Distributed ARIMA models for ultra-long time series

Providing forecasts for ultra-long time series plays a vital role in various activities, such as investment decisions, industrial production arrangements, and farm management. This paper develops a novel distributed forecasting framework to tackle the challenges of forecasting ultra-long time series using the industry-standard MapReduce framework. The proposed model combination approach retains the local time dependency. It utilizes a straightforward splitting across samples to facilitate distributed forecasting by combining the local estimators of time series models delivered from worker nodes and minimizing a global loss function. Instead of unrealistically assuming the data generating process (DGP) of an ultra-long time series stays invariant, we only make assumptions on the DGP of subseries spanning shorter time periods. We investigate the performance of the proposed approach with AutoRegressive Integrated Moving Average (ARIMA) models using the real data application as well as numerical simulations. Our approach improves forecasting accuracy and computational efficiency in point forecasts and prediction intervals, especially for longer forecast horizons, compared to directly fitting the whole data with ARIMA models. Moreover, we explore some potential factors that may affect the forecasting performance of our approach.     

Forecasting electricity prices using bid data

Market liberalization and the expansion of variable renewable energy sources in power systems have made the dynamics of electricity prices more uncertain, leading them to show high volatility with sudden, unexpected price spikes. Thus, developing more accurate price modeling and forecasting techniques is a challenge for all market participants and regulatory authorities. This paper proposes a forecasting approach based on using auction data to fit supply and demand electricity curves. More specifically, we fit linear (LinX-Model) and logistic (LogX-Model) curves to historical sale and purchase bidding data from the Iberian electricity market to estimate structural parameters from 2015 to 2019. Then we use time series models on structural parameters to predict day-ahead prices. Our results provide a solid framework for forecasting electricity prices by capturing the structural characteristics of markets.     

Forecasting the UK economy with a medium-scale Bayesian VAR

We estimate a Bayesian VAR (BVAR) for the UK economy and assess its performance in forecasting GDP growth and CPI inflation in real time relative to forecasts from COMPASS, the Bank of England’s DSGE model, and other benchmarks. We find that the BVAR outperformed COMPASS when forecasting both GDP and its expenditure components. In contrast, their performances when forecasting CPI were similar. We also find that the BVAR density forecasts outperformed those of COMPASS, despite under-predicting inflation at most forecast horizons. Both models over-predicted GDP growth at all forecast horizons, but the issue was less pronounced in the BVAR. The BVAR’s point and density forecast performances are also comparable to those of a Bank of England in-house statistical suite for both GDP and CPI inflation, as well as to the official Inflation Report projections. Our results are broadly consistent with the findings of similar studies for other advanced economies.     

Forecasting methods for marketing: Review of empirical research

This paper reviews the empirical research on forecasting in marketing. In addition, it presents results from some small scale surveys. We offer a framework for discussing forecasts in the area of marketing, and then review the literature in light of that framework. Particular emphasis is given to a pragmatic interpretation of the literature and findings. Suggestions are made on what research is needed.     

Improving Electricity Market Price Forecasting with Factor Models for the Optimal Generation Bid

In liberalized electricity markets, the electricity generation companies usually manage their production by developing hourly bids that are sent to the day‐ahead market. As the prices at which the energy will be purchased are unknown until the end of the bidding process, forecasting of spot prices has become an essential element in electricity management strategies. In this article, we apply forecasting factor models to the market framework in Spain and Portugal and study their performance. Although their goodness of fit is similar to that of autoregressive integrated moving average models, they are easier to implement. The second part of the paper uses the spot‐price forecasting model to generate inputs for a stochastic programming model, which is then used to determine the company's optimal generation bid. The resulting optimal bidding curves are presented and analyzed in the context of the Iberian day‐ahead electricity market.     

Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition

In this work we introduce the forecasting model with which we participated in the NN5 forecasting competition (the forecasting of 111 time series representing daily cash withdrawal amounts at ATM machines). The main idea of this model is to utilize the concept of forecast combination, which has proven to be an effective methodology in the forecasting literature. In the proposed system we attempted to follow a principled approach, and make use of some of the guidelines and concepts that are known in the forecasting literature to lead to superior performance. For example, we considered various previous comparison studies and time series competitions as guidance in determining which individual forecasting models to test (for possible inclusion in the forecast combination system). The final model ended up consisting of neural networks, Gaussian process regression, and linear models, combined by simple average. We also paid extra attention to the seasonality aspect, decomposing the seasonality into weekly (which is the strongest one), day of the month, and month of the year seasonality.     

Forecasting macroeconomic variables using disaggregate survey data

We construct factor models based on disaggregate survey data for forecasting national aggregate macroeconomic variables. Our methodology applies regional and sectoral factor models to Norges Bank’s regional survey and to the Swedish Business Tendency Survey. The analysis identifies which of the pieces of information extracted from the individual regions in Norges Bank’s survey and the sectors for the two surveys perform particularly well at forecasting different variables at various horizons. The results show that several factor models beat an autoregressive benchmark in forecasting inflation and the unemployment rate. However, the factor models are most successful at forecasting GDP growth. Forecast combinations using the past performances of regional and sectoral factor models yield the most accurate forecasts in the majority of the cases.     

Evaluating factor forecasts for the UK: The role of asset prices

This paper applies a large data set, consisting of 167 monthly time series for the UK, both economic and financial, to simulate out-of-sample predictions of industrial production, inflation, 3-month Treasury Bills, and other variables. Fifteen dynamic factor models that allow forecasting based on large panels of time series are considered. The performances of these factor models are then compared to the following competing models: a simple univariate autoregressive, a vector autoregressive, a leading indicator, and a Phillips curve models. The results show that the best dynamic factor models outperform the competing models in forecasting at 6-, 12-, and 24-month horizons. Thus, the financial markets may have predictive power for the economic activity. This can be a useful tool for central banks and financial institutions, which may use the factor models to construct leading indicators of the economic conditions. In addition, researchers can see a strategic application of factor models.     

M5 competition uncertainty: Overdispersion,distributional forecasting,GAMLSS, and beyond

The M5 competition uncertainty track aims for probabilistic forecasting of sales of thousands of Walmart retail goods. We show that the M5 competition data face strong overdispersion and sporadic demand, especially zero demand. We discuss modeling issues concerning adequate probabilistic forecasting of such count data processes. Unfortunately, the majority of popular prediction methods used in the M5 competition (e.g. lightgbm and xgboost GBMs) fail to address the data characteristics, due to the considered objective functions. Distributional forecasting provides a suitable modeling approach to overcome those problems. The GAMLSS framework allows for flexible probabilistic forecasting using low-dimensional distributions. We illustrate how the GAMLSS approach can be applied to M5 competition data by modeling the location and scale parameters of various distributions, e.g. the negative binomial distribution. Finally, we discuss software packages for distributional modeling and their drawbacks, like the R package gamlss with its package extensions, and (deep) distributional forecasting libraries such as TensorFlow Probability.     

Comments on “An analysis of the international tourism demand in Spain” by P. González and P. Moral

Although the state-space, unobserved component approach to forecasting has many advantages, it must be applied carefully in practice and should not be used in an uncritical, ‘black box’ fashion. In particular, such an approach to the modelling and forecasting of Spanish tourism data is inappropriate and leads to misleading conclusions, particularly in relation to the uncritical selection and use of explanatory regression variables.     

Recent advances in intra-hour solar forecasting: A review of ground-based sky image methods

As the penetration of solar energy generation into power systems keeps rising, intra-hour solar forecasting (IHSF) is becoming increasingly important for the secure and economical operation of a power system. One major difficulty in providing very accurate IHSF emanates from rapid cloud changes in the sky. The ground-based sky image (GSI) provides the intuitive information of intra-hour cloud changes and has thus been widely utilized in studies on IHSF. This paper presents a systematic review of the state-of-the-art of ground-based sky image-based intra-hour solar forecasting (GSI-IHSF). To our knowledge, we first propose a generic framework of GSI-IHSF consisting of four modules, i.e., sky image acquisition, sky image preprocessing, cloud forecasting, and solar forecasting. Then, as for each module, this paper introduces its core function, shows the major challenges, briefly reviews several extensively used techniques, summarizing research trends. Finally, this paper offers a prospect of GSI-IHSF research, discusses recent advances that demonstrate the potential for a great improvement in forecast accuracy, pointing out some new requirements and challenges that should be further investigated in the future.     

