Structural breaks and GARCH models of exchange rate volatility

We investigate the empirical relevance of structural breaks for GARCH models of exchange rate volatility using both in‐sample and out‐of‐sample tests. We find significant evidence of structural breaks in the unconditional variance of seven of eight US dollar exchange rate return series over the 1980–2005 period—implying unstable GARCH processes for these exchange rates—and GARCH(1,1) parameter estimates often vary substantially across the subsamples defined by the structural breaks. We also find that it almost always pays to allow for structural breaks when forecasting exchange rate return volatility in real time. Combining forecasts from different models that accommodate structural breaks in volatility in various ways appears to offer a reliable method for improving volatility forecast accuracy given the uncertainty surrounding the timing and size of the structural breaks. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecast combinations under structural break uncertainty

This paper proposes two new weighting schemes that average forecasts based on different estimation windows in order to account for possible structural change. The first scheme weights the forecasts according to the values of reversed ordered CUSUM (ROC) test statistics, while the second weighting method simply assigns heavier weights to forecasts that use more recent information. Simulation results show that, when structural breaks are present, forecasts based on the first weighting scheme outperform those based on a procedure that simply uses ROC tests to choose and forecast from a single post-break estimation window. Combination forecasts based on our second weighting scheme outperform equally weighted combination forecasts. An empirical application based on a NAIRU Phillips curve model for the G7 countries illustrates these findings, and also shows that combination forecasts can outperform the random walk forecasting model.     

Multi-step forecasting in emerging economies: An investigation of the South African GDP

To forecast at several, say h, periods into the future, a modeller faces a choice between iterating one-step-ahead forecasts (the IMS technique), or directly modeling the relationship between observations separated by an h-period interval and using it for forecasting (DMS forecasting). It is known that structural breaks, unit-root non-stationarity and residual autocorrelation may improve DMS accuracy in finite samples, all of which occur when modelling the South African GDP over the period 1965–2000. This paper analyzes the forecasting properties of 779 multivariate and univariate models that combine different techniques of robust forecasting. We find strong evidence supporting the use of DMS and intercept correction, and attribute their superior forecasting performance to their robustness in the presence of breaks.     

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.     

Modelling and Forecasting Fiscal Variables for the Euro Area*

In this paper, we assess the possibility of producing unbiased forecasts for fiscal variables in the Euro area by comparing a set of procedures that rely on different information sets and econometric techniques. In particular, we consider autoregressive moving average models, Vector autoregressions, small‐scale semistructural models at the national and Euro area level, institutional forecasts (Organization for Economic Co‐operation and Development), and pooling. Our small‐scale models are characterized by the joint modelling of fiscal and monetary policy using simple rules, combined with equations for the evolution of all the relevant fundamentals for the Maastricht Treaty and the Stability and Growth Pact. We rank models on the basis of their forecasting performance using the mean square and mean absolute error criteria at different horizons. Overall, simple time‐series methods and pooling work well and are able to deliver unbiased forecasts, or slightly upward‐biased forecast for the debt–GDP dynamics. This result is mostly due to the short sample available, the robustness of simple methods to structural breaks, and to the difficulty of modelling the joint behaviour of several variables in a period of substantial institutional and economic changes. A bootstrap experiment highlights that, even when the data are generated using the estimated small‐scale multi‐country model, simple time‐series models can produce more accurate forecasts, because of their parsimonious specification.     

The Contribution of Structural Break Models to Forecasting Macroeconomic Series

This paper compares the forecasting performance of models that have been proposed for forecasting in the presence of structural breaks. They differ in their treatment of the break process, the model applied in each regime and the out‐of‐sample probability of a break. In an extensive empirical evaluation, we demonstrate the presence of breaks and their importance for forecasting. We find no single model that consistently works best in the presence of breaks. In many cases, the formal modeling of the break process is important in achieving a good forecast performance. However, there are also many cases where rolling window forecasts perform well. Copyright © 2014 John Wiley & Sons, Ltd.     

