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.     

Bayesian analysis of random coefficient logit models using aggregate data

We present a Bayesian approach for analyzing aggregate level sales data in a market with differentiated products. We consider the aggregate share model proposed by Berry et al. [Berry, Steven, Levinsohn, James, Pakes, Ariel, 1995. Automobile prices in market equilibrium. Econometrica. 63 (4), 841–890], which introduces a common demand shock into an aggregated random coefficient logit model. A full likelihood approach is possible with a specification of the distribution of the common demand shock. We introduce a reparameterization of the covariance matrix to improve the performance of the random walk Metropolis for covariance parameters. We illustrate the usefulness of our approach with both actual and simulated data. Sampling experiments show that our approach performs well relative to the GMM estimator even in the presence of a mis-specified shock distribution. We view our approach as useful for those who are willing to trade off one additional distributional assumption for increased efficiency in estimation.     

Integrated variance forecasting: Model based vs. reduced form

This paper compares model-based and reduced-form forecasts of financial volatility when high-frequency return data are available. We derived exact formulas for the forecast errors and analyzed the contribution of the “wrong” data modeling and errors in forecast inputs. The comparison is made for “feasible” forecasts, i.e., we assumed that the true data generating process, latent states and parameters are unknown. As an illustration, the same comparison is carried out empirically for spot 5 min returns of DM/USD exchange rates.It is shown that the comparison between feasible reduced-form and model-based forecasts is not always in favor of the latter in contrast to their infeasible versions. The reduced-form approach is generally better for long-horizon forecasting and for short-horizon forecasting in the presence of microstructure noise.     

Aggregate vs. disaggregate data analysis—a paradox in the estimation of a money demand function of Japan under the low interest rate policy

We use Japanese aggregate and disaggregate money demand data to show that conflicting inferences can arise. The aggregate data appears to support the contention that there was no stable money demand function. The disaggregate data shows that there was a stable money demand function. Neither was there any indication of the presence of a liquidity trap. Possible sources of discrepancy are explored and the diametrically opposite results between the aggregate and disaggregate analysis are attributed to the neglected heterogeneity among micro units. We provide necessary and sufficient conditions for the existence of a cointegrating relation among aggregate variables when heterogeneous cointegration relations among micro units exist. We also conduct simulation analysis to show that when such conditions are violated, it is possible to observe stable micro relations, but unit root phenomena among macro variables. Moreover, the prediction of aggregate outcomes, using aggregate data, is less accurate than the prediction based on micro equations, and policy evaluation based on aggregate data ignoring heterogeneity in micro units can be grossly misleading. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

The performance of the global bottom-up approach in the M5 accuracy competition: A robustness check

The M5 accuracy competition has presented a large-scale hierarchical forecasting problem in a realistic grocery retail setting in order to evaluate an extended range of forecasting methods, particularly those adopting machine learning. The top ranking solutions adopted a global bottom-up approach, by which is meant using global forecasting methods to generate bottom level forecasts in the hierarchy and then using a bottom-up strategy to obtain coherent forecasts for aggregate levels. However, whether the observed superior performance of the global bottom-up approach is robust over various test periods or only an accidental result, is an important question for retail forecasting researchers and practitioners. We conduct experiments to explore the robustness of the global bottom-up approach, and make comments on the efforts made by the top-ranking teams to improve the core approach. We find that the top-ranking global bottom-up approaches lack robustness across time periods in the M5 data. This inconsistent performance makes the M5 final rankings somewhat of a lottery. In future forecasting competitions, we suggest the use of multiple rolling test sets to evaluate the forecasting performance in order to reward robustly performing forecasting methods, a much needed characteristic in any application.     

Forecasting Macroeconomic Labour Market Flows: What Can We Learn from Micro‐level Analysis?

