というNBER論文が上がっている（ungated版へのリンクがある著者の一人のページ）。原題は「Forecasting Natural Gas Prices in Real Time」で、著者はChristiane Baumeister（ノートルダム大）、Florian Huber（ザルツブルク大）、Thomas K. Lee（米国エネルギー情報局）、 Francesco Ravazzolo（ボーツェン＝ボルツァーノ自由大）。
以下はその要旨。
This paper provides a comprehensive analysis of the forecastability of the real price of natural gas in the United States at the monthly frequency considering a universe of models that differ in their complexity and economic content. Our key finding is that considerable reductions in mean-squared prediction error relative to a random walk benchmark can be achieved in real time for forecast horizons of up to two years. A particularly promising model is a six-variable Bayesian vector autoregressive model that includes the fundamental determinants of the supply and demand for natural gas. To capture real-time data constraints of these and other predictor variables, we assemble a rich database of historical vintages from multiple sources. We also compare our model-based forecasts to readily available model-free forecasts provided by experts and futures markets. Given that no single forecasting method dominates all others, we explore the usefulness of pooling forecasts and find that combining forecasts from individual models selected in real time based on their most recent performance delivers the most accurate forecasts.
（拙訳）
本稿は、複雑性と経済的内容において相異なるモデルのユニバースを基に、米国における月次頻度の天然ガスの実質価格の予測可能性について包括的な分析を提供する。我々の主要な発見は、ランダムウォークのベンチマークに比べて予測誤差の平均二乗を顕著に減らすことは、2年までの予測期間についてリアルタイムで達成できる、ということである*1。特に有望なモデルは、天然ガスの需給のファンダメンタルな決定要因を含む6変数ベイジアンベクトル自己回帰モデルである。それらや他の予測子変数のリアルタイムのデータ制約を捕捉するために我々は、複数のソースから豊富なヒストリカルデータ系列のデータベースを構築した*2。我々はまた、我々のモデルベースの予測を、専門家と先物市場が提供する簡単に利用可能なモデルに依らない予測と比較した。どの単一の予測も他の全てに対し優位に立つことが無いということに鑑み*3、我々はプールした予測の有用性を追究し、最も直近のパフォーマンスに基づいてリアルタイムに選択された個別のモデルの予測を組み合わせることが最も正確な予測をもたらすことを見い出した。
*1:ランダムウォークをベンチマークとして使うことについて本文では「The MSPE results of all our candidate models are normalized relative to the monthly random walk without drift, which is the established benchmark in the energy price forecasting literature (see, e.g., Hamilton, 2009; Baumeister, Kilian, and Lee, 2017; Ferrari, Ravazzolo, and Vespignani, 2021; Baumeister, Korobilis, and Lee, 2022; Baumeister, Huber, and Marcellino, 2024).」と説明している。
*2:本文では「Throughout the analysis, we mimic as closely as possible the situation of a real-life forecaster who can rely only on the information available at the point in time the forecast is generated. This means working with preliminary data that are subject to revisions later on and taking delays in data releases into account to accurately reflect real-time data constraints when assessing the out-of-sample performance of forecasting methods. Since our focus is on the real price of natural gas, we deflate the price by the U.S. consumer price index (CPI) in real time. For this purpose, we update the real-time vintages of the monthly seasonally adjusted U.S. consumer price index for all urban consumers originally compiled by Baumeister and Kilian (2012) up to February 2024. These real-time data are obtained from Economic Indicators published by the Council of Economic Advisers and made available in the FRASER database of the Federal Reserve Bank of St. Louis. While the nominal spot price is available in real time, CPI data are published with a one-month lag; we nowcast the missing observation for each vintage using the past average inflation rate. We produce out-of-sample forecasts for monthly horizons h of up to two years. Model-based forecasts are obtained by recursively re-estimating the model at each forecast origin t based on data contained in the real-time vintage t. The evaluation period starts in February 1997 determined by the EIA’s earliest reporting of the Henry Hub spot price. Thus, the initial recursive estimation window runs from 1976M1 to 1997M1 using data from the January 1997 vintage. After generating h-step-ahead forecasts, we move to the February 1997 data vintage which adds one observation to our sample. We repeat estimation and forecasting for all the vintages until February 2024 which is the last available vintage and thus the endpoint of our evaluation period.」、結論部では「The assessment was conducted in a real-time setting that accounted for delays in the availability of predictor variables and revisions as preliminary data were updated. For this purpose, we compiled a rich database of fundamental determinants of the real price of natural gas from multiple sources. It consists of vintages from January 1991 to February 2024, each covering data going back to January 1973, that report only the information that a real-life forecaster would have had at his disposal at the time the forecasts were generated.」と説明している。
*3:本文では「Our analysis reveals that several forecasting methods perform quite well in real time compared to the no-change benchmark for horizons up to 24 months. At the nearest horizon, using the most recent daily observation of the natural gas price to forecast the average price next month delivers the most accurate forecast, but this approach is superseded at the three- and six-month horizons by more precise forecasts based on futures prices and various economic models of the natural gas market that differ in the number of predictor variables and how these are measured but have in common parsimonious dynamics of order one. Forecasting the real price of natural gas at intermediate horizons, ranging from nine to 15 months out, is most successful with futures prices, exponential smoothing, and an economic model that includes the full set of fundamental drivers. Exponential smoothing remains competitive at the longest horizons, but adding stochastic volatility to some of the economic models also achieves substantial improvements in forecasting performance. While these are the most promising models across horizons, the differences in average performance with the next best tier of models are often small.」と説明している。
