Why do regime‐switching models forecast so badly?

Most non‐linear techniques give good in‐sample fits to exchange rate data but are usually outperformed by random walks or random walks with drift when used for out‐of‐sample forecasting. In the case of regime‐switching models it is possible to understand why forecasts based on the true model can have higher mean squared error than those of a random walk or random walk with drift. In this paper we provide some analytical results for the case of a simple switching model, the segmented trend model. It requires only a small misclassification, when forecasting which regime the world will be in, to lose any advantage from knowing the correct model specification. To illustrate this we discuss some results for the DM/dollar exchange rate. We conjecture that the forecasting result is more general and describes limitations to the use of switching models for forecasting. This result has two implications. First, it questions the leading role of the random walk hypothesis for the spot exchange rate. Second, it suggests that the mean square error is not an appropriate way to evaluate forecast performance for non‐linear models. Copyright © 1999 John Wiley & Sons, Ltd.     

Economic factors and the stock market: a new perspective

It has been widely accepted that many financial and economic variables are non‐linear, and neural networks can model flexible linear or non‐linear relationships among variables. The present paper deals with an important issue: Can the many studies in the finance literature evidencing predictability of stock returns by means of linear regression be improved by a neural network? We show that the predictive accuracy can be improved by a neural network, and the results largely hold out‐of‐sample. Both the neural network and linear forecasts show significant market timing ability. While the switching portfolio based on the linear forecasts outperforms the buy‐and‐hold market portfolio under all three transaction cost scenarios, the switching portfolio based on the neural network forecasts beats the market only if there is no transaction cost. Copyright © 1999 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.     

Non‐linear,non‐parametric,non‐fundamental exchange rate forecasting

This paper employs a non‐parametric method to forecast high‐frequency Canadian/US dollar exchange rate. The introduction of a microstructure variable, order flow, substantially improves the predictive power of both linear and non‐linear models. The non‐linear models outperform random walk and linear models based on a number of recursive out‐of‐sample forecasts. Two main criteria that are applied to evaluate model performance are root mean squared error (RMSE) and the ability to predict the direction of exchange rate moves. The artificial neural network (ANN) model is consistently better in RMSE to random walk and linear models for the various out‐of‐sample set sizes. Moreover, ANN performs better than other models in terms of percentage of correctly predicted exchange rate changes. The empirical results suggest that optimal ANN architecture is superior to random walk and any linear competing model for high‐frequency exchange rate forecasting. Copyright © 2006 John Wiley & Sons, Ltd.     

A Bayesian structural model for predicting algal blooms

A Bayesian structural model with two components is proposed to forecast the occurrence of algal blooms, multivariate mean‐reverting diffusion process (MMRD), and a binary probit model with latent Markov regime‐switching process (BPMRS). The model has three features: (a) forecast of the occurrence probability of algal bloom is directly based on oceanographic parameters, not the forecasting of special indicators in traditional approaches, such as phytoplankton or chlorophyll‐a; (b) augmentation of daily oceanographic parameters from the data collected every 2 weeks is based on MMRD. The proposed method solves the problem of unavailability of daily oceanographic parameters in practice; (c) BPMRS captures the unobservable factors which affect algal bloom occurrence and therefore improve forecast accuracy. We use panel data collected in Tolo Harbour, Hong Kong, to validate the model. The model demonstrates good forecasting for out‐of‐sample rolling forecasts, especially for algal bloom appearing for a longer period, which severely damages fisheries and the marine environment.     

Realized Volatility Forecast of Stock Index Under Structural Breaks

We investigate the realized volatility forecast of stock indices under the structural breaks. We utilize a pure multiple mean break model to identify the possibility of structural breaks in the daily realized volatility series by employing the intraday high‐frequency data of the Shanghai Stock Exchange Composite Index and the five sectoral stock indices in Chinese stock markets for the period 4 January 2000 to 30 December 2011. We then conduct both in‐sample tests and out‐of‐sample forecasts to examine the effects of structural breaks on the performance of ARFIMAX‐FIGARCH models for the realized volatility forecast by utilizing a variety of estimation window sizes designed to accommodate potential structural breaks. The results of the in‐sample tests show that there are multiple breaks in all realized volatility series. The results of the out‐of‐sample point forecasts indicate that the combination forecasts with time‐varying weights across individual forecast models estimated with different estimation windows perform well. In particular, nonlinear combination forecasts with the weights chosen based on a non‐parametric kernel regression and linear combination forecasts with the weights chosen based on the non‐negative restricted least squares and Schwarz information criterion appear to be the most accurate methods in point forecasting for realized volatility under structural breaks. We also conduct an interval forecast of the realized volatility for the combination approaches, and find that the interval forecast for nonlinear combination approaches with the weights chosen according to a non‐parametric kernel regression performs best among the competing models. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Unemployment variation over the business cycles: a comparison of forecasting models

