An unobserved component model for multi-rate forecasting of telephone call demand: the design of a forecasting support system

An Unobserved Components (UC) Model based on an enhanced version of the Dynamic Harmonic Regression model, including new multi-rate and modulated cycle procedures, is used to develop a customised package for forecasting and signal extraction applied to hourly telephone call numbers made to Barclaycard plc. service centres, with a forecasting horizon of up to several weeks in advance. The paper outlines both the methodological and algorithmic aspects of the modelling, forecasting and signal extraction procedures, including the design and implementation of forecasting support software with a specially designed Graphical User Interface within the ^® computing environment. The forecasting performance is evaluated comprehensively in comparison with the well-known seasonal ARIMA approach.     

The comparative forecast performance of univariate and multivariate models: an application to real interest rate forecasting

Does the use of information on the past history of the nominal interest rates and inflation entail improvement in forecasts of the ex ante real interest rate over its forecasts obtained from using just the past history of the realized real interest rates? To answer this question we set up a univariate unobserved components model for the realized real interest rates and a bivariate model for the nominal rate and inflation which imposes cointegration restrictions between them. The two models are estimated under normality with the Kalman filter. It is found that the error-correction model provides more accurate one-period ahead forecasts of the real rate within the estimation sample whereas the unobserved components model yields forecasts with smaller forecast variances. In the post-sample period, the forecasts from the bivariate model are not only more accurate but also have tighter confidence bounds than the forecasts from the unobserved components model.     

On the selection of forecasting models

It is standard in applied work to select forecasting models by ranking candidate models by their prediction mean squared error (PMSE) in simulated out-of-sample (SOOS) forecasts. Alternatively, forecast models may be selected using information criteria (IC). We compare the asymptotic and finite-sample properties of these methods in terms of their ability to mimimize the true out-of-sample PMSE, allowing for possible misspecification of the forecast models under consideration. We show that under suitable conditions the IC method will be consistent for the best approximating model among the candidate models. In contrast, under standard assumptions the SOOS method, whether based on recursive or rolling regressions, will select overparameterized models with positive probability, resulting in excessive finite-sample PMSEs.     

Online adaptive lasso estimation in vector autoregressive models for high dimensional wind power forecasting

Wind power forecasts with lead times of up to a few hours are essential to the optimal and economical operation of power systems and markets. Vector autoregression (VAR) is a framework that has been shown to be well suited to predicting for several wind farms simultaneously by considering the spatio-temporal dependencies in their time series. Lasso penalisation yields sparse models and can avoid overfitting the large numbers of coefficients in higher dimensional settings. However, estimation in VAR models usually does not account for changes in the spatio-temporal wind power dynamics that are related to factors such as seasons or wind farm setup changes, for example. This paper tackles this problem by proposing a time-adaptive lasso estimator and an efficient coordinate descent algorithm for updating the VAR model parameters recursively online. The approach shows good abilities to track changes in the multivariate time series dynamics on simulated data. Furthermore, in two case studies it shows clearly better predictive performances than the non-adaptive lasso VAR and univariate autoregression.     

Stochastic volatility models with ARMA innovations: An application to G7 inflation forecasts

We introduce a new class of stochastic volatility models with autoregressive moving average (ARMA) innovations. The conditional mean process has a flexible form that can accommodate both a state space representation and a conventional dynamic regression. The ARMA component introduces serial dependence, which results in standard Kalman filter techniques not being directly applicable. To overcome this hurdle, we develop an efficient posterior simulator that builds on recently developed precision-based algorithms. We assess the usefulness of these new models in an inflation forecasting exercise across all G7 economies. We find that the new models generally provide competitive point and density forecasts compared to standard benchmarks, and are especially useful for Canada, France, Italy, and the U.S.     

Beyond point forecasting: Evaluation of alternative prediction intervals for tourist arrivals

This paper evaluates the performances of prediction intervals generated from alternative time series models, in the context of tourism forecasting. The forecasting methods considered include the autoregressive (AR) model, the AR model using the bias-corrected bootstrap, seasonal ARIMA models, innovations state space models for exponential smoothing, and Harvey’s structural time series models. We use thirteen monthly time series for the number of tourist arrivals to Hong Kong and Australia. The mean coverage rates and widths of the alternative prediction intervals are evaluated in an empirical setting. It is found that all models produce satisfactory prediction intervals, except for the autoregressive model. In particular, those based on the bias-corrected bootstrap perform best in general, providing tight intervals with accurate coverage rates, especially when the forecast horizon is long.     

