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.     

Time series forecasting using functional partial least square regression with stochastic volatility,GARCH, and exponential smoothing

We propose a method for improving the predictive ability of standard forecasting models used in financial economics. Our approach is based on the functional partial least squares (FPLS) model, which is capable of avoiding multicollinearity in regression by efficiently extracting information from the high‐dimensional market data. By using its well‐known ability, we can incorporate auxiliary variables that improve the predictive accuracy. We provide an empirical application of our proposed methodology in terms of its ability to predict the conditional average log return and the volatility of crude oil prices via exponential smoothing, Bayesian stochastic volatility, and GARCH (generalized autoregressive conditional heteroskedasticity) models, respectively. In particular, what we call functional data analysis (FDA) traces in this article are obtained via the FPLS regression from both the crude oil returns and auxiliary variables of the exchange rates of major currencies. For forecast performance evaluation, we compare out‐of‐sample forecasting accuracy of the standard models with FDA traces to the accuracy of the same forecasting models with the observed crude oil returns, principal component regression (PCR), and least absolute shrinkage and selection operator (LASSO) models. We find evidence that the standard models with FDA traces significantly outperform our competing models. Finally, they are also compared with the test for superior predictive ability and the reality check for data snooping. Our empirical results show that our new methodology significantly improves predictive ability of standard models in forecasting the latent average log return and the volatility of financial time series.     

Modeling eBay price using stochastic differential equations

Online auctions have become increasingly popular in recent years. There is a growing body of research on this topic, whereas modeling online auction price curves constitutes one of the most interesting problems. Most research treats price curves as deterministic functions, which ignores the random effects of external and internal factors. To account for the randomness, a more realistic model using stochastic differential equations is proposed in this paper. The online auction price is modeled by a stochastic differential equation in which the deterministic part is equivalent to the second‐order differential equation model proposed in Wang et al. (Journal of the American Statistical Association, 2008, 103, 1100–1118). The model also includes a component representing the measurement errors. Explicit expressions for the likelihood function are also obtained, from which statistical inference can be conducted. Forecast accuracy of the proposed model is compared with the ODE (ordinary differential equation) approach. Simulation results show that the proposed model performs better.     

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.     

Modeling and forecasting the oil volatility index

The increase in oil price volatility in recent years has raised the importance of forecasting it accurately for valuing and hedging investments. The paper models and forecasts the crude oil exchange‐traded funds (ETF) volatility index, which has been used in the last years as an important alternative measure to track and analyze the volatility of future oil prices. Analysis of the oil volatility index suggests that it presents features similar to those of the daily market volatility index, such as long memory, which is modeled using well‐known heterogeneous autoregressive (HAR) specifications and new extensions that are based on net and scaled measures of oil price changes. The aim is to improve the forecasting performance of the traditional HAR models by including predictors that capture the impact of oil price changes on the economy. The performance of the new proposals and benchmarks is evaluated with the model confidence set (MCS) and the Generalized‐AutoContouR (G‐ACR) tests in terms of point forecasts and density forecasting, respectively. We find that including the leverage in the conditional mean or variance of the basic HAR model increases its predictive ability. Furthermore, when considering density forecasting, the best models are a conditional heteroskedastic HAR model that includes a scaled measure of oil price changes, and a HAR model with errors following an exponential generalized autoregressive conditional heteroskedasticity specification. In both cases, we consider a flexible distribution for the errors of the conditional heteroskedastic process.     

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%.     

The Forecasting Performance of a Finite Mixture Regime‐Switching Model for Daily Electricity Prices

Forecasting prices in electricity markets is a crucial activity for both risk management and asset optimization. Intra‐day power prices have a fine structure and are driven by an interaction of fundamental, behavioural and stochastic factors. Furthermore, there are reasons to expect the functional forms of price formation to be nonlinear in these factors and therefore specifying forecasting models that perform well out‐of‐sample is methodologically challenging. Markov regime switching has been widely advocated to capture some aspects of the nonlinearity, but it may suffer from overfitting and unobservability in the underlying states. In this paper we compare several extensions and alternative regime‐switching formulations, including logistic specifications of the underlying states, logistic smooth transition and finite mixture regression. The finite mixture approach to regime switching performs well in an extensive, out‐of‐sample forecasting comparison. Copyright © 2014 John Wiley & Sons, Ltd.     

Price forecasting and evaluation: An application in agriculture

Because of the high volatility of prices of agricultural commodities over the past decade, the importance of accurate price forecasting for decision makers has become even more acute. This paper reviews literature on forecasting and evaluation. An application with forecasting U.S. hog prices is presented which includes both economic and statistical evaluation measures. Seven forecasting approaches are described and their performances are examined over 24 quarters from 1976 to 1981. These methods include exponential smoothing, an autoregressive integrated moving average process, an econometric model, expert judgement, and a composite forecasting approach. The application gives results which support previous findings in the forecasting literature and suggests that forecasting methods can provide valuable information to the decision maker.     