Forecasting labour market flows is important for budgeting and decision‐making in government departments and public administration. Macroeconomic forecasts are normally obtained from time series data. In this article, we follow another approach that uses individual‐level statistical analysis to predict the number of exits out of unemployment insurance claims. We present a comparative study of econometric, actuarial and statistical methodologies that base on different data structures. The results with records of the German unemployment insurance suggest that prediction based on individual‐level statistical duration analysis constitutes an interesting alternative to aggregate data‐based forecasting. In particular, forecasts of up to six months ahead are surprisingly precise and are found to be more precise than considered time series forecasts.     

Differencing versus nondifferencing in factor-based forecasting

This paper studies performance of factor-based forecasts using differenced and nondifferenced data. Approximate variances of forecasting errors from the two forecasts are derived and compared. It is reported that the forecast using nondifferenced data tends to be more accurate than that using differenced data. This paper conducts simulations to compare root mean squared forecasting errors of the two competing forecasts. Simulation results indicate that forecasting using nondifferenced data performs better. The advantage of using nondifferenced data is more pronounced when a forecasting horizon is long and the number of factors is large. This paper applies the two competing forecasting methods to 68 I(1) monthly US macroeconomic variables across a range of forecasting horizons and sampling periods. We also provide detailed forecasting analysis on US inflation and industrial production. We find that forecasts using nondifferenced data tend to outperform those using differenced data.     

Macroeconomic forecasting for Australia using a large number of predictors

A popular approach to forecasting macroeconomic variables is to utilize a large number of predictors. Several regularization and shrinkage methods can be used to exploit such high-dimensional datasets, and have been shown to improve forecast accuracy for the US economy. To assess whether similar results hold for economies with different characteristics, an Australian dataset containing observations on 151 aggregate and disaggregate economic series as well as 185 international variables, is introduced. An extensive empirical study is carried out investigating forecasts at different horizons, using a variety of methods and with information sets containing an increasing number of predictors. In contrast to other countries the results show that it is difficult to forecast Australian key macroeconomic variables more accurately than some simple benchmarks. In line with other studies we also find that there is little to no improvement in forecast accuracy when the number of predictors is expanded beyond 20–40 variables and international factors do not seem to help.     

INCOME PERSISTENCE AND MACRO-POLICY FEEDBACKS IN THE US*

This paper analyses and forecasts annual time series of aggregate real income per head in the US. The approach integrates elements from recent univariate time series analyses with multi-equation macromodels in which policy feedback rules have been endogenized. The main conclusions are as follows. Firstly, aggregate real per capita income is subject to significant trend reversion. This conclusion comes through more clearly by examining the data at an annual rather than the more usual quarterly frequency and by incorporating multivariate economic content in the income process. Secondly, there is significant evidence for the Lucas (1976) or Haavelmo (1944) critique: in the US there appears to have been a shift in the structural macropolicy reaction function causing a corresponding shift in the reduced form income forecasting equation. This is associated with increased concern in the late 1980's over the size of US budget deficits. Thirdly, with the above proviso, useful real income forecasts can be made as far as three years ahead. Finally, the paper provides empirical evidence for the effectiveness of monetary policy on real output or income. The change in the short-term interest rate is highly significant in forecasting income growth up to three years after the change.     

A reformulation of the aggregate planning problem

This article proposes a reformulation of the aggregate planning problem which more closely agrees with situations frequently encountered in practice. The proposed reformulation assumes that a firm's production planners want to determine the expected service and inventory levels for a given production profile in the face of uncertain seasonal demand. By using several different production profiles that are each consistent with the firm's staffing, subcontracting, and overtime policies, it is possible to pick the profile that best meets the firm's preferences for service level and inventory turns. Actually, the trade-offs between inventory and service levels are examined so that an informed choice can be made by all of those concerned.One of the advantages of the proposed model is that communications can be established among production, marketing, and finance managers who often have conflicting goals. Also, levels for inventory turns, service, and production can be set that are consistent with each other. Furthermore, several alternative production profiles can be examined in a relatively short time through the use of the simulation model proposed.An application of the model to the Wagner Spray Tech Company, a producer of painting equipment, is presented. In this particular case, where forecasting errors are quite high, some of the potential uses of the model are presented. Also, reasons are given why this particular reformulation of the aggregate planning problem was found to be useful.     

