Joint Forecasts Research Articles

Density forecast combinations: The real‐time dimension

AbstractEuro area real‐time density forecasts from three dynamic stochastic general equilibrium (DSGE) and three Bayesian vector autoregression (BVAR) models are compared with six combination methods over the sample 2001Q1–2019Q4. The terms information and observation lag are introduced to distinguish time shifts between data vintages and actuals used to compute model weights and compare the forecast, respectively. Bounds for finite mixture combinations are presented, allowing for benchmarking them given the models. Empirically, combinations with limited weight variation often improve upon the individual models for the output and the joint forecasts with inflation. This reflects overconfident BVAR forecasts before the Great Recession. For inflation, a BVAR model typically performs best.

Sex Differential Dynamics in Coherent Mortality Models

The main purpose of coherent mortality models is to produce plausible, joint forecasts for related populations avoiding, e.g., crossing or diverging mortality trajectories; however, the coherence assumption is very restrictive and it enforces trends that may be at odds with data. In this paper we focus on coherent, two-sex mortality models and we prove, under suitable conditions, that the coherence assumption implies sex gap unimodality, i.e., we prove that the difference in life expectancy between women and men will first increase and then decrease. Moreover, we demonstrate that, in the model, the sex gap typically peaks when female life expectancy is between 30 to 50 years. This explains why coherent mortality models predict narrowing sex gaps for essentially all Western European countries and all jump-off years since the 1950s, despite the fact that the actual sex gap was widening until the 1980s. In light of these findings, we discuss the current role of coherence as the gold standard for multi-population mortality models.

A Data-Driven Model of a Firm's Operations With Application to Cash Flow Forecasting

The cash flow from the operations of a firm is an endogenous function of the operational variables of the firm -- sales, operating cost, inventory, payables, receivables, etc. Cash flow depends on these variables, and in turn, these variables depend on cash flow and each other through the decisions made by the firm. Consequently, cash flow forecasting is a challenging problem. In this paper, we propose a generalizable and data-driven model of a firm's operations to disentangle this endogeneity and estimate causal impacts among variables. By estimating our model using quarterly public operational and financial data from S&P's Compustat database for 1990-2020, we obtain joint forecasts for cash flows and other operational variables as functions of their lagged values. We show that these joint forecasts are more accurate than those generated from univariate time-series models. Our model also helps quantify the short- and long-run impacts of structural shocks in variables on the entire system, which has applications in assessing the impact of exogenous macroeconomic factors such as recessions (or the COVID-19 pandemic) on future operational performance.

Dynamic Bayesian temporal modeling and forecasting of short-term wind measurements

Abstract We present a new Bayesian modeling approach for joint analysis of wind components and short-term wind prediction. This approach considers a truncated bivariate matrix Bayesian dynamic linear model (TMDLM) that jointly models the u (zonal) and v (meridional) wind components of observed hourly wind speed and direction data. The TMDLM takes into account calm wind observations and provides joint forecasts of hourly wind speed and direction at a given location. The proposed model is compared to alternative empirically-based time series approaches that are often used for short-term wind prediction, including the persistence method (naive predictor), as well as univariate and bivariate ARIMA models. Model performance is measured predictively in terms of mean squared errors associated to 1-h and 24-h ahead forecasts. We show that our approach generally leads to more accurate short term predictions than these alternative approaches in the context of analysis and forecasting of hourly wind measurements in 3 locations in Northern California for winter and summer months.

Mortality projections for non-converging groups of populations

We propose a nested multi-population mortality projection model in which the forces of mortality are modelled via an extended version of the Cairns-Blake-Dowd (CBD) model, and the resulting model parameters are forecast using a Vector Error Correction Model (VECM). Dependencies between different populations are accounted for by both cross-correlation and cointegration terms. The hierarchical set-up is flexible, easily interpretable, and leads to biologically plausible joint forecasts for middle and higher ages. Bayesian model estimation assures coherent forecasts and allows for quantifying the underlying joint uncertainty. We study two European empirical examples which suggest that -- contrary to the commonly stated convergence of mortality patterns -- significant differences seem to be an inherent feature in multi-national mortality. This calls for a modelling that does not enforce convergence through strict a priori assumptions.

Euro area real-time density forecasting with financial or labor market frictions

We compare real-time density forecasts for the euro area using three DSGE models. The benchmark is the Smets and Wouters model, and its forecasts of real GDP growth and inflation are compared with those from two extensions. The first adds financial frictions and expands the observables to include a measure of the external finance premium. The second allows for the extensive labor-market margin and adds the unemployment rate to the observables. The main question that we address is whether these extensions improve the density forecasts of real GDP and inflation and their joint forecasts up to an eight-quarter horizon. We find that adding financial frictions leads to a deterioration in the forecasts, with the exception of longer-term inflation forecasts and the period around the Great Recession. The labor market extension improves the medium- to longer-term real GDP growth and shorter- to medium-term inflation forecasts weakly compared with the benchmark model.

