Ensemble forecast of photovoltaic power with online CRPS learning

We provide probabilistic forecasts of photovoltaic (PV) production, for several PV plants located in France up to 6 days of lead time, with a 30-min timestep. First, we derive multiple forecasts from numerical weather predictions (ECMWF and Météo France), including ensemble forecasts. Second, our parameter-free online learning technique generates a weighted combination of the production forecasts for each PV plant. The weights are computed sequentially before each forecast using only past information. Our strategy is to minimize the Continuous Ranked Probability Score (CRPS). We show that our technique provides forecast improvements for both deterministic and probabilistic evaluation tools.     

Combining forecasts: Performance and coherence

There is general agreement in many forecasting contexts that combining individual predictions leads to better final forecasts. However, the relative error reduction in a combined forecast depends upon the extent to which the component forecasts contain unique/independent information. Unfortunately, obtaining independent predictions is difficult in many situations, as these forecasts may be based on similar statistical models and/or overlapping information. The current study addresses this problem by incorporating a measure of coherence into an analytic evaluation framework so that the degree of independence between sets of forecasts can be identified easily. The framework also decomposes the performance and coherence measures in order to illustrate the underlying aspects that are responsible for error reduction. The framework is demonstrated using UK retail prices index inflation forecasts for the period 1998–2014, and implications for forecast users are discussed.     

Prediction in the Panel Data Model with Spatial Correlation: the Case of Liquor

Abstract

This paper considers the problem of prediction in a panel data regression model with spatial autocorrelation in the context of a simple demand equation for liquor. This is based on a panel of 43 states over the period 1965–1994. The spatial autocorrelation due to neighbouring states and the individual heterogeneity across states is taken explicitly into account. We compare the performance of several predictors of the states’ demand for liquor for 1 year and 5 years ahead. The estimators whose predictions are compared include OLS, fixed effects ignoring spatial correlation, fixed effects with spatial correlation, random-effects GLS estimator ignoring spatial correlation and random-effects estimator accounting for the spatial correlation. Based on RMSE forecast performance, estimators that take into account spatial correlation and heterogeneity across the states perform the best for forecasts 1 year ahead. However, for forecasts 2–5 years ahead, estimators that take into account the heterogeneity across the states yield the best forecasts.     

Forecast revisions of Mexican inflation and GDP growth

We analyze the forecasts of inflation and GDP growth contained in the Banco de México’s Survey of Professional Forecasters for the period 1995–2009. The forecasts are for the current and the following year, and comprise an unbalanced three-dimensional panel with multiple individual forecasters, target years, and forecast horizons. The fixed-event nature of the forecasts enables us to examine their efficiency by looking at the revision process. The panel structure allows us to control for aggregate shocks and to construct a measure of the news that impacted expectations in the period under study. We find that respondents anchor to their initial forecasts, updating their revisions smoothly as they receive more information. In addition, they do not seem to use publicly-known information in an efficient manner. These inefficiencies suggest clear areas of opportunity for improving the accuracy of the forecasts, for instance by taking into account the positive autocorrelation found in forecast revisions.     

Forecasting week-to-week television ratings using reduced-form and structural dynamic models

Rather than being sold several months before a program is aired, more than 20% of TV advertising slots are retained for sale weekly near the program’s broadcast time. Distinct from the literature that mainly focuses on the forecasting of program ratings for advanced sales of advertising slots, we explore approaches that can provide more accurate forecasts for near real-time ratings. We propose two dynamic models that mainly employ individual viewing records for past episodes to forecast viewers’ decisions on episodes in the coming week, and therefore the ratings for these episodes. One is a reduced-form dynamic model that measures the influence of past watching experience by the weighted average of the viewers’ choices of past episodes. The other is a structural dynamic model that goes deeper in its use of previous viewing information by modeling the underlying process of this influence based on the Bayesian updating theory. Using data from the Hong Kong TV industry, we test and compare the two models. Results show that the reduced-form model generally performs better when the variance of ratings across episodes is small, while the structural model generates more accurate forecasts in other cases.     