Forecasting macroeconomic variables using collapsed dynamic factor analysis

We explore a new approach to the forecasting of macroeconomic variables based on a dynamic factor state space analysis. Key economic variables are modeled jointly with principal components from a large time series panel of macroeconomic indicators using a multivariate unobserved components time series model. When the key economic variables are observed at a low frequency and the panel of macroeconomic variables is at a high frequency, we can use our approach for both nowcasting and forecasting purposes. Given a dynamic factor model as the data generation process, we provide Monte Carlo evidence of the finite-sample justification of our parsimonious and feasible approach. We also provide empirical evidence for a US macroeconomic dataset. The unbalanced panel contains quarterly and monthly variables. The forecasting accuracy is measured against a set of benchmark models. We conclude that our dynamic factor state space analysis can lead to higher levels of forecasting precision when the panel size and time series dimensions are moderate.     

Exponentially weighted information criteria for selecting among forecasting models

Information criteria (IC) are often used to decide between forecasting models. Commonly used criteria include Akaike's IC and Schwarz's Bayesian IC. They involve the sum of two terms: the model's log likelihood and a penalty for the number of model parameters. The likelihood is calculated with equal weight being given to all observations. We propose that greater weight should be put on more recent observations in order to reflect more recent accuracy. This seems particularly pertinent when selecting among exponential smoothing methods, as they are based on an exponential weighting principle. In this paper, we use exponential weighting within the calculation of the log likelihood for the IC. Our empirical analysis uses supermarket sales and call centre arrivals data. The results show that basing model selection on the new exponentially weighted IC can outperform individual models and selection based on the standard IC.     

Robust recurrent network model for intermittent time-series forecasting

This paper describes a deep-learning-based time-series forecasting method that was ranked third in the accuracy challenge of the M5 competition. We solved the problem using a deep-learning approach based on DeepAR, which is an auto-regressive recurrent network model conditioned on historical inputs. To address the intermittent and irregular characteristics of sales demand, we modified the training procedure of DeepAR; instead of using actual values for the historical inputs, our model uses values sampled from a trained distribution and feeds them to the network as past values. We obtained the final result using an ensemble of multiple models to make a robust and stable prediction. To appropriately select a model for the ensemble, each model was evaluated using the average weighted root mean squared scaled error, calculated for all levels of a wide range of past periods.     

Use and misuse of information in supply chain forecasting of promotion effects

Demand forecasting is critical to sales and operations planning (S&OP), but the effects of sales promotions can be difficult to forecast. Typically, a baseline statistical forecast is judgmentally adjusted on receipt of information from different departments. However, much of this information either has no predictive value or its value is unknown. Research into base rate discounting has suggested that such information may distract forecasters from the average uplift and reduce accuracy. This has been investigated in situations in which forecasters were able to adjust the statistical forecasts for promotions via a forecasting support system (FSS). In two ecologically valid experiments, forecasters were provided with the mean level of promotion uplift, a baseline statistical forecast, and quantitative and qualitative information. However, the forecasters were distracted from the base rate and misinterpreted the information available to them. These findings have important implications for the design of organizational S&OP processes, and for the implementation of FSSs.     

Bayesian inference for nonlinear structural time series models

We consider efficient methods for likelihood inference applied to structural models. In particular, we introduce a particle filter method which concentrates upon disturbances in the Markov state of the approximating solution to the structural model. A particular feature of such models is that the conditional distribution of interest for the disturbances is often multimodal. We provide a fast and effective method for approximating such distributions. We estimate a neoclassical growth model using this approach. An asset pricing model with persistent habits is also considered. The methodology we employ allows many fewer particles to be used than alternative procedures for a given precision.     

Predicting equity premium using dynamic model averaging. Does the state–space representation matter?

Dynamic model averaging (DMA) has become a very useful tool with regards to dealing with two important aspects of time-series analysis, namely, parameter instability and model uncertainty. An important component of DMA is the Kalman filter. It is used to filter out the latent time-varying regression coefficients of the predictive regression of interest, and produce the model predictive likelihood, which is needed to construct the probability of each model in the model set. To apply the Kalman filter, one must write the model of interest in linear state–space form. In this study, we demonstrate that the state–space representation has implications on out-of-sample prediction performance, and the degree of shrinkage. Using Monte Carlo simulations as well as financial data at different sampling frequencies, we document that the way in which the current literature tends to formulate the candidate time-varying parameter predictive regression in linear state–space form ignores empirical features that are often present in the data at hand, namely, predictor persistence and predictor endogeneity. We suggest a straightforward way to account for these features in the DMA setting. Results using the widely applied Goyal and Welch (2008) dataset document that modifying the DMA framework as we suggest has a bearing on equity premium point prediction performance from a statistical as well as an economic viewpoint.     

