Does Disagreement Amongst Forecasters Have Predictive Value?

In the present study we examine the predictive power of disagreement amongst forecasters. In our empirical work, we find that in some situations this variable can signal upcoming structural and temporal changes in an economic process and in the predictive power of the survey forecasts. We examine a variety of macroeconomic variables, and we use different measurements for the degree of disagreement, together with measures for location of the survey data and autoregressive components. Forecasts from simple linear models and forecasts from Markov regime‐switching models with constant and with time‐varying transition probabilities are constructed in real time and compared on forecast accuracy. Copyright © 2015 John Wiley & Sons, Ltd.     

A Method of Retail Mortgage Stress Testing: Based on Time‐Frame and Magnitude Analysis

In this study, a non‐stationary Markov chain model and a vector autoregressive moving average with exogenous variables coupled with a logistic function (VARMAX‐L) are used to analyze and predict the stability of a retail mortgage portfolio, based on the stress test framework. The method introduced in this paper can be used to forecast the transition probabilities in a retail mortgage over pre‐specified states, given a shock with a certain magnitude. Hence this method provides a dynamic picture of the portfolio transition process through which one can assess its behavior over time. While the paper concentrates on retail mortgages, the methodology of this study can be adapted also to analyze other credit products in banks. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian Model Averaging under Regime Switching with Application to Cyclical Macro Variable Forecasting

Model uncertainty and recurrent or cyclical structural changes in macroeconomic time series dynamics are substantial challenges to macroeconomic forecasting. This paper discusses a macro variable forecasting methodology that combines model uncertainty and regime switching simultaneously. The proposed predictive regression specification permits both regime switching of the regression parameters and uncertainty about the inclusion of forecasting variables by employing Bayesian model averaging. In an empirical exercise involving quarterly US inflation, we observed that our Bayesian model averaging with regime switching leads to substantial improvements in forecast performance, particularly in the medium horizon (two to four quarters). Copyright © 2015 John Wiley & Sons, Ltd.     

Forecasting US interest rates and business cycle with a nonlinear regime switching VAR model

This paper introduces a regime switching vector autoregressive model with time‐varying regime probabilities, where the regime switching dynamics is described by an observable binary response variable predicted simultaneously with the variables subject to regime changes. Dependence on the observed binary variable distinguishes the model from various previously proposed multivariate regime switching models, facilitating a handy simulation‐based multistep forecasting method. An empirical application shows a strong bidirectional predictive linkage between US interest rates and NBER business cycle recession and expansion periods. Due to the predictability of the business cycle regimes, the proposed model yields superior out‐of‐sample forecasts of the US short‐term interest rate and the term spread compared with the linear and nonlinear vector autoregressive (VAR) models, including the Markov switching VAR model.     

The extended switching regression model: allowing for multiple latent state variables

In this paper we extend the widely followed approach of switching regression models, i.e. models in which the parameters are determined by a latent discrete state variable. We construct a model with several latent state variables, where the model parameters are partitioned into disjoint groups, each one of which is independently determined by a corresponding state variable. Such a model is called an extended switching regression (ESR) model. We develop an EM algorithm to estimate the model parameters, and discuss the consistency and asymptotic normality of the maximum likelihood estimates. Finally, we use the ESR model to combine volatility forecasts of foreign exchange rates. The resulting forecast combination using the ESR model tends to dominate those generated by traditional procedures. Copyright © 2007 John Wiley & Sons, Ltd.     

Forecasting with an econometric model: The ‘ragged edge’ problem

In practical econometric forecasting exercises, incomplete data on current and immediate past values of endogenous variables are available. This paper considers various approaches to this ‘ragged edge’ problem, including the common device of treating as ‘temporarily exogenous’ an endogenous variable whose value is known, by deleting it from the set of endogenous variables for whose forecast values the model is solved and suppressing the corresponding structural equation. It is seen that this forecast can be adjusted to coincide with the optimal forecast. The initial discussion concerns the textbook linear simultaneous equation model; extensions to non-linear dynamic models are described.     

Causality and forecasting in incomplete systems

In this paper we examine how causality inference and forecasting within a bivariate VAR, consisting of y(t) and x(t), are affected by the omission of a third variable, w(t), which causes (a) none, (b) one, and (c) both variables in the bivariate system. We also derive conditions under which causality inference and forecasting are invariant to the selection of a bivariate or a trivariate model. The most general condition for the invariance of both causality and forecasting to model selection is shown to require the omitted variable not to cause any of the variables in the bivariate system, although it allows the omitted variable to be caused by the other two. We also show that the conditions for one-way causality inference to be invariant to model selection are not sufficient to ensure that forecasting will also be invariant to the model selected. Finally, we present a numerical illustration of the potential losses, in terms of the variance of the forecast, as a function of the forecast horizon and for alternative parameter values—they can be rather large, as the omission of a variable can make the incomplete model unstable. © 1997 John Wiley & Sons, Ltd.     