Quantile regression for the qualifying match of GEFCom2017 probabilistic load forecasting

We present a simple quantile regression-based forecasting method that was applied in the probabilistic load forecasting framework of the Global Energy Forecasting Competition 2017 (GEFCom2017). The hourly load data are log transformed and split into a long-term trend component and a remainder term. The key forecasting element is the quantile regression approach for the remainder term, which takes into account both weekly and annual seasonalities, such as their interactions. Temperature information is used only for stabilizing the forecast of the long-term trend component. Information on public holidays is ignored. However, the forecasting method still placed second in the open data track and fourth in the definite data track, which is remarkable given the simplicity of the model. The method also outperforms the Vanilla benchmark consistently.     

An accurate and fully-automated ensemble model for weekly time series forecasting

Many businesses and industries require accurate forecasts for weekly time series nowadays. However, the forecasting literature does not currently provide easy-to-use, automatic, reproducible and accurate approaches dedicated to this task. We propose a forecasting method in this domain to fill this gap, leveraging state-of-the-art forecasting techniques, such as forecast combination, meta-learning, and global modelling. We consider different meta-learning architectures, algorithms, and base model pools. Based on all considered model variants, we propose to use a stacking approach with lasso regression which optimally combines the forecasts of four base models: a global Recurrent Neural Network (RNN) model, Theta, Trigonometric Box–Cox ARMA Trend Seasonal (TBATS), and Dynamic Harmonic Regression ARIMA (DHR-ARIMA), as it shows the overall best performance across seven experimental weekly datasets on four evaluation metrics. Our proposed method also consistently outperforms a set of benchmarks and state-of-the-art weekly forecasting models by a considerable margin with statistical significance. Our method can produce the most accurate forecasts, in terms of mean sMAPE, for the M4 weekly dataset among all benchmarks and all original competition participants.     

Macroeconomic forecasting using structural factor analysis

The use of a small number of underlying factors to summarize the information from a much larger set of information variables is one of the new frontiers in forecasting. In prior work, the estimated factors have not usually had a structural interpretation and the factors have not been chosen on a theoretical basis. In this paper we propose several variants of a general structural factor forecasting model, and use these to forecast certain key macroeconomic variables. We make the choice of factors more structurally meaningful by estimating factors from subsets of information variables, where these variables can be assigned to subsets on the basis of economic theory. We compare the forecasting performance of the structural factor forecasting model with that of a univariate AR model, a standard VAR model, and some non-structural factor forecasting models. The results suggest that our structural factor forecasting model performs significantly better in forecasting real activity variables, especially at short horizons.     

A novel text-based framework for forecasting agricultural futures using massive online news headlines

The agricultural futures prices are generally considered difficult to forecast because the causes of fluctuations are incredibly complicated. We propose a text-based forecasting framework, which can effectively identify and quantify factors affecting agricultural futures based on massive online news headlines. A comprehensive list of influential factors can be formed using a text mining method called topic modeling. A new sentiment-analysis-based way is designed to quantify the factors such as the weather and policies that are important yet difficult to quantify. The proposed framework is empirically tested at forecasting soybean futures prices in the Chinese market. Testing was based on 9715 online news headlines from July 19, 2012 to July 9, 2018. The results show that the identified influential factors and sentiment-based variables are effective, and the proposed framework performs significantly better in medium-term and long-term forecasting than the benchmark model.     