Probabilistic wind forecasting up to three months ahead using ensemble predictions for geopotential height

We develop a method for forecasting the distribution of the daily surface wind speed at timescales from 15-days to 3-months in France. On such long-term timescales, ensemble predictions of the surface wind speed have poor performance, however, the wind speed distribution may be related to the large-scale circulation of the atmosphere, for which the ensemble forecasts have better skill. The information from the large-scale circulation, represented by the 500 hPa geopotential height, is summarized into a single index by first running a PCA and then a polynomial regression. We estimate, over 20 years of daily data, the conditional probability density of the wind speed at a specific location given the index. We then use the ECMWF seasonal forecast ensemble to predict the index for horizons from 15-days to 3-months. These predictions are plugged into the conditional density to obtain a distributional forecast of surface wind. These probabilistic forecasts remain sharper than the climatology up to 1-month forecast horizon. Using a statistical postprocessing method to recalibrate the ensemble leads to further improvement of our probabilistic forecast, which then remains calibrated and sharper than the climatology up to 3-months horizon, particularly in the north of France in winter and fall.     

Do survey joiners and leavers differ from regular participants? The US SPF GDP growth and inflation forecasts

If ‘learning by doing’ is important for macro-forecasting, newcomers might be different from regular, established participants. Stayers may also differ from the soon-to-leave. We test these conjectures for macro-forecasters’ point predictions of output growth and inflation, and for their histogram forecasts. Histogram forecasts of inflation by both joiners and leavers are found to be less accurate, especially if we suppose that joiners take time to learn. For GDP growth, there is no evidence of differences between the groups in terms of histogram forecast accuracy, although GDP point forecasts by leavers are less accurate. These findings are predicated on forecasters being homogeneous within groups. Allowing for individual fixed effects suggests fewer differences, including leavers’ inflation histogram forecasts being no less accurate.     

南博会助力广西旅游电子商务

当前一种崭新的商务模式——旅游电子商务,正在全球蓬勃兴起。旅游活动与电子商务的结合将成为旅游业未来的一个主要发展方向。旅游业是广西正在全力培育和打造的支柱产业。国家对此也给予极高的重视,宣布自2003年起每年11月都将在广西首府南宁市举办中国-东盟博览会,这使得广西旅游业面临着史无前例的发展机遇与挑战。从广西旅游产业的现状及存在问题、“南博会”为广西旅游电子商务带来发展机遇和旅游电子商务反哺广西旅游产业三个角度进行了论述,并针对广西旅游电子商务如何利用优势把握机会、避免威胁提出了个人建议。     

Forecasting U.S. population totals with the Box-Jenkins approach

"The use of the Box-Jenkins approach for forecasting the population of the United States up to the year 2080 is discussed. It is shown that the Box-Jenkins approach is equivalent to a simple trend model when making long-range predictions for the United States. An investigation of forecasting accuracy indicates that the Box-Jenkins method produces population forecasts that are at least as reliable as those done with more traditional demographic methods."     

A hybrid system-identification method for forecasting telecommunications product demands

A crucial challenge for telecommunications companies is how to forecast changes in demand for specific products over the next 6 to 18 months—the length of a typical short-range capacity-planning and capital-budgeting planning horizon. The problem is especially acute when only short histories of product sales are available. This paper presents a new two-level approach to forecasting demand from short-term data. The lower of the two levels consists of adaptive system-identification algorithms borrowed from signal processing, especially, Hidden Markov Model (HMM) methods [Hidden Markov Models: Estimation and Control (1995) Springer Verlag]. Although they have primarily been used in engineering applications such as automated speech recognition and seismic data processing, HMM techniques also appear to be very promising for predicting probabilities of individual customer behaviors from relatively short samples of recent product-purchasing histories. The upper level of our approach applies a classification tree algorithm to combine information from the lower-level forecasting algorithms. In contrast to other forecast-combination algorithms, such as weighted averaging or Bayesian aggregation formulas, the classification tree approach exploits high-order interactions among error patterns from different predictive systems. It creates a hybrid, forecasting algorithm that out-performs any of the individual algorithms on which it is based. This tree-based approach to hybridizing forecasts provides a new, general way to combine and improve individual forecasts, whether or not they are based on HMM algorithms. The paper concludes with the results of validation tests. These show the power of HMM methods to forecast what individual customers are likely to do next. They also show the gain from classification tree post-processing of the predictions from lower-level forecasts. In essence, these techniques enhance the limited techniques available for new product forecasting.     

