. A comparison of forecast intervals for net migration obtained from an ARIMA model to intervals in official Dutch national population forecasts shows that the uncertainty on migration has been underestimated in past official forecasts."     

Robust model rankings of forecasting performance

This paper investigates robust model rankings in out‐of‐sample, short‐horizon forecasting. We provide strong evidence that rolling window averaging consistently produces robust model rankings while improving the forecasting performance of both individual models and model averaging. The rolling window averaging outperforms the (ex post) “optimal” window forecasts in more than 50% of the times across all rolling windows.     

On the Predictive Content of Autoregression Residuals: A Semiparametric,Copula‐Based Approach to Time Series Prediction

This paper proposes an adjustment of linear autoregressive conditional mean forecasts that exploits the predictive content of uncorrelated model residuals. The adjustment is motivated by non‐Gaussian characteristics of model residuals, and implemented in a semiparametric fashion by means of conditional moments of simulated bivariate distributions. A pseudo ex ante forecasting comparison is conducted for a set of 494 macroeconomic time series recently collected by Dees et al. (Journal of Applied Econometrics 2007; 22: 1–38). In total, 10,374 time series realizations are contrasted against competing short‐, medium‐ and longer‐term purely autoregressive and adjusted predictors. With regard to all forecast horizons, the adjusted predictions consistently outperform conditionally Gaussian forecasts according to cross‐sectional mean group evaluation of absolute forecast errors and directional accuracy. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal forecast error as an unbiased estimator of abnormal return: A proposition

In the event studies, the accuracy of the abnormal returns assessment is highly dependent on the accuracy of the preceding expected return model. If the expected return model is inadequate, there is a possibility that a part of returns is labeled as abnormal returns even though they are not. Currently, we have a variety of options to set up an expected return model. To obtain unbiased abnormal returns, one should pay attention to the performance of the expected return model. In this research, we propose that the optimal forecast lemma can be consulted beforehand so that minimizing the optimal forecast error in the expected return model will yield unbiased abnormal returns. We introduce and prove a proposition that the optimal forecast error is an unbiased estimator for abnormal return. The proposition induces assessing the performance of abnormal return estimation to preemptively evaluate the out-sample forecast accuracy of the model employed. In an illustrative dataset, we examine various models. The approach requires preliminary computational effort; however, it is useful for accurately obtaining the abnormal return predictions.