Forecasting bulk prices of Bordeaux wines using leading indicators

Agricultural price forecasting has been being abandoned progressively by researchers ever since the development of large-scale agricultural futures markets. However, as with many other agricultural goods, there is no futures market for wine. This paper draws on the agricultural prices forecasting literature to develop a forecasting model for bulk wine prices. The price data include annual and monthly series for various wine types that are produced in the Bordeaux region. The predictors include several leading economic indicators of supply and demand shifts. The stock levels and quantities produced are found to have the highest predictive power. The preferred annual and monthly forecasting models outperform naive random walk forecasts by 27.1% and 3.4% respectively; their mean absolute percentage errors are 2.7% and 3.4% respectively. A simple trading strategy based on monthly forecasts is estimated to increase profits by 3.3% relative to a blind strategy that consists of always selling at the spot price.     

Modeling and forecasting of Brazilian reservoir inflows via dynamic linear models

This work focuses on developing a forecasting model for the water inflow at an hydroelectric plant’s reservoir for operations planning. The planning horizon is 5 years in monthly steps. Due to the complex behavior of the monthly inflow time series we use a Bayesian dynamic linear model that incorporates seasonal and autoregressive components. We also use climate variables like monthly precipitation, El Niño and other indices as predictor variables when relevant. The Brazilian power system has 140 hydroelectric plants. Based on geographical considerations, these plants are collated by basin and classified into 15 groups that correspond to the major river basins, in order to reduce the dimension of the problem. The model is then tested for these 15 groups. Each group will have a different forecasting model that can best describe its unique seasonality and characteristics. The results show that the forecasting approach taken in this paper produces substantially better predictions than the current model adopted in Brazil (see Maceira & Damazio, 2006), leading to superior operations planning.     

Probabilistic forecasting of industrial electricity load with regime switching behavior

This paper suggests a novel inhomogeneous Markov switching approach for the probabilistic forecasting of industrial companies’ electricity loads, for which the load switches at random times between production and standby regimes. The model that we propose describes the transitions between the regimes using a hidden Markov chain with time-varying transition probabilities that depend on calendar variables. We model the demand during the production regime using an autoregressive moving-average (ARMA) process with seasonal patterns, whereas we use a much simpler model for the standby regime in order to reduce the complexity. The maximum likelihood estimation of the parameters is implemented using a differential evolution algorithm. Using the continuous ranked probability score (CRPS) to evaluate the goodness-of-fit of our model for probabilistic forecasting, it is shown that this model often outperforms classical additive time series models, as well as homogeneous Markov switching models. We also propose a simple procedure for classifying load profiles into those with and without regime-switching behaviors.     

Conformal prediction interval estimation and applications to day-ahead and intraday power markets

In this study, we investigated the application of the conformal prediction (CP) concept in the context of short-term electricity price forecasting. In particular, we determined the most important aspects related to the utility of CP, as well as explaining why this simple but highly effective idea has proved useful in other application areas and why its characteristics make it promising for short-term power applications. We compared the performance of CP with various state-of-the-art electricity price forecasting models, such as quantile regression averaging, in an empirical out-of-sample study of three short-term electricity time series. We combined CP with various underlying point forecast models to demonstrate its versatility and behavior under changing conditions. Our findings suggest that CP yields sharp and reliable prediction intervals in short-term power markets. We also inspected the effects of each of the model components to provide path-based guideline regarding how to find the best CP model for each market.     

VIX forecasting based on GARCH-type model with observable dynamic jumps: A new perspective

This paper proposes to study VIX forecasting based on discrete time GARCH-type model with observable dynamic jump intensity by incorporating high frequency information (DJI-GARCH model). The analytical expression is obtained by deducing the forward iteration relations of vector composed of conditional variance and jump intensity, and parameters are estimated via maximum likelihood functions. To compare the pricing ability, we also present VIX forecasting under four simple GARCH-type models. Results find that DJI-GARCH model outperforms other GARCH-type models for the whole sample and stable period in terms of both in-sample and out-of-sample forecasting, and for the in-sample forecasting during crisis period. This indicates that incorporating both realized bipower and jump variations, and combining VIX information in the estimation can obtain more accuracy forecasting. However, the out-of-sample forecasting using parameters estimated from crisis period shows that GARCH and GJR-GARCH models performs relatively better, which reminds us to be cautious when making out-of-sample prediction.