Quantile Aggregation of Density Forecasts

Quantile aggregation (or ‘Vincentization’) is a simple and intuitive way of combining probability distributions, originally proposed by S.B. Vincent in 1912. In certain cases, such as under Gaussianity, the Vincentized distribution belongs to the same family as that of the individual distributions and it can be obtained by averaging the individual parameters. This article compares the properties of quantile aggregation with those of the forecast combination schemes normally adopted in the econometric forecasting literature, based on linear or logarithmic averages of the individual densities. Analytical results and Monte Carlo experiments indicate that the properties of quantile aggregation are between those of the linear and the logarithmic pool. Larger differences among the combination schemes occur when there are biases in the individual forecasts: in that case quantile aggregation seems preferable on the whole. The practical usefulness of Vincentization is illustrated empirically in the context of linear forecasting models for Italian GDP and quantile predictions of euro area inflation.     

Individual versus group spot price forecasting in the international petroleum market: A case study

This paper utilizes the conventional statistical tests associated with the rational expectations hypothesis so as to compare the relative accuracy of individual versus group forecasting within the organization. In order to maintain comparability between forecasting regimens the study employs like information sets for the two prediction methods. Using the rational expectations tests as criteria, the statistical results show group forecasts inferior to individually produced predictions These findings imply that group-produced forecasting accuracy may be hampered by the psychological interaction associated with consensus behavior. Conversely, we find forecasting accuracy improves when predictions are elicited from individuals in an isolated laboratory-like setting.     

Predictive financial models of the euro area: A new evaluation test

This paper investigates the predictive ability of financial variables for euro area growth. Our forecasts are built from univariate autoregressive and single equation models. Euro area aggregate forecasts are constructed both by employing aggregate variables and by aggregating country-specific forecasts. The forecast evaluation is based on a recently developed test for equal predictive ability between nested models. Employing a monthly dataset from the period between January 1988 and May 2005 and setting the out-of-sample period to be from 2001 onwards, we find that the single most powerful predictor on a country basis is the stock market returns, followed by money supply growth. However, for the euro area aggregate, the set of most powerful predictors includes interest rate variables as well. The forecasts from pooling individual country models outperform those from the aggregate itself for short run forecasts, while for longer horizons this pattern is reversed. Additional benefits are obtained when combining information from a range of variables or combining model forecasts.     

Forecasting (aggregate) demand for US commercial air travel

We analyze whether it is better to forecast air travel demand using aggregate data at (say) a national level, or to aggregate the forecasts derived for individual airports using airport-specific data. We compare the US Federal Aviation Administration’s (FAA) practice of predicting the total number of passengers using macroeconomic variables with an equivalently specified AIM (aggregating individual markets) approach. The AIM approach outperforms the aggregate forecasting approach in terms of its out-of-sample air travel demand predictions for different forecast horizons. Variants of AIM, where we restrict the coefficient estimates of some explanatory variables to be the same across individual airports, generally dominate both the aggregate and AIM approaches. The superior out-of-sample performances of these so-called quasi-AIM approaches depend on the trade-off between heterogeneity and estimation uncertainty. We argue that the quasi-AIM approaches exploit the heterogeneity across individual airports efficiently, without suffering from as much estimation uncertainty as the AIM approach.     

Evaluating Point and Density Forecasts of DSGE Models

This paper investigates the accuracy of forecasts from four dynamic stochastic general equilibrium (DSGE) models for inflation, output growth and the federal funds rate using a real‐time dataset synchronized with the Fed's Greenbook projections. Conditioning the model forecasts on the Greenbook nowcasts leads to forecasts that are as accurate as the Greenbook projections for output growth and the federal funds rate. Only for inflation are the model forecasts dominated by the Greenbook projections. A comparison with forecasts from Bayesian vector autoregressions shows that the economic structure of the DSGE models which is useful for the interpretation of forecasts does not lower the accuracy of forecasts. Combining forecasts of several DSGE models increases precision in comparison to individual model forecasts. Comparing density forecasts with the actual distribution of observations shows that DSGE models overestimate uncertainty around point forecasts. Copyright © 2013 John Wiley & Sons, Ltd.     