Robust Forecast Evaluation of Expected Shortfall*

Abstract Motivated by the Basel III regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to evaluate forecast performance in this context. However, little intuitive or empirical guidance is currently available, which renders the choice of scoring function awkward in practice. We therefore develop graphical checks of whether one forecast method dominates another under a relevant class of scoring functions, and propose an associated hypothesis test. We illustrate these tools with simulation examples and an empirical analysis of S&P 500 and DAX returns.

Euro Area Real-Time Density Forecasting with Financial or Labor Market Frictions

Abstract We compare real-time density forecasts for the euro area using three DSGE models. The benchmark is the Smets and Wouters model, and its forecasts of real GDP growth and inflation are compared with those from two extensions. The first adds financial frictions and expands the observables to include a measure of the external finance premium. The second allows for the extensive labor-market margin and adds the unemployment rate to the observables. The main question that we address is whether these extensions improve the density forecasts of real GDP and inflation and their joint forecasts up to an eight-quarter horizon. We find that adding financial frictions leads to a deterioration in the forecasts, with the exception of longer-term inflation forecasts and the period around the Great Recession. The labor market extension improves the medium- to longer-term real GDP growth and shorter- to medium-term inflation forecasts weakly compared with the benchmark model.

Modelling tourist flow association for tourism demand forecasting

The purpose of this study is to examine tourism demand for Singapore from 1995 to 2013 by six major origin countries which belong to three different regions. Unlike prior tourism research, we take into account the dependence relations among the different tourist flows via copula. Copula is a statistical model of dependence and measurement of association. Specifically, we investigate the association between two tourist flows in each region. Based on empirical copula estimation, the Frank function has been identified as the most appropriate to capture the pairwise dependence structures of tourist flows. The copula-based approach combined with econometric models is proposed for tourism demand analysis that can be used to predict tourist arrivals. We apply the copula-ARDL and copula-ECM frameworks to generate joint forecasts of tourist arrivals from three regions. The findings show that the forecast performance of the Frank copula-based model outperforms the benchmark model which corresponds to the independence structure (no association) of tourist flows.

Multivariate test for forecast rationality under asymmetric loss functions: Recent evidence from MMS survey of inflation–output forecasts

We propose a multivariate test for forecast rationality under asymmetric loss functions and test jointly the rationality of inflation–output forecasts of the MMS survey for the US. Our results indicate that even though the rationality of the forecasts individually may be rejected under two popular univariate asymmetric loss functions, Linlin and Linex, there is evidence that rationality of the joint forecasts of inflation and output cannot be rejected. We find that allowing for multivariate asymmetric loss functions does improve the evidence for rationality.

Forecasting the Price of Oil

Abstract We address some of the key questions that arise in forecasting the price of crude oil. What do applied forecasters need to know about the choice of sample period and about the tradeoffs between alternative oil price series and model specifications? Are real and nominal oil prices predictable based on macroeconomic aggregates? Does this predictability translate into gains in out-of-sample forecast accuracy compared with conventional no-change forecasts? How useful are oil futures prices in forecasting the spot price of oil? How useful are survey forecasts? How does one evaluate the sensitivity of a baseline oil price forecast to alternative assumptions about future oil demand and oil supply conditions? How does one quantify risks associated with oil price forecasts? Can joint forecasts of the price of oil and of U.S. real GDP growth be improved upon by allowing for asymmetries?

Management Insights

Management Insights

Forecasting the Price of Oil

We address some of the key questions that arise in forecasting the price of crude oil. What do applied forecasters need to know about the choice of sample period and about the tradeoffs between alternative oil price series and model specifications? Are real or nominal oil prices predictable based on macroeconomic aggregates? Does this predictability translate into gains in out-of-sample forecast accuracy compared with conventional no-change forecasts? How useful are oil futures markets in forecasting the price of oil? How useful are survey forecasts? How does one evaluate the sensitivity of a baseline oil price forecast to alternative assumptions about future demand and supply conditions? How does one quantify risks associated with oil price forecasts? Can joint forecasts of the price of oil and of U.S. real GDP growth be improved upon by allowing for asymmetries?

Systemic Risks and the Macroeconomy

This paper presents a modeling framework that delivers joint forecasts of indicators of systemic real risk and systemic financial risk, as well as stress-tests of these indicators as impulse responses to structural shocks identified by standard macroeconomic and banking theory. This framework is implemented using large sets of quarterly time series of indicators of financial and real activity for the G-7 economies for the 1980Q1-2009Q3 period. We obtain two main results. First, there is evidence of out-of sample forecasting power for tail risk realizations of real activity for several countries, suggesting the usefulness of the model as a risk monitoring tool. Second, in all countries aggregate demand shocks are the main drivers of the real cycle, and bank credit demand shocks are the main drivers of the bank lending cycle. These results challenge the common wisdom that constraints in the aggregate supply of credit have been a key driver of the sharp downturn in real activity experienced by the G-7 economies in 2008Q4- 2009Q1.