Transferability of disaggregate mode choice models

Predictions of aggregate transport mode split for inter-city trips are derived from a disaggregate model of travel demand. A series of tests are performed to assess the limitations of the prediction methodology for disaggregate models, and it is shown that disaggregate models are capable of predictions across diverse travel situations. The disaggregate model predictions are compared with predictions derived from aggregate models such as are currently used in urban transportation planning, and it is shown that disaggregate models based on much smaller data sets predict better than aggregate models while requiring no more information about the predicted population.     

Regional heterogeneity and U.S. presidential elections: Real-time 2020 forecasts and evaluation

This paper exploits cross-sectional variation at the level of U.S. counties to generate real-time forecasts for the 2020 U.S. presidential election. The forecasting models are trained on data covering the period 2000–2016, using high-dimensional variable selection techniques. Our county-based approach contrasts the literature that focuses on national and state level data but uses longer time periods to train their models. The paper reports forecasts of popular and electoral college vote outcomes and provides a detailed ex-post evaluation of the forecasts released in real time before the election. It is shown that all of these forecasts outperform autoregressive benchmarks. A pooled national model using One-Covariate-at-a-time-Multiple-Testing (OCMT) variable selection significantly outperformed all models in forecasting the U.S. mainland national vote share and electoral college outcomes (forecasting 236 electoral votes for the Republican party compared to 232 realized). This paper also shows that key determinants of voting outcomes at the county level include incumbency effects, unemployment, poverty, educational attainment, house price changes, and international competitiveness. The results are also supportive of myopic voting: economic fluctuations realized a few months before the election tend to be more powerful predictors of voting outcomes than their long-horizon analogs.     

Modeling and forecasting the time series of US fertility: age distribution,range, and ultimate level

This discussion of modeling focuses on the difficulties in longterm, time-series forecasting of US fertility. Four possibilities are suggested. One difficulty with the traditional approach of using high or low bounds on fertility and mortality is that forecast errors are perfectly correlated over time, which means there are no cancellation of errors over time. The shape of future fertility intervals first increases, then stabilizes, and then decreases instead of remaining stable. This occurs because the number of terms being averaged increases with horizontal length. Alho and Spencer attempted to reduce these errors in time-series. Other difficulties are the idiosyncratic behavior of age specific fertility over time, biological bounds for total fertility rates (TFR) of 16 and zero, the integration of knowledge about fertility behavior that narrows the bounds, the unlikelihood of some probability outcomes of stochastic models with a normally distributed error term, the small relative change in TFR between years, a US fertility cycle of about 40 years, unimportant extrapolation of past trends in child and infant mortality, and the unlikelihood of reversals in mortality and contraceptive use trends. Another problem is the unsuitability of longterm forecasts. New methods include a model which estimates a one parameter family of fertility schedules and then forecasts that single parameter. Another method is a logistic transformation to account for prior information on the bounds on fertility estimates; this method is similar to Bayesian methods for ARMA models developed by Monahan. Models include information on the ultimate level of fertility and assume that the equilibrium level is a stochastic process trending over time. The horizon forecast method is preferred unless the effects of the outliers are known. Estimates of fertility are presented for the equilibrium constrained and logistic transformed model. Forecasts of age specific fertility rates can be calculated from forecasts of the fertility index (a single time varying parameter). The model of fertility fits poorly at older ages but captures some of the wide swings in the historical pattern. Age variations are not accounted for very well. Longterm forecasts tell a great deal about the uncertainty of forecast errors. Estimates are too sensitive to model specification for accuracy and ignore the biological and socioeconomic context.     

Forecasting the M4 competition weekly data: Forecast Pro’s winning approach

Forecast Pro forecasted the weekly series in the M4 competition more accurately than all other entrants. Our approach was to follow the same forecasting process that we recommend to our users. This approach involves determining the Key Performance Metric (KPI), establishing baseline forecasts using our automated expert selection algorithm, reviewing those baseline forecasts and customizing forecasts where needed. This article explores why this approach worked well for weekly data, discusses the applicability of the M4 competition to business forecasting and proposes some potential improvements for future competitions to make them more relevant to business forecasting.     