Combining Forecasts from Nested Models*

Motivated by the common finding that linear autoregressive models often forecast better than models that incorporate additional information, this paper presents analytical, Monte Carlo and empirical evidence on the effectiveness of combining forecasts from nested models. In our analytics, the unrestricted model is true, but a subset of the coefficients is treated as being local‐to‐zero. This approach captures the practical reality that the predictive content of variables of interest is often low. We derive mean square error‐minimizing weights for combining the restricted and unrestricted forecasts. Monte Carlo and empirical analyses verify the practical effectiveness of our combination approach.     

Nonparametric and semiparametric regressions subject to monotonicity constraints: Estimation and forecasting

This paper considers nonparametric and semiparametric regression models subject to monotonicity constraint. We use bagging as an alternative approach to Hall and Huang (2001). Asymptotic properties of our proposed estimators and forecasts are established. Monte Carlo simulation is conducted to show their finite sample performance. An application to predicting equity premium is taken for illustration. We introduce a new forecasting evaluation criterion based on the second order stochastic dominance in the size of forecast errors and compare models over different sizes of forecast errors. Imposing monotonicity constraint can mitigate the chance of making large size forecast errors.     

Testing for structural breaks in dynamic factor models

In this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest procedures for testing for structural breaks. It is shown that structural breaks severely inflate the number of factors identified by the usual information criteria. The hypothesis of a structural break is tested by using LR, LM and Wald statistics. The LM test (which performs best in our Monte Carlo simulations) is generalized to test for structural breaks in factor models where the break date is unknown and the common factors and idiosyncratic components are serially correlated. The proposed test procedures are applied to datasets from the US and the euro area.     

Least squares model averaging by Mallows criterion

This paper is in response to a recent paper by Hansen (2007) who proposed an optimal model average estimator with weights selected by minimizing a Mallows criterion. The main contribution of Hansen’s paper is a demonstration that the Mallows criterion is asymptotically equivalent to the squared error, so the model average estimator that minimizes the Mallows criterion also minimizes the squared error in large samples. We are concerned with two assumptions that accompany Hansen’s approach. The first is the assumption that the approximating models are strictly nested in a way that depends on the ordering of regressors. Often there is no clear basis for the ordering and the approach does not permit non-nested models which are more realistic from a practical viewpoint. Second, for the optimality result to hold the model weights are required to lie within a special discrete set. In fact, Hansen noted both difficulties and called for extensions of the proof techniques. We provide an alternative proof which shows that the result on the optimality of the Mallows criterion in fact holds for continuous model weights and under a non-nested set-up that allows any linear combination of regressors in the approximating models that make up the model average estimator. These results provide a stronger theoretical basis for the use of the Mallows criterion in model averaging by strengthening existing findings.     

An efficient Bayesian approach to multiple structural change in multivariate time series

This paper provides a feasible approach to estimation and forecasting of multiple structural breaks for vector autoregressions and other multivariate models. Owing to conjugate prior assumptions we obtain a very efficient sampler for the regime allocation variable. A new hierarchical prior is introduced to allow for learning over different structural breaks. The model is extended to independent breaks in regression coefficients and the volatility parameters. Two empirical applications show the improvements the model has over benchmarks. In a macro application with seven variables we empirically demonstrate the benefits from moving from a multivariate structural break model to a set of univariate structural break models to account for heterogeneous break patterns across data series.     

Bayesian forecast combination using time-varying features

In this work, we propose a novel framework for density forecast combination by constructing time-varying weights based on time-varying features. Our framework estimates weights in the forecast combination via Bayesian log predictive scores, in which the optimal forecast combination is determined by time series features from historical information. In particular, we use an automatic Bayesian variable selection method to identify the importance of different features. To this end, our approach has better interpretability compared to other black-box forecasting combination schemes. We apply our framework to stock market data and M3 competition data. Based on our structure, a simple maximum-a-posteriori scheme outperforms benchmark methods, and Bayesian variable selection can further enhance the accuracy for both point forecasts and density forecasts.     