Forecasting the US Term Structure of Interest Rates Using Nonparametric Functional Data Analysis

In this paper we consider a novel procedure to forecasting the US zero coupon bond yields for a continuum of maturities by using the methodology of nonparametric functional data analysis (NP‐FDA). We interpret the US yields as curves since the term structure of interest rates defines a relation between the yield of a bond and its maturity. Within the NP‐FDA approach, each curve is viewed as a functional random variable and the dynamics present in the sample are modeled without imposing any parametric structure. In order to evaluate forecast the performance of the proposed estimator, we consider forecast horizons h = 1,3,6,12… months and the results are compared with widely known benchmark models. Our estimates with NP‐FDA present predictive performance superior to its competitors in many situations considered, especially for short‐term maturities. Copyright © 2016 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.     

An Adaptive Multiscale Ensemble Learning Paradigm for Nonstationary and Nonlinear Energy Price Time Series Forecasting

For forecasting nonstationary and nonlinear energy prices time series, a novel adaptive multiscale ensemble learning paradigm incorporating ensemble empirical mode decomposition (EEMD), particle swarm optimization (PSO) and least square support vector machines (LSSVM) with kernel function prototype is developed. Firstly, the extrema symmetry expansion EEMD, which can effectively restrain the mode mixing and end effects, is used to decompose the energy price into simple modes. Secondly, by using the fine‐to‐coarse reconstruction algorithm, the high‐frequency, low‐frequency and trend components are identified. Furthermore, autoregressive integrated moving average is applicable to predicting the high‐frequency components. LSSVM is suitable for forecasting the low‐frequency and trend components. At the same time, a universal kernel function prototype is introduced for making up the drawbacks of single kernel function, which can adaptively select the optimal kernel function type and model parameters according to the specific data using the PSO algorithm. Finally, the prediction results of all the components are aggregated into the forecasting values of energy price time series. The empirical results show that, compared with the popular prediction methods, the proposed method can significantly improve the prediction accuracy of energy prices, with high accuracy both in the level and directional predictions. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting of electricity price through a functional prediction of sale and purchase curves

This work proposes a new approach for the prediction of the electricity price based on forecasting aggregated purchase and sale curves. The basic idea is to model the hourly purchase and the sale curves, to predict them and to find the intersection of the predicted curves in order to obtain the predicted equilibrium market price and volume. Modeling and forecasting of purchase and sale curves is performed by means of functional data analysis methods. More specifically, parametric (FAR) and nonparametric (NPFAR) functional autoregressive models are considered and compared to some benchmarks. An appealing feature of the functional approach is that, unlike other methods, it provides insights into the sale and purchase mechanism connected with the price and demand formation process and can therefore be used for the optimization of bidding strategies. An application to the Italian electricity market (IPEX) is also provided, showing that NPFAR models lead to a statistically significant improvement in the forecasting accuracy.     

Dynamic relationship analysis of us gasoline and crude oil prices

This paper studies the dynamic relationships between US gasoline prices, crude oil prices, and the stock of gasoline. Using monthly data between January 1973 and December 1987, we find that the US gasoline price is mainly influenced by the price of crude oil. The stock of gasoline has little or no influence on the price of gasoline during the period before the second energy crisis, and seems to have some influence during the period after. We also find that the dynamic relationship between the prices of gasoline and crude oil changes over time, shifting from a longer lag response to a shorter lag response. Box-Jenkins ARIMA and transfer function models are employed in this study. These models are estimated using estimation procedure with and without outlier adjustment. For model estimation with outlier adjustment, an iterative procedure for the joint estimation of model parameters and outlier effects is employed. The forecasting performance of these models is carefully examined. For the purpose of illustration, we also analyze these time series using classical white-noise regression models. The results show the importance of using appropriate time-series methods in modeling and forecasting when the data are serially correlated. This paper also demonstrates the problems of time-series modeling when outliers are present.     

The role of prices in models of innovation diffusion

When evaluating the launch of a new product or service, forecasts of the diffusion path and the effects of the marketing mix are critically important. Currently no unified framework exists to provide guidelines on the inclusion and specification of marketing mix variables into models of innovation diffusion. The objective of this research is to examine empirically the role of prices in diffusion models, in order to establish whether price can be incorporated effectively into the simpler time-series models. Unlike existing empirical research which examines the models' fit to historical data, we examine the predictive validity of alternative models. Only if the incorporation of prices improves the predictive performance of diffusion models can it be argued that these models have validity. A series of diffusion models which include prices are compared against a number of well-accepted diffusion models, including the Bass (1969) model, and more recently developed ‘flexible’ diffusion models. For short data series and long-lead time forecasting, the situation typical of practical situations, price rarely added to the forecasting capability of simpler time-series models. Copyright © 1998 John Wiley & Sons, Ltd.     

