Ensemble Forecasting for Complex Time Series Using Sparse Representation and Neural Networks

Based on the concept of ‘decomposition and ensemble’, a novel ensemble forecasting approach is proposed for complex time series by coupling sparse representation (SR) and feedforward neural network (FNN), i.e. the SR‐based FNN approach. Three main steps are involved: data decomposition via SR, individual forecasting via FNN and ensemble forecasting via a simple addition method. In particular, to capture various coexisting hidden factors, the effective decomposition tool of SR with its unique virtues of flexibility and generalization is introduced to formulate an overcomplete dictionary covering diverse bases, e.g. exponential basis for main trend, Fourier basis for cyclical (and seasonal) features and wavelet basis for transient actions, different from other techniques with a single basis. Using crude oil price (a typical complex time series) as sample data, the empirical study statistically confirms the superiority of the SR‐based FNN method over some other popular forecasting models and similar ensemble models (with other decomposition tools). Copyright © 2016 John Wiley & Sons, Ltd.     

Choosing among competing econometric forecasts: Regression‐based forecast combination using model selection

Forecast combination based on a model selection approach is discussed and evaluated. In addition, a combination approach based on ex ante predictive ability is outlined. The model selection approach which we examine is based on the use of Schwarz (SIC) or the Akaike (AIC) Information Criteria. Monte Carlo experiments based on combination forecasts constructed using possibly (misspecified) models suggest that the SIC offers a potentially useful combination approach, and that further investigation is warranted. For example, combination forecasts from a simple averaging approach MSE‐dominate SIC combination forecasts less than 25% of the time in most cases, while other ‘standard’ combination approaches fare even worse. Alternative combination approaches are also compared by conducting forecasting experiments using nine US macroeconomic variables. In particular, artificial neural networks (ANN), linear models, and professional forecasts are used to form real‐time forecasts of the variables, and it is shown via a series of experiments that SIC, t‐statistic, and averaging combination approaches dominate various other combination approaches. An additional finding is that while ANN models may not MSE‐dominate simpler linear models, combinations of forecasts from these two models outperform either individual forecast, for a subset of the economic variables examined. Copyright © 2001 John Wiley & Sons, Ltd.     

Forecasting business failure in China using case‐based reasoning with hybrid case respresentation

Case‐based reasoning (CBR) is a very effective and easily understandable method for solving real‐world problems. Business failure prediction (BFP) is a forecasting tool that helps people make more precise decisions. CBR‐based BFP is a hot topic in today's global financial crisis. Case representation is critical when forecasting business failure with CBR. This research describes a pioneer investigation on hybrid case representation by employing principal component analysis (PCA), a feature extraction method, along with stepwise multivariate discriminant analysis (MDA), a feature selection approach. In this process, sample cases are represented with all available financial ratios, i.e., features. Next, the stepwise MDA is used to select optimal features to produce a reduced‐case representation. Finally, PCA is employed to extract the final information representing the sample cases. All data signified by hybrid case representation are recorded in a case library, and the k‐nearest‐neighbor algorithm is used to make the forecasting. Thus we constructed a hybrid CBR (HCBR) by integrating hybrid case representation into the forecasting tool. We empirically tested the performance of HCBR with data collected for short‐term BFP of Chinese listed companies. Empirical results indicated that HCBR can produce more promising prediction performance than MDA, logistic regression, classical CBR, and support vector machine. Copyright © 2009 John Wiley & Sons, Ltd.     