Time-varying combinations of predictive densities using nonlinear filtering

We propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics driven by the past performance of the predictive densities and the use of learning mechanisms. In the proposed approach the model set can be incomplete, meaning that all models can be individually misspecified. A Sequential Monte Carlo method is proposed to approximate the filtering and predictive densities. The combination approach is assessed using statistical and utility-based performance measures for evaluating density forecasts of simulated data, US macroeconomic time series and surveys of stock market prices. Simulation results indicate that, for a set of linear autoregressive models, the combination strategy is successful in selecting, with probability close to one, the true model when the model set is complete and it is able to detect parameter instability when the model set includes the true model that has generated subsamples of data. Also, substantial uncertainty appears in the weights when predictors are similar; residual uncertainty reduces when the model set is complete; and learning reduces this uncertainty. For the macro series we find that incompleteness of the models is relatively large in the 1970’s, the beginning of the 1980’s and during the recent financial crisis, and lower during the Great Moderation; the predicted probabilities of recession accurately compare with the NBER business cycle dating; model weights have substantial uncertainty attached. With respect to returns of the S&P 500 series, we find that an investment strategy using a combination of predictions from professional forecasters and from a white noise model puts more weight on the white noise model in the beginning of the 1990’s and switches to giving more weight to the professional forecasts over time. Information on the complete predictive distribution and not just on some moments turns out to be very important, above all during turbulent times such as the recent financial crisis. More generally, the proposed distributional state space representation offers great flexibility in combining densities.     

Instrumental variables estimators of nonparametric models with discrete endogenous regressors

This paper discusses estimation of nonparametric models whose regressor vectors consist of a vector of exogenous variables and a univariate discrete endogenous regressor with finite support. Both identification and estimators are derived from a transform of the model that evaluates the nonparametric structural function via indicator functions in the support of the discrete regressor. A two-step estimator is proposed where the first step constitutes nonparametric estimation of the instrument and the second step is a nonparametric version of two-stage least squares. Linear functionals of the model are shown to be asymptotically normal, and a consistent estimator of the asymptotic covariance matrix is described. For the binary endogenous regressor case, it is shown that one functional of the model is a conditional (on covariates) local average treatment effect, that permits both unobservable and observable heterogeneity in treatments. Finite sample properties of the estimators from a Monte Carlo simulation study illustrate the practicability of the proposed estimators.     

fETSmcs: Feature-based ETS model component selection

The well-developed ETS (ExponenTial Smoothing, or Error, Trend, Seasonality) method incorporates a family of exponential smoothing models in state space representation and is widely used for automatic forecasting. The existing ETS method uses information criteria for model selection by choosing an optimal model with the smallest information criterion among all models fitted to a given time series. The ETS method under such a model selection scheme suffers from computational complexity when applied to large-scale time series data. To tackle this issue, we propose an efficient approach to ETS model selection by training classifiers on simulated data to predict appropriate model component forms for a given time series. We provide a simulation study to show the model selection ability of the proposed approach on simulated data. We evaluate our approach on the widely used M4 forecasting competition dataset in terms of both point forecasts and prediction intervals. To demonstrate the practical value of our method, we showcase the performance improvements from our approach on a monthly hospital dataset.     

Bayesian Model Averaging and exchange rate forecasts

Exchange rate forecasting is hard and the seminal result of Meese and Rogoff [Meese, R., Rogoff, K., 1983. Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics 14, 3–24] that the exchange rate is well approximated by a driftless random walk, at least for prediction purposes, still stands despite much effort at constructing other forecasting models. However, in several other macro and financial forecasting applications, researchers in recent years have considered methods for forecasting that effectively combine the information in a large number of time series. In this paper, I apply one such method for pooling forecasts from several different models, Bayesian Model Averaging, to the problem of pseudo out-of-sample exchange rate predictions. For most currency–horizon pairs, the Bayesian Model Averaging forecasts using a sufficiently high degree of shrinkage, give slightly smaller out-of-sample mean square prediction error than the random walk benchmark. The forecasts generated by this model averaging methodology are however very close to, but not identical to, those from the random walk forecast.     