Asymmetry has been well documented in the business cycle literature. The asymmetric business cycle suggests that major macroeconomic series, such as a country's unemployment rate, are non‐linear and, therefore, the use of linear models to explain their behaviour and forecast their future values may not be appropriate. Many researchers have focused on providing evidence for the non‐linearity in the unemployment series. Only recently have there been some developments in applying non‐linear models to estimate and forecast unemployment rates. A major concern of non‐linear modelling is the model specification problem; it is very hard to test all possible non‐linear specifications, and to select the most appropriate specification for a particular model. Artificial neural network (ANN) models provide a solution to the difficulty of forecasting unemployment over the asymmetric business cycle. ANN models are non‐linear, do not rely upon the classical regression assumptions, are capable of learning the structure of all kinds of patterns in a data set with a specified degree of accuracy, and can then use this structure to forecast future values of the data. In this paper, we apply two ANN models, a back‐propagation model and a generalized regression neural network model to estimate and forecast post‐war aggregate unemployment rates in the USA, Canada, UK, France and Japan. We compare the out‐of‐sample forecast results obtained by the ANN models with those obtained by several linear and non‐linear times series models currently used in the literature. It is shown that the artificial neural network models are able to forecast the unemployment series as well as, and in some cases better than, the other univariate econometrics time series models in our test. Copyright © 2004 John Wiley & Sons, Ltd.     

Forecasting the recent behavior of US business fixed investment spending: an analysis of competing models

We evaluate forecasting models of US business fixed investment spending growth over the recent 1995:1–2004:2 out‐of‐sample period. The forecasting models are based on the conventional Accelerator, Neoclassical, Average Q, and Cash‐Flow models of investment spending, as well as real stock prices and excess stock return predictors. The real stock price model typically generates the most accurate forecasts, and forecast‐encompassing tests indicate that this model contains most of the information useful for forecasting investment spending growth relative to the other models at longer horizons. In a robustness check, we also evaluate the forecasting performance of the models over two alternative out‐of‐sample periods: 1975:1–1984:4 and 1985:1–1994:4. A number of different models produce the most accurate forecasts over these alternative out‐of‐sample periods, indicating that while the real stock price model appears particularly useful for forecasting the recent behavior of investment spending growth, it may not continue to perform well in future periods. Copyright © 2007 John Wiley & Sons, Ltd.     

Forecasting VaR models under Different Volatility Processes and Distributions of Return Innovations

This paper provides clear‐cut evidence that the out‐of‐sample VaR (value‐at‐risk) forecasting performance of alternative parametric volatility models, like EGARCH (exponential general autoregressive conditional heteroskedasticity) or GARCH, and Markov regime‐switching models, can be considerably improved if they are combined with skewed distributions of asset return innovations. The performance of these models is found to be similar to that of the EVT (extreme value theory) approach. The performance of the latter approach can also be improved if asset return innovations are assumed to be skewed distributed. The performance of the Markov regime‐switching model is considerably improved if this model allows for EGARCH effects, for all different volatility regimes considered. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting UK industrial production over the business cycle

This paper examines the information available through leading indicators for modelling and forecasting the UK quarterly index of production. Both linear and non‐linear specifications are examined, with the latter being of the Markov‐switching type as used in many recent business cycle applications. The Markov‐switching models perform relatively poorly in forecasting the 1990s production recession, but a three‐indicator linear specification does well. The leading indicator variables in this latter model include a short‐term interest rate, the stock market dividend yield and the optimism balance from the quarterly CBI survey. Copyright © 2001 John Wiley & Sons, Ltd.     

Predicting returns and volatility with macroeconomic variables: evidence from tests of encompassing

Tests of forecast encompassing are used to evaluate one‐step‐ahead forecasts of S&P Composite index returns and volatility. It is found that forecasts over the 1990s made from models that include macroeconomic variables tend to be encompassed by those made from a benchmark model which does not include macroeconomic variables. However, macroeconomic variables are found to add significant information to forecasts of returns and volatility over the 1970s. Often in empirical research on forecasting stock index returns and volatility, in‐sample information criteria are used to rank potential forecasting models. Here, none of the forecasting models for the 1970s that include macroeconomic variables are, on the basis of information criteria, preferred to the relevant benchmark specification. Thus, had investors used information criteria to choose between the models used for forecasting over the 1970s considered in this paper, the predictability that tests of encompassing reveal would not have been exploited. Copyright © 2005 John Wiley & Sons, Ltd.     