Non‐linear forecasts of stock returns

Following recent non‐linear extensions of the present‐value model, this paper examines the out‐of‐sample forecast performance of two parametric and two non‐parametric nonlinear models of stock returns. The parametric models include the standard regime switching and the Markov regime switching, whereas the non‐parametric are the nearest‐neighbour and the artificial neural network models. We focused on the US stock market using annual observations spanning the period 1872–1999. Evaluation of forecasts was based on two criteria, namely forecast accuracy and forecast encompassing. In terms of accuracy, the Markov and the artificial neural network models produce at least as accurate forecasts as the other models. In terms of encompassing, the Markov model outperforms all the others. Overall, both criteria suggest that the Markov regime switching model is the most preferable non‐linear empirical extension of the present‐value model for out‐of‐sample stock return forecasting. Copyright © 2003 John Wiley & Sons, Ltd.     

A high–low model of daily stock price ranges

We observe that daily highs and lows of stock prices do not diverge over time and, hence, adopt the cointegration concept and the related vector error correction model (VECM) to model the daily high, the daily low, and the associated daily range data. The in‐sample results attest to the importance of incorporating high–low interactions in modeling the range variable. In evaluating the out‐of‐sample forecast performance using both mean‐squared forecast error and direction of change criteria, it is found that the VECM‐based low and high forecasts offer some advantages over alternative forecasts. The VECM‐based range forecasts, on the other hand, do not always dominate—the forecast rankings depend on the choice of evaluation criterion and the variables being forecast. Copyright © 2008 John Wiley & Sons, Ltd.     

Realized Volatility Forecasting of Agricultural Commodity Futures Using Long Memory and Regime Switching

We investigate the dynamic properties of the realized volatility of five agricultural commodity futures by employing the high‐frequency data from Chinese markets and find that the realized volatility exhibits both long memory and regime switching. To capture these properties simultaneously, we utilize a Markov switching autoregressive fractionally integrated moving average (MS‐ARFIMA) model to forecast the realized volatility by combining the long memory process with regime switching component, and compare its forecast performances with the competing models at various horizons. The full‐sample estimation results show that the dynamics of the realized volatility of agricultural commodity futures are characterized by two levels of long memory: one associated with the low‐volatility regime and the other with the high‐volatility regime, and the probability to stay in the low‐volatility regime is higher than that in the high‐volatility regime. The out‐of‐sample volatility forecast results show that the combination of long memory with switching regimes improves the performance of realized volatility forecast, and the proposed model represents a superior out‐of‐sample realized volatility forecast to the competing models. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting Daily and Monthly Exchange Rates with Machine Learning Techniques

In this paper we propose and test a forecasting model on monthly and daily spot prices of five selected exchange rates. In doing so, we combine a novel smoothing technique (initially applied in signal processing) with a variable selection methodology and two regression estimation methodologies from the field of machine learning (ML). After the decomposition of the original exchange rate series using an ensemble empirical mode decomposition (EEMD) method into a smoothed and a fluctuation component, multivariate adaptive regression splines (MARS) are used to select the most appropriate variable set from a large set of explanatory variables that we collected. The selected variables are then fed into two distinctive support vector machines (SVR) models that produce one‐period‐ahead forecasts for the two components. Neural networks (NN) are also considered as an alternative to SVR. The sum of the two forecast components is the final forecast of the proposed scheme. We show that the above implementation exhibits a superior in‐sample and out‐of‐sample forecasting ability when compared to alternative forecasting models. The empirical results provide evidence against the efficient market hypothesis for the selected foreign exchange markets. Copyright © 2015 John Wiley & Sons, Ltd.     

Forecasting under model uncertainty: Non-homogeneous hidden Markov models with Pòlya-Gamma data augmentation

We consider finite state-space non-homogeneous hidden Markov models for forecasting univariate time series. Given a set of predictors, the time series are modeled via predictive regressions with state-dependent coefficients and time-varying transition probabilities that depend on the predictors via a logistic/multinomial function. In a hidden Markov setting, inference for logistic regression coefficients becomes complicated and in some cases impossible due to convergence issues. In this paper, we aim to address this problem utilizing the recently proposed Pólya-Gamma latent variable scheme. Also, we allow for model uncertainty regarding the predictors that affect the series both linearly — in the mean — and non-linearly — in the transition matrix. Predictor selection and inference on the model parameters are based on an automatic Markov chain Monte Carlo scheme with reversible jump steps. Hence the proposed methodology can be used as a black box for predicting time series. Using simulation experiments, we illustrate the performance of our algorithm in various setups, in terms of mixing properties, model selection and predictive ability. An empirical study on realized volatility data shows that our methodology gives improved forecasts compared to benchmark models.     

New Evidence on the Ability of Asset Prices and Real Economic Activity Forecast Errors to Predict Inflation Forecast Errors

This paper investigates the impact of both asset and macroeconomic forecast errors on inflation forecast errors in the USA by making use of a two‐regime model. The findings document a significant contribution of both types of forecast errors to the explanation of inflation forecast errors, with the pass‐through being stronger when these errors move within the high‐volatility regime. Copyright © 2016 John Wiley & Sons, Ltd.     