Joint forecasts of Dow Jones stocks under general multivariate loss function

When forecasts are assessed by a general loss (cost-of-error) function, the optimal point forecast is, in general, not the conditional mean, and depends on the conditional volatility—which, for stock returns, is time-varying. In order to provide forecasts of daily returns of 30 DJIA stocks under a general multivariate loss function, the following issues are addressed. We discuss what conditions define a multivariate loss function, and a simple class of such functions is proposed. Based on suitable combinations of univariate losses, the suggested multivariate functions are convenient for practical applications with many variables. To keep the computational aspect tractable, a flexible multivariate GARCH model is employed in estimating the conditional forecast distributions. The model easily copes with large number of series while allowing for skewness, fat tails, non-ellipticity, and tail dependence. Based on Engle’s DCC GARCH, it uses multivariate affine generalized hyperbolic distributions as conditional probability law, and the number of parameters to be estimated simultaneously does not depend on the number of series. The model is fitted using daily data from 2002 to 2007 (keeping data from 2008 for out-of-sample forecasts), and a bootstrap procedure is used to derive point forecasts under several multivariate loss functions of the proposed type.

Do Inventory and Gross Margin Data Improve Sales Forecasts for U.S. Public Retailers?

Firm-level sales forecasts for retailers can be improved if we incorporate cost of goods sold, inventory, and gross margin (defined by us as the ratio of sales to cost of goods sold) as three endogenous variables. We construct a simultaneous equations model, estimated using public financial and nonfinancial data, to provide joint forecasts of annual cost of goods sold, inventory, and gross margin for retailers using historical data. We show that sales forecasts from this model are more accurate than consensus forecasts from equity analysts. Further, the residuals from this model for one fiscal year are used to predict retailers for whom the relative advantage of model forecasts over consensus forecasts would be large in the next fiscal year. Our results show that historical inventory and gross margin contain information useful to forecast sales, and that equity analysts do not fully utilize this information in their sales forecasts.

Joint forecasts of Southern European fertility rates with non-stationary dynamic factor models

Fertility forecasting is the weak point of stochastic population forecasts. Changing trends account for large forecasting errors even a few years ahead. On the other hand, fertility trends have been shown to be common to different European countries. This paper explores the possibility of improving forecasts by jointly modelling total fertility rate (TFR) trends within relatively homogeneous clusters of countries. We propose different varieties of non-stationary dynamic factor models applied to Southern European countries. The forecasting performance of the common factor models is compared to alternative univariate and multivariate forecasting methods using data for the period 1950–2000. Joint forecasts show forecasting gains in terms of root mean square error of prediction (RMSE), particularly for longer forecast horizons. This corroborates the convenience of modelling fertility jointly for population forecasting.

Modeling and forecasting US sex differentials in mortality

This paper examines forecasted differentials in age-sex-specific mortality in the United States, 1990–2065. A non-linear model, m x,t = exp( a x + b x k t + e x,t ), is fitted for each sex age-specific US death rates, 1933–1988, using SVD to derive a single time-varying index of mortality, k t . Box-Jenkins techniques are used to estimate and forecast k t . These forecasts are used to generate age-specific mortality rates and life expectancies to 2065. Independent forecasts of male and female e 0's are 82.0 and 90.4, respectively, for 2065, a difference of 8.4 years. These forecasts are substantially higher with narrower confidence intervals than those prepared regularly by the Actuary of the Social Security Administration [ Wade (1989)]. These k t , generated forecasts of e 0 appear more plausible than direct forecasts of e 0 Life expectancies derived from jointly estimated and forecasted k t are competitive with the independent sex forecasts, but have some problems. Joint forecasts of k t are juxtaposed to co-integration speculatively as a direction for future research into linkages between male and female mortality.

Joint Forecasts of U.S. Marital Fertility, Nuptiality, Births, and Marriages Using Time Series Models

Joint Forecasts of U.S. Marital Fertility, Nuptiality, Births, and Marriages Using Time Series Models

Joint Forecasts of U.S. Marital Fertility, Nuptiality, Births, and Marriages Using Time Series Models

Abstract This article presents a new approach to forecasting U.S. marital fertility, nuptiality, births, and marriages. The analysis represents a wedding of demographic and statistical time series in models amenable to Box-Jenkins techniques of model identification, estimation, diagnosis, and forecasting. The models demonstrate the advantages in this approach in forecasting both rates and events as opposed to the common practice of simply forecasting events. Using the best models of indexes of fertility and nuptiality, forecasts of births and first marriages are made for the U.S. for the years 1983–2000. Analyses of these forecasts are made with discussions of their demographic realism in terms of their forecast confidence intervals.