The role of observed and unobserved heterogeneity in the duration of unemployment

This paper studies the degree to which observable and unobservable worker characteristics account for the variation in the aggregate duration of unemployment. I model the distribution of unobserved worker heterogeneity as time varying to capture the interaction of latent attributes with changes in labor-market conditions. Unobserved heterogeneity is the main explanation for the duration dependence of unemployment hazards. Both cyclical and low-frequency variations in the mean duration of unemployment are mainly driven by one subgroup: workers who, for unobserved reasons, stay unemployed for a long time. In contrast, changes in the composition of observable characteristics of workers have negligible effects.     

Rethinking weather station selection for electric load forecasting using genetic algorithms

Demand forecasting is and has been for years a topic of great interest in the electricity sector, being the temperature one of its major drivers. Indeed, one of the challenges when modelling the load is to choose the right weather station, or set of stations, for a given load time series. However, only a few research papers have been devoted to this topic. This paper reviews the most relevant methods that were applied during the Global Energy Forecasting Competition of 2014 (GEFCom2014) and presents a new approach to weather station selection, based on Genetic Algorithms (GA), which allows finding the best set of stations for any demand forecasting model, and outperforms the results of existing methods. Furthermore its performance has also been tested using GEFCom2012 data, providing significant error improvements. Finally, the possibility of combining the weather stations selected by the proposed GA using the BFGS algorithm is briefly tested, providing promising results.     

Data visualization and forecast combination for probabilistic load forecasting in GEFCom2017 final match

This paper describes the methods used by Team Cassandra, a joint effort between IBM Research Australia and the University of Melbourne, in the GEFCom2017 load forecasting competition. An important first phase in the forecasting effort involved a deep exploration of the underlying dataset. Several data visualisation techniques were applied to help us better understand the nature and size of gaps, outliers, the relationships between different entities in the dataset, and the relevance of custom date ranges. Improved, cleaned data were then used to train multiple probabilistic forecasting models. These included a number of standard and well-known approaches, as well as a neural-network based quantile forecast model that was developed specifically for this dataset. Finally, model selection and forecast combination were used to choose a custom forecasting model for every entity in the dataset.     

Forecasting correlated time series with exponential smoothing models

This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.     

A literature review of decision-making models and approaches for partner selection in agile supply chains

The paper reviews the literature on supply partner decision-making published between 2001 and 2011, a period that has seen a significant increase in work published in this field. The progress made in developing new models and methods that can be applied to this task is assessed in the context of the previous literature. Particular attention is given to those methods that are especially relevant for use in agile supply chains. The paper uses a classification framework that enables models intended for similar purposes to be compared and tracked over time. It is also used to identify a number of gaps in the literature. The findings highlight an on-going need to develop methods that are able to meet the combination of qualitative and quantitative objectives that are typically found in partner selection problems in practice.     

Can Google search data help predict macroeconomic series?

We make use of Google search data in an attempt to predict unemployment, CPI and consumer confidence for the US, UK, Canada, Germany and Japan. Google search queries have previously proven valuable in predicting macroeconomic variables in an in-sample context. However, to the best of our knowledge, the more challenging question of whether such data have out-of-sample predictive value has not yet been answered satisfactorily. We focus on out-of-sample nowcasting, and extend the Bayesian structural time series model using the Hamiltonian sampler for variable selection. We find that the search data retain their value in an out-of-sample predictive context for unemployment, but not for CPI or consumer confidence. It is possible that online search behaviours are a relatively reliable gauge of an individual’s personal situation (employment status), but less reliable when it comes to variables that are unknown to the individual (CPI) or too general to be linked to specific search terms (consumer confidence).     

A Markov chain model for forecasting results of mixed martial arts contests

In this paper, we present a new methodology for forecasting the results of mixed martial arts contests. Our approach utilises data scraped from freely available websites to estimate fighters’ skills in various key aspects of the sport. With these skill estimates, we simulate the contest as an actual fight using Markov chains, rather than predicting a binary outcome. We compare the model’s accuracy to that of the bookmakers using their historical odds and show that the model can be used as the basis of a successful betting strategy.