Forecasting category sales and market share for wireless telephone subscribers: a combined approach

The ability to forecast market share remains a challenge for many managers especially in dynamic markets, such as the telecommunications sector. In order to accommodate the unique dynamic characteristics of the telecommunications market, we use a multi-component model, called MSHARE. Our method involves a two-phase process. The first phase consists of three components: a projection method, a ring down survey methodology and a purchase intentions survey. The predictions from these components are combined to forecast category sales for the wireless subscribers market. In the second phase, market shares for the various brands are generated using the forecast of the number of subscribers that are obtained in Phase 1 and the share predictions from the ring down methodology. The proposed methodology produces the minimum Relative Absolute Error for each market as compared to the forecasts from each individual component in the first phase. The value of the proposed model is illustrated by its application to a real world scenario. The managerial implications of the proposed model are also discussed.     

Forecasting annual and harvest pecan prices

Pecan price forecasting is important to growers attempting to reduce income variability. Random coefficient regression (RCR) and OLS approaches were applied to annual price forecasts. Variance analysis was conducted to forecast pecan price during harvest. Price variation was postulated to be caused by two sets of variables: structural economic variables and unknown factors. RCR results consistently outperformed OLS results in annual price forecasting. The variation of harvest prices was found to be generated by a different process each year, making accurate predictions difficult. Annual price forecasts, however, can provide additional information to pecan growers and shellers for marketing decision-making.     

Is there a consensus among financial forecasters?

This paper examines the interest rate forecasts of a cross-section of financial forecasters to determine whether these analysts make predictions which have the characteristics of a consensus. The forecasts are published semi-annually in The Wall Street Journal. The techniques for determining whether a consensus exists are developed and are applied to the predictions of the interest rates of the 90-day T-bill and the 30-year Treasury bond. The methodology provides bounds on the number of distributions which may be classified as consensus and the results indicate that central moments should not be used as consensus predictions.     

LoMEF: A framework to produce local explanations for global model time series forecasts

Global forecasting models (GFMs) that are trained across a set of multiple time series have shown superior results in many forecasting competitions and real-world applications compared with univariate forecasting approaches. One aspect of the popularity of statistical forecasting models such as ETS and ARIMA is their relative simplicity and interpretability (in terms of relevant lags, trend, seasonality, and other attributes), while GFMs typically lack interpretability, especially relating to particular time series. This reduces the trust and confidence of stakeholders when making decisions based on the forecasts without being able to understand the predictions. To mitigate this problem, we propose a novel local model-agnostic interpretability approach to explain the forecasts from GFMs. We train simpler univariate surrogate models that are considered interpretable (e.g., ETS) on the predictions of the GFM on samples within a neighbourhood that we obtain through bootstrapping, or straightforwardly as the one-step-ahead global black-box model forecasts of the time series which needs to be explained. After, we evaluate the explanations for the forecasts of the global models in both qualitative and quantitative aspects such as accuracy, fidelity, stability, and comprehensibility, and are able to show the benefits of our approach.     

Evaluating quantile-bounded and expectile-bounded interval forecasts

In many different contexts, decision-making is improved by the availability of probabilistic predictions. The accuracy of probabilistic forecasting methods can be compared using scoring functions and insight provided by calibration tests. These tests evaluate the consistency of predictions with the observations. Our main agenda in this paper is interval forecasts and their evaluation. Such forecasts are usually bounded by two quantile forecasts. However, a limitation of quantiles is that they convey no information regarding the size of potential exceedances. By contrast, the location of an expectile is dictated by the whole distribution. This prompts us to propose expectile-bounded intervals. We provide interpretation, a consistent scoring function and a calibration test. Before doing this, we reflect on the evaluation of forecasts of quantile-bounded intervals and expectiles, and suggest extensions of previously proposed calibration tests in order to guard against strategic forecasting. We illustrate ideas using day-ahead electricity price forecasting.