A New‐Keynesian DSGE model for forecasting the South African economy

This paper develops a New‐Keynesian Dynamic Stochastic General Equilibrium (NKDSGE) model for forecasting the growth rate of output, inflation, and the nominal short‐term interest rate (91 days Treasury Bill rate) for the South African economy. The model is estimated via maximum likelihood technique for quarterly data over the period of 1970:1–2000:4. Based on a recursive estimation using the Kalman filter algorithm, out‐of‐sample forecasts from the NKDSGE model are compared with forecasts generated from the classical and Bayesian variants of vector autoregression (VAR) models for the period 2001:1–2006:4. The results indicate that in terms of out‐of‐sample forecasting, the NKDSGE model outperforms both the classical and Bayesian VARs for inflation, but not for output growth and nominal short‐term interest rate. However, differences in RMSEs are not significant across the models. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting inflation in Malaysia

This paper aims to identify the best indicator in forecasting inflation in Malaysia. In methodology, the study constructs a simple forecasting model that incorporates the indicator/variable using the vector error correction (VECM) model of quasi‐tradable inflation index and selected indicators: commodity prices, financial indicators and economic activities. For each indicator, the forecasting horizon used is 24 months and the VECM model is applied for seven sample windows over sample periods starting with the first month of 1980 and ending with the 12th month of every 2 years from 1992 to 2004. The degree of independence of each indicator from inflation is tested by analyzing the variance decomposition of each indicator and Granger causality between each indicator and inflation. We propose that a simple model using an aggregation of indices improves the accuracy of inflation forecasts. The results support our hypothesis. Copyright © 2009 John Wiley & Sons, Ltd.     

Forecasting in the presence of level shifts

This article addresses the problem of forecasting time series that are subject to level shifts. Processes with level shifts possess a nonlinear dependence structure. Using the stochastic permanent breaks (STOPBREAK) model, I model this nonlinearity in a direct and flexible way that avoids imposing a discrete regime structure. I apply this model to the rate of price inflation in the United States, which I show is subject to level shifts. These shifts significantly affect the accuracy of out‐of‐sample forecasts, causing models that assume covariance stationarity to be substantially biased. Models that do not assume covariance stationarity, such as the random walk, are unbiased but lack precision in periods without shifts. I show that the STOPBREAK model outperforms several alternative models in an out‐of‐sample inflation forecasting experiment. Copyright © 2005 John Wiley & Sons, Ltd.     

Exploring Survey‐Based Inflation Forecasts

This paper first shows that survey‐based expectations (SBE) outperform standard time series models in US quarterly inflation out‐of‐sample prediction and that the term structure of survey‐based inflation forecasts has predictive power over the path of future inflation changes. It then proposes some empirical explanations for the forecasting success of survey‐based inflation expectations. We show that SBE pool a large amount of heterogeneous information on inflation expectations and react more flexibly and accurately to macro conditions both contemporaneously and dynamically. We illustrate the flexibility of SBE forecasts in the context of the 2008 financial crisis. Copyright © 2011 John Wiley & Sons, Ltd.     

When are Direct Multi‐step and Iterative Forecasts Identical?

Although both direct multi‐step‐ahead forecasting and iterated one‐step‐ahead forecasting are two popular methods for predicting future values of a time series, it is not clear that the direct method is superior in practice, even though from a theoretical perspective it has lower mean squared error (MSE). A given model can be fitted according to either a multi‐step or a one‐step forecast error criterion, and we show here that discrepancies in performance between direct and iterative forecasting arise chiefly from the method of fitting, and is dictated by the nuances of the model's misspecification. We derive new formulas for quantifying iterative forecast MSE, and present a new approach for assessing asymptotic forecast MSE. Finally, the direct and iterative methods are compared on a retail series, which illustrates the strengths and weaknesses of each approach. Copyright © 2015 John Wiley & Sons, Ltd.     

LASSO‐Type Penalties for Covariate Selection and Forecasting in Time Series

This paper studies some forms of LASSO‐type penalties in time series to reduce the dimensionality of the parameter space as well as to improve out‐of‐sample forecasting performance. In particular, we propose a method that we call WLadaLASSO (weighted lag adaptive LASSO), which assigns not only different weights to each coefficient but also further penalizes coefficients of higher‐lagged covariates. In our Monte Carlo implementation, the WLadaLASSO is superior in terms of covariate selection, parameter estimation precision and forecasting, when compared to both LASSO and adaLASSO, especially for a higher number of candidate lags and a stronger linear dependence between predictors. Empirical studies illustrate our approach for US risk premium and US inflation forecasting with good results. Copyright © 2016 John Wiley & Sons, Ltd.     