Forecasting Performance of Nonlinear Models for Intraday Stock Returns

We studied the predictability of intraday stock market returns using both linear and nonlinear time series models. For the S&P 500 index we compared simple autoregressive and random walk linear models with a range of nonlinear models, including smooth transition, Markov switching, artificial neural network, nonparametric kernel regression and support vector machine models for horizons of 5, 10, 20, 30 and 60 minutes. The empirical results indicate that nonlinear models outperformed linear models on the basis of both statistical and economic criteria. Specifically, although return serial correlation receded by around 10 minutes, return predictability still persisted for up to 60 minutes according to nonlinear models, even though profitability decreases as time elapses. More flexible nonlinear models such as support vector machines and artificial neural network did not clearly outperform other nonlinear models. Copyright © 2011 John Wiley & Sons, Ltd.     

On SETAR non‐linearity and forecasting

We compare linear autoregressive (AR) models and self‐exciting threshold autoregressive (SETAR) models in terms of their point forecast performance, and their ability to characterize the uncertainty surrounding those forecasts, i.e. interval or density forecasts. A two‐regime SETAR process is used as the data‐generating process in an extensive set of Monte Carlo simulations, and we consider the discriminatory power of recently developed methods of forecast evaluation for different degrees of non‐linearity. We find that the interval and density evaluation methods are unlikely to show the linear model to be deficient on samples of the size typical for macroeconomic data. Copyright © 2003 John Wiley & Sons, Ltd.     

Long‐memory forecasting of US monetary indices

Several studies have tested for long‐range dependence in macroeconomic and financial time series but very few have assessed the usefulness of long‐memory models as forecast‐generating mechanisms. This study tests for fractional differencing in the US monetary indices (simple sum and divisia) and compares the out‐of‐sample fractional forecasts to benchmark forecasts. The long‐memory parameter is estimated using Robinson's Gaussian semi‐parametric and multivariate log‐periodogram methods. The evidence amply suggests that the monetary series possess a fractional order between one and two. Fractional out‐of‐sample forecasts are consistently more accurate (with the exception of the M3 series) than benchmark autoregressive forecasts but the forecasting gains are not generally statistically significant. In terms of forecast encompassing, the fractional model encompasses the autoregressive model for the divisia series but neither model encompasses the other for the simple sum series. Copyright © 2006 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 Forecasting Performance of a Finite Mixture Regime‐Switching Model for Daily Electricity Prices

Forecasting prices in electricity markets is a crucial activity for both risk management and asset optimization. Intra‐day power prices have a fine structure and are driven by an interaction of fundamental, behavioural and stochastic factors. Furthermore, there are reasons to expect the functional forms of price formation to be nonlinear in these factors and therefore specifying forecasting models that perform well out‐of‐sample is methodologically challenging. Markov regime switching has been widely advocated to capture some aspects of the nonlinearity, but it may suffer from overfitting and unobservability in the underlying states. In this paper we compare several extensions and alternative regime‐switching formulations, including logistic specifications of the underlying states, logistic smooth transition and finite mixture regression. The finite mixture approach to regime switching performs well in an extensive, out‐of‐sample forecasting comparison. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting volatility

In this paper, we investigate the time series properties of S&P 100 volatility and the forecasting performance of different volatility models. We consider several nonparametric and parametric volatility measures, such as implied, realized and model‐based volatility, and show that these volatility processes exhibit an extremely slow mean‐reverting behavior and possible long memory. For this reason, we explicitly model the near‐unit root behavior of volatility and construct median unbiased forecasts by approximating the finite‐sample forecast distribution using bootstrap methods. Furthermore, we produce prediction intervals for the next‐period implied volatility that provide important information about the uncertainty surrounding the point forecasts. Finally, we apply intercept corrections to forecasts from misspecified models which dramatically improve the accuracy of the volatility forecasts. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive modelling and forecasting of offshore wind power fluctuations with Markov‐switching autoregressive models

Wind power production data at temporal resolutions of a few minutes exhibit successive periods with fluctuations of various dynamic nature and magnitude, which cannot be explained (so far) by the evolution of some explanatory variable. Our proposal is to capture this regime‐switching behaviour with an approach relying on Markov‐switching autoregressive (MSAR) models. An appropriate parameterization of the model coefficients is introduced, along with an adaptive estimation method allowing accommodation of long‐term variations in the process characteristics. The objective criterion to be recursively optimized is based on penalized maximum likelihood, with exponential forgetting of past observations. MSAR models are then employed for one‐step‐ahead point forecasting of 10 min resolution time series of wind power at two large offshore wind farms. They are favourably compared against persistence and autoregressive models. It is finally shown that the main interest of MSAR models lies in their ability to generate interval/density forecasts of significantly higher skill. Copyright © 2010 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.