Shrinkage‐Based Tests of Predictability

In this paper we derive a test of predictability by exploring the possibility that forecasts from a given model, adjusted by a shrinkage factor, will display lower mean squared prediction errors than forecasts from a simple random walk. This generalizes most previous tests which compare forecast errors of a benchmark model with errors of a proposed alternative model, not allowing for shrinkage. We show that our test is a particular extension of a recently developed test of the martingale difference hypothesis. Using simulations we explore the behavior of our test in small and moderate samples. Numerical results indicate that the test has good size and power properties. Finally, we illustrate the use of our test in an empirical application within the exchange rate literature. Copyright © 2012 John Wiley & Sons, Ltd.     

Prediction from the regression model with two‐way error components

In this paper we extend the Baillie and Baltagi ( 1999 ) paper (Prediction from the regression model with one‐way error components. In Analysis of Panels and Limited Dependent Variables Models, Hsiao C, Lahiri K, Lee LF, Pesaran H (eds). Cambridge University Press, Cambridge, UK). In particular, we derive six predictors for the two‐way error components model, as well as their associated asymptotic mean squared error (AMSE) of multi‐step prediction. In addition, we also provide both theoretical and simulation evidence as to the relative efficiency of our six alternative predictors. The adequacy of the prediction AMSE formula is also investigated by the use of Monte Carlo methods which indicate that the ordinary optimal predictors perform well for various accuracy criteria. Copyright © 2010 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.     

Prediction from the One‐Way Error Components Model with AR(1) Disturbances

In this paper we extend the works of Baillie and Baltagi (1999, in Analysis of Panels and Limited Dependent Variables Models, Hsiao C et al. (eds). Cambridge University Press: Cambridge, UK; 255–267) and generalize certain results from the Baltagi and Li (1992, Journal of Forecasting 11 : 561–567) paper accounting for AR(1) errors in the disturbance term. In particular, we derive six predictors for the one‐way error components model, as well as their associated asymptotic mean squared error of multi‐step prediction in the presence of AR(1) errors in the disturbance term. In addition, we also provide both theoretical and simulation evidence as to the relative efficiency of our alternative predictors. The adequacy of the prediction AMSE formula is also investigated by the use of Monte Carlo methods and indicates that the ordinary optimal predictor performs well for various accuracy criteria. Copyright © 2011 John Wiley & Sons, Ltd.     

Improvement of the Liu‐type Shiller estimator for distributed lag models

The problem of multicollinearity produces undesirable effects on ordinary least squares (OLS), Almon and Shiller estimators for distributed lag models. Therefore, we introduce a Liu‐type Shiller estimator to deal with multicollinearity for distributed lag models. Moreover, we theoretically compare the predictive performance of the Liu‐type Shiller estimator with OLS and the Shiller estimators by the prediction mean square error criterion under the target function. Furthermore, an extensive Monte Carlo simulation study is carried out to evaluate the predictive performance of the Liu‐type Shiller estimator.     

The Predictive Performance Evaluation of Biased Regression Predictors With Correlated Errors

When the interdependence of disturbances is present in a regression model, the pattern of sample residuals contains information which is useful in the prediction of post‐sample drawings and when multicollinearity among regressors is also present, it is useful to use biased regression estimators. This information is exploited in the biased predictors derived here. Also, the predictive performance of various biased predictors with correlated errors is discussed and all pair‐wise comparisons are made among these predictors. The theoretical results are illustrated by a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

Statistical estimation of optimal portfolios for non‐Gaussian dependent returns of assets

This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector‐valued non‐Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ? for non‐Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ?. First, it is shown that there are some cases when the asymptotic variance of ? under non‐Gaussianity can be smaller than that under Gaussianity. The result shows that non‐Gaussianity of the returns does not always affect the efficiency badly. Second, we give a necessary and sufficient condition for ? to be asymptotically efficient when the return process is Gaussian, which shows that ? is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g, which are asymptotically efficient. Furthermore, we investigate the problem of predicting the one‐step‐ahead optimal portfolio return by the estimated portfolio based on ? and examine the