The Informational Content of the Term Spread in Forecasting the US Inflation Rate: A Nonlinear Approach

The difficulty in modelling inflation and the significance in discovering the underlying data‐generating process of inflation is expressed in an extensive literature regarding inflation forecasting. In this paper we evaluate nonlinear machine learning and econometric methodologies in forecasting US inflation based on autoregressive and structural models of the term structure. We employ two nonlinear methodologies: the econometric least absolute shrinkage and selection operator (LASSO) and the machine‐learning support vector regression (SVR) method. The SVR has never been used before in inflation forecasting considering the term spread as a regressor. In doing so, we use a long monthly dataset spanning the period 1871:1–2015:3 that covers the entire history of inflation in the US economy. For comparison purposes we also use ordinary least squares regression models as a benchmark. In order to evaluate the contribution of the term spread in inflation forecasting in different time periods, we measure the out‐of‐sample forecasting performance of all models using rolling window regressions. Considering various forecasting horizons, the empirical evidence suggests that the structural models do not outperform the autoregressive ones, regardless of the model's method. Thus we conclude that the term spread models are not more accurate than autoregressive models in inflation forecasting. 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 regional house price inflation: a comparison between dynamic factor models and vector autoregressive models

This paper uses the dynamic factor model framework, which accommodates a large cross‐section of macroeconomic time series, for forecasting regional house price inflation. In this study, we forecast house price inflation for five metropolitan areas of South Africa using principal components obtained from 282 quarterly macroeconomic time series in the period 1980:1 to 2006:4. The results, based on the root mean square errors of one to four quarters ahead out‐of‐sample forecasts over the period 2001:1 to 2006:4 indicate that, in the majority of the cases, the Dynamic Factor Model statistically outperforms the vector autoregressive models, using both the classical and the Bayesian treatments. We also consider spatial and non‐spatial specifications. Our results indicate that macroeconomic fundamentals in forecasting house price inflation are important. Copyright © 2010 John Wiley & Sons, Ltd.     

Forecasting Government Bond Yields with Neural Networks Considering Cointegration

This paper discusses techniques that might be helpful in predicting interest rates and tries to evaluate a new hybrid forecasting approach. Results of examining government bond yields in Germany and France reported in this study indicate that a hybrid forecasting approach which combines techniques of cointegration analysis with neural network (NN) forecasting models can produce superior results to the use of NN forecasting models alone. The findings documented in this paper could be a consequence of the fact that examining differenced data under certain conditions will lead to a loss of information and that the inclusion of the error correction term from the cointegration model can help to cope with this problem. The paper also discusses some possibly interesting directions for further research. Copyright © 2015 John Wiley & Sons, Ltd.     

Hybridizing kernel‐based fuzzy c‐means with hierarchical selective neural network ensemble model for business failure prediction

More and more ensemble models are used to forecast business failure. It is generally known that the performance of an ensemble relies heavily on the diversity between each base classifier. To achieve diversity, this study uses kernel‐based fuzzy c‐means (KFCM) to organize firm samples and designs a hierarchical selective ensemble model for business failure prediction (BFP). First, three KFCM methods—Gaussian KFCM (GFCM), polynomial KFCM (PFCM), and Hyper‐tangent KFCM (HFCM)—are employed to partition the financial data set into three data sets. A neural network (NN) is then adopted as a basis classifier for BFP, and three sets, which are derived from three KFCM methods, are used to build three classifier pools. Next, classifiers are fused by the two‐layer hierarchical selective ensemble method. In the first layer, classifiers are ranked based on their prediction accuracy. The stepwise forward selection method is employed to selectively integrate classifiers according to their accuracy. In the second layer, three selective ensembles in the first layer are integrated again to acquire the final verdict. This study employs financial data from Chinese listed companies to conduct empirical research, and makes a comparative analysis with other ensemble models and all its component models. It is the conclusion that the two‐layer hierarchical selective ensemble is good at forecasting business failure.     