Subjective confidence in forecasts: A response to fischhoff and MacGregor

Here we evaluate the generalizability of calibration studies which have used general knowledge questions, and argue that on conceptual, methodological and empirical grounds the results have limited applicability to judgemental forecasting. We also review evidence which suggests that judgemental forecast probabilities are influenced by variables such as the desirability, imminence, time period and perceived controllability of the event to be forecast. As these variables do not apply to judgement in the domain of general knowledge, a need for research recognizing and exploring the psychological processes underlying uncertainty about the future is apparent.     

A fractal forecasting model for financial time series

Financial market time series exhibit high degrees of non‐linear variability, and frequently have fractal properties. When the fractal dimension of a time series is non‐integer, this is associated with two features: (1) inhomogeneity—extreme fluctuations at irregular intervals, and (2) scaling symmetries—proportionality relationships between fluctuations over different separation distances. In multivariate systems such as financial markets, fractality is stochastic rather than deterministic, and generally originates as a result of multiplicative interactions. Volatility diffusion models with multiple stochastic factors can generate fractal structures. In some cases, such as exchange rates, the underlying structural equation also gives rise to fractality. Fractal principles can be used to develop forecasting algorithms. The forecasting method that yields the best results here is the state transition‐fitted residual scale ratio (ST‐FRSR) model. A state transition model is used to predict the conditional probability of extreme events. Ratios of rates of change at proximate separation distances are used to parameterize the scaling symmetries. Forecasting experiments are run using intraday exchange rate futures contracts measured at 15‐minute intervals. The overall forecast error is reduced on average by up to 7% and in one instance by nearly a quarter. However, the forecast error during the outlying events is reduced by 39% to 57%. The ST‐FRSR reduces the predictive error primarily by capturing extreme fluctuations more accurately. Copyright © 2004 John Wiley & Sons, Ltd.     

A simple parameter-driven binary time series model

We introduce a parameter-driven, state-space model for binary time series data. The model is based on a state process with a binomial-beta dynamics, which has a Markov, endogenous switching regime representation. The model allows for recursive prediction and filtering formulas with extremely low computational cost, and hence avoids the use of computational intensive simulation-based filtering algorithms. Case studies illustrate the advantage of our model over popular intensity-based observation-driven models, both in terms of fit and out-of-sample forecast.     

Consistent forecast intervals when the forecast-period exogenous variables are stochastic

Derivation of prediction intervals in the k-variable regression model is problematic when future-period values of exogenous variables are not known with certainty. Even in the most favourable case when the forecasts of the exogenous variables are jointly normal, the distribution of the forecast error is non-normal, and thus traditional asymptotic normal theory does not apply. This paper presents an alternative bootstrap method. In contrast to the traditional predictor of the future value of the endogenous variable, which is known to be inconsistent, the bootstrap predictor converges weakly to the true value. Monte Carlo results show that the bootstrap prediction intervals can achieve approximately nominal coverage.     

Forecasting time‐varying covariance with a robust Bayesian threshold model

This paper proposes a robust multivariate threshold vector autoregressive model with generalized autoregressive conditional heteroskedasticities and dynamic conditional correlations to describe conditional mean, volatility and correlation asymmetries in financial markets. In addition, the threshold variable for regime switching is formulated as a weighted average of endogenous variables to eliminate excessively subjective belief in the threshold variable decision and to serve as the proxy in deciding which market should be the price leader. The estimation is performed using Markov chain Monte Carlo methods. Furthermore, several meaningful criteria are introduced to assess the forecasting performance in the conditional covariance matrix. The proposed methodology is illustrated using daily S&P500 futures and spot prices. Copyright © 2010 John Wiley & Sons, Ltd.     

Forecast covariances in the linear multiregression dynamic model

The linear multiregression dynamic model (LMDM) is a Bayesian dynamic model which preserves any conditional independence and causal structure across a multivariate time series. The conditional independence structure is used to model the multivariate series by separate (conditional) univariate dynamic linear models, where each series has contemporaneous variables as regressors in its model. Calculating the forecast covariance matrix (which is required for calculating forecast variances in the LMDM) is not always straightforward in its current formulation. In this paper we introduce a simple algebraic form for calculating LMDM forecast covariances. Calculation of the covariance between model regression components can also be useful and we shall present a simple algebraic method for calculating these component covariances. In the LMDM formulation, certain pairs of series are constrained to have zero forecast covariance. We shall also introduce a possible method to relax this restriction. Copyright © 2008 John Wiley & Sons, Ltd.     

A new Bayesian formulation for Holt's exponential smoothing

In this paper we propose a Bayesian forecasting approach for Holt's additive exponential smoothing method. Starting from the state space formulation, a formula for the forecast is derived and reduced to a two‐dimensional integration that can be computed numerically in a straightforward way. In contrast to much of the work for exponential smoothing, this method produces the forecast density and, in addition, it considers the initial level and initial trend as part of the parameters to be evaluated. Another contribution of this paper is that we have derived a way to reduce the computation of the maximum likelihood parameter estimation procedure to that of evaluating a two‐dimensional grid, rather than applying a five‐variable optimization procedure. Simulation experiments confirm that both proposed methods give favorable performance compared to other approaches. Copyright © 2008 John Wiley & Sons, Ltd.