LoMEF: A framework to produce local explanations for global model time series forecasts

Global forecasting models (GFMs) that are trained across a set of multiple time series have shown superior results in many forecasting competitions and real-world applications compared with univariate forecasting approaches. One aspect of the popularity of statistical forecasting models such as ETS and ARIMA is their relative simplicity and interpretability (in terms of relevant lags, trend, seasonality, and other attributes), while GFMs typically lack interpretability, especially relating to particular time series. This reduces the trust and confidence of stakeholders when making decisions based on the forecasts without being able to understand the predictions. To mitigate this problem, we propose a novel local model-agnostic interpretability approach to explain the forecasts from GFMs. We train simpler univariate surrogate models that are considered interpretable (e.g., ETS) on the predictions of the GFM on samples within a neighbourhood that we obtain through bootstrapping, or straightforwardly as the one-step-ahead global black-box model forecasts of the time series which needs to be explained. After, we evaluate the explanations for the forecasts of the global models in both qualitative and quantitative aspects such as accuracy, fidelity, stability, and comprehensibility, and are able to show the benefits of our approach.     

Forecasting economic and financial variables with global VARs

This paper considers the problem of forecasting economic and financial variables across a large number of countries in the global economy. To this end a global vector autoregressive (GVAR) model, previously estimated by Dees, di Mauro, Pesaran, and Smith (2007) and Dees, Holly, Pesaran, and Smith (2007) over the period 1979Q1–2003Q4, is used to generate out-of-sample forecasts one and four quarters ahead for real output, inflation, real equity prices, exchange rates and interest rates over the period 2004Q1–2005Q4. Forecasts are obtained for 134 variables from 26 regions, which are made up of 33 countries and cover about 90% of the world output. The forecasts are compared to typical benchmarks: univariate autoregressive and random walk models. Building on the forecast combination literature, the effects of model and estimation uncertainty on forecast outcomes are examined by pooling forecasts obtained from different GVAR models estimated over alternative sample periods. Given the size of the modelling problem, and the heterogeneity of the economies considered–industrialised, emerging, and less developed countries–as well as the very real likelihood of possibly multiple structural breaks, averaging forecasts across both models and windows makes a significant difference. Indeed, the double-averaged GVAR forecasts perform better than the benchmark competitors, especially for output, inflation and real equity prices.     

Inference and prediction in a multiple-structural-break model

This paper develops a new Bayesian approach to structural break modeling. The focuses of the approach are the modeling of in-sample structural breaks and forecasting time series allowing out-of-sample breaks. The model has several desirable features. First, the number of regimes is not fixed but is treated as a random variable. Second, the model adopts a hierarchical prior for regime coefficients, which allows for the coefficients of one regime to contain information about coefficients of other regimes. Third, the regime coefficients can be integrated analytically in the posterior density; as a consequence the posterior simulator is fast and reliable. An application to US real GDP quarterly growth rates links groups of regimes to specific historical periods and provides forecasts of future growth rates.     

Adding dummy variables: A simple approach for improved volatility forecasting in electricity market

This study used dummy variables to measure the influence of day-of-the-week effects and structural breaks on volatility. Considering day-of-the-week effects, structural breaks, or both, we propose three classes of HAR models to forecast electricity volatility based on existing HAR models. The estimation results of the models showed that day-of-the-week effects only improve the fitting ability of HAR models for electricity volatility forecasting at the daily horizon, whereas structural breaks can improve the in-sample performance of HAR models when forecasting electricity volatility at daily, weekly, and monthly horizons. The out-of-sample analysis indicated that both day-of-the-week effects and structural breaks contain additional ex ante information for predicting electricity volatility, and in most cases, dummy variables used to measure structural breaks contain more out-of-sample predictive information than those used to measure day-of-the-week effects. The out-of-sample results were robust across three different methods. More importantly, we argue that adding dummy variables to measure day-of-the-week effects and structural breaks can improve the performance of most other existing HAR models for volatility forecasting in the electricity market.