Forecasting inflation using economic indicators: the case of France

In order to provide short‐run forecasts of headline and core HICP inflation for France, we assess the forecasting performance of a large set of economic indicators, individually and jointly, as well as using dynamic factor models. We run out‐of‐sample forecasts implementing the Stock and Watson (1999) methodology. We find that, according to usual statistical criteria, the combination of several indicators—in particular those derived from surveys—provides better results than factor models, even after pre‐selection of the variables included in the panel. However, factors included in VAR models exhibit more stable forecasting performance over time. Results for the HICP excluding unprocessed food and energy are very encouraging. Moreover, we show that the aggregation of forecasts on subcomponents exhibits the best performance for projecting total inflation and that it is robust to data snooping. Copyright © 2007 John Wiley & Sons, Ltd.     

Can forecasting performance be improved by considering the steady state? An application to Swedish inflation and interest rate

This paper investigates whether the forecasting performance of Bayesian autoregressive and vector autoregressive models can be improved by incorporating prior beliefs on the steady state of the time series in the system. Traditional methodology is compared to the new framework—in which a mean‐adjusted form of the models is employed—by estimating the models on Swedish inflation and interest rate data from 1980 to 2004. Results show that the out‐of‐sample forecasting ability of the models is practically unchanged for inflation but significantly improved for the interest rate when informative prior distributions on the steady state are provided. The findings in this paper imply that this new methodology could be useful since it allows us to sharpen our forecasts in the presence of potential pitfalls such as near unit root processes and structural breaks, in particular when relying on small samples. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting the 10‐year US Treasury rate

This study compares the performance of two forecasting models of the 10‐year Treasury rate: a random walk (RW) model and an augmented‐autoregressive (A‐A) model which utilizes the information in the expected inflation rate. For 1993–2008, the RW and A‐A forecasts (with different lead times and forecast horizons) are generally unbiased and accurately predict directional change under symmetric loss. However, the A‐A forecasts outperform the RW, suggesting that the expected inflation rate (as a leading indicator) helps improve forecast accuracy. This finding is important since bond market efficiency implies that the RW forecasts are optimal and cannot be improved. Copyright © 2009 John Wiley & Sons, Ltd.     

Volatility Forecasting via MIDAS,HAR and their Combination: An Empirical Comparative Study for IBOVESPA

In this paper we compare several multi‐period volatility forecasting models, specifically from MIDAS and HAR families. We perform our comparisons in terms of out‐of‐sample volatility forecasting accuracy. We also consider combinations of the models' forecasts. Using intra‐daily returns of the BOVESPA index, we calculate volatility measures such as realized variance, realized power variation and realized bipower variation to be used as regressors in both models. Further, we use a nonparametric procedure for separately measuring the continuous sample path variation and the discontinuous jump part of the quadratic variation process. Thus MIDAS and HAR specifications with the continuous sample path and jump variability measures as separate regressors are estimated. Our results in terms of mean squared error suggest that regressors involving volatility measures which are robust to jumps (i.e. realized bipower variation and realized power variation) are better at forecasting future volatility. However, we find that, in general, the forecasts based on these regressors are not statistically different from those based on realized variance (the benchmark regressor). Moreover, we find that, in general, the relative forecasting performances of the three approaches (i.e. MIDAS, HAR and forecast combinations) are statistically equivalent. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive learning from model space

Dynamic model averaging (DMA) is used extensively for the purpose of economic forecasting. This study extends the framework of DMA by introducing adaptive learning from model space. In the conventional DMA framework all models are estimated independently and hence the information of the other models is left unexploited. In order to exploit the information in the estimation of the individual time‐varying parameter models, this paper proposes not only to average over the forecasts but, in addition, also to dynamically average over the time‐varying parameters. This is done by approximating the mixture of individual posteriors with a single posterior, which is then used in the upcoming period as the prior for each of the individual models. The relevance of this extension is illustrated in three empirical examples involving forecasting US inflation, US consumption expenditures, and forecasting of five major US exchange rate returns. In all applications adaptive learning from model space delivers improvements in out‐of‐sample forecasting performance.     

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.