Combination of long term and short term forecasts, with application to tourism demand forecasting

Forecast combination is a well-established and well-tested approach for improving the forecasting accuracy. One beneficial strategy is to use constituent forecasts that have diverse information. In this paper we consider the idea of diversity being accomplished by using different time aggregations. For example, we could create a yearly time series from a monthly time series and produce forecasts for both, then combine the forecasts. These forecasts would each be tracking the dynamics of different time scales, and would therefore add diverse types of information. A comparison of several forecast combination methods, performed in the context of this setup, shows that this is indeed a beneficial strategy and generally provides a forecasting performance that is better than the performances of the individual forecasts that are combined.As a case study, we consider the problem of forecasting monthly tourism numbers for inbound tourism to Egypt. Specifically, we consider 33 individual source countries, as well as the aggregate. The novel combination strategy also produces a generally improved forecasting accuracy.     

Forecasting Errors: the Track Record

This Briefing Paper is the last of a series of three about forecasting. In this one we examine our forecasting record; it complements the February paper in which we analysed the properties of our forecasting model in terms of the error bands attached to the central forecast.
There are many ways of measuring forecasting errors, and in the first part of this Briefing Paper we describe briefing how we have tackled the problem. (A more detailed analysis can be found in the Appendix.) In Part II we report and comment upon the errors in our forecasts of annual growth rates and show how our forecasting performance has improved over the years. In Part III we focus on quarterly forecasts up to 8 quarters ahead, and compare our forecasting errors with measurement errors in the oficial statistics; with the estimation errors built into our forecast equations; and with the stochastic model errors we reported last February. A brief summary of the main conclusions is given below.     

Reconciled boosted models for GEFCom2017 hierarchical probabilistic load forecasting

When forecasting time series in a hierarchical configuration, it is necessary to ensure that the forecasts reconcile at all levels. The 2017 Global Energy Forecasting Competition (GEFCom2017) focused on addressing this topic. Quantile forecasts for eight zones and two aggregated zones in New England were required for every hour of a future month. This paper presents a new methodology for forecasting quantiles in a hierarchy which outperforms a commonly-used benchmark model. A simulation-based approach was used to generate demand forecasts. Adjustments were made to each of the demand simulations to ensure that all zonal forecasts reconciled appropriately, and a weighted reconciliation approach was implemented to ensure that the bottom-level zonal forecasts summed correctly to the aggregated zonal forecasts. We show that reconciling in this manner improves the forecast accuracy. A discussion of the results and modelling performances is presented, and brief reviews of hierarchical time series forecasting and gradient boosting are also included.     

Are macroeconomic density forecasts informative?

We consider whether survey density forecasts (such as the inflation and output growth histograms of the US Survey of Professional Forecasters) are superior to unconditional density forecasts. The unconditional forecasts assume that the average level of uncertainty that has been experienced in the past will continue to prevail in the future, whereas the SPF projections ought to be adapted to the current conditions and the outlook at each forecast origin. The SPF forecasts might be expected to outperform the unconditional densities at the shortest horizons, but it transpires that such is not the case for the aggregate forecasts of either variable, or for the majority of the individual respondents for forecasting inflation.     

VAR,ERROR CORRECTION AND PRETEST FORECASTS AT LONG HORIZONS

This paper focuses on the construction of forecasts over long horizons where a typical long-horizon forecast might span four years using 20 to 40 years’ data. It is argued that the presence of persistence in the form of unit or near-unit autoregressive roots poses substantial difficulties for long-horizon interval and point forecasting. These difficulties may not be overcome even by efficient pre-testing or model-selection procedures and might, in general, lead to point forecasts with large asymptotic root mean squared errors and undesirably wide prediction intervals.