A hybrid model considering cointegration for interval-valued pork price forecasting in China

Compared with point forecasting, interval forecasting is believed to be more effective and helpful in decision making, as it provides more information about the data generation process. Based on the well-established “linear and nonlinear” modeling framework, a hybrid model is proposed by coupling the vector error correction model (VECM) with artificial intelligence models which consider the cointegration relationship between the lower and upper bounds (Coin-AIs). VECM is first employed to fit the original time series with the residual error series modeled by Coin-AIs. Using pork price as a research sample, the empirical results statistically confirm the superiority of the proposed VECM-CoinAIs over other competing models, which include six single models and six hybrid models. This result suggests that considering the cointegration relationship is a workable direction for improving the forecast performance of the interval-valued time series. Moreover, with a reasonable data transformation process, interval forecasting is proven to be more accurate than point forecasting.     

Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?

We study the performance of recently developed linear regression models for interval data when it comes to forecasting the uncertainty surrounding future stock returns. These interval data models use easy‐to‐compute daily return intervals during the modeling, estimation and forecasting stage. They have to stand up to comparable point‐data models of the well‐known capital asset pricing model type—which employ single daily returns based on successive closing prices and might allow for GARCH effects—in a comprehensive out‐of‐sample forecasting competition. The latter comprises roughly 1000 daily observations on all 30 stocks that constitute the DAX, Germany's main stock index, for a period covering both the calm market phase before and the more turbulent times during the recent financial crisis. The interval data models clearly outperform simple random walk benchmarks as well as the point‐data competitors in the great majority of cases. This result does not only hold when one‐day‐ahead forecasts of the conditional variance are considered, but is even more evident when the focus is on forecasting the width or the exact location of the next day's return interval. Regression models based on interval arithmetic thus prove to be a promising alternative to established point‐data volatility forecasting tools. Copyright ©2015 John Wiley & Sons, Ltd.     

Forecasting the recent behavior of US business fixed investment spending: an analysis of competing models

We evaluate forecasting models of US business fixed investment spending growth over the recent 1995:1–2004:2 out‐of‐sample period. The forecasting models are based on the conventional Accelerator, Neoclassical, Average Q, and Cash‐Flow models of investment spending, as well as real stock prices and excess stock return predictors. The real stock price model typically generates the most accurate forecasts, and forecast‐encompassing tests indicate that this model contains most of the information useful for forecasting investment spending growth relative to the other models at longer horizons. In a robustness check, we also evaluate the forecasting performance of the models over two alternative out‐of‐sample periods: 1975:1–1984:4 and 1985:1–1994:4. A number of different models produce the most accurate forecasts over these alternative out‐of‐sample periods, indicating that while the real stock price model appears particularly useful for forecasting the recent behavior of investment spending growth, it may not continue to perform well in future periods. Copyright © 2007 John Wiley & Sons, Ltd.     

On Forecasting Conflict in the Sudan: 2009–2012

This paper considers univariate and multivariate models to forecast monthly conflict events in the Sudan over the out‐of‐sample period 2009–2012. The models used to generate these forecasts were based on a specification from a machine learning algorithm fit to 2000–2008 monthly data. The model that includes previous month's wheat price performs better than a similar model which does not include past wheat prices (the univariate model). Both models did not perform well in forecasting conflict in a neighborhood of the 2012 ‘Heglig crisis’. Copyright © 2015 John Wiley & Sons, Ltd.     

An intelligent model selection and forecasting system

In this paper we present an intelligent decision‐support system based on neural network technology for model selection and forecasting. While most of the literature on the application of neural networks in forecasting addresses the use of neural network technology as an alternative forecasting tool, limited research has focused on its use for selection of forecasting methods based on time‐series characteristics. In this research, a neural network‐based decision support system is presented as a method for forecast model selection. The neural network approach provides a framework for directly incorporating time‐series characteristics into the model‐selection phase. Using a neural network, a forecasting group is initially selected for a given data set, based on a set of time‐series characteristics. Then, using an additional neural network, a specific forecasting method is selected from a pool of three candidate methods. The results of training and testing of the networks are presented along with conclusions. Copyright © 1999 John Wiley & Sons, Ltd.     

Do professional forecasters believe in the Phillips curve? evidence from the G7 countries

This paper uses monthly survey data for the G7 countries for the time period 1989–2007 to explore the link between expectations on nominal wages, prices and unemployment rates as suggested by the wage and price Phillips curves. Four major findings stand out. First, we find that survey participants trust in both types of Phillips curve relationships. Second, we find evidence in favor of nonlinearities in the price Phillips curve. Third, we take into account a kink in the price Phillips curve to indicate that the slope of the Phillips curve differs during the business cycle. We find strong evidence of this feature in the data which confirms recent theoretical discussions. Fourth, we employ our data to the expectations‐augmented Phillips curve model. The results suggest that professional forecasters adopt this model when forecasting macroeconomic variables. Copyright © 2010 John Wiley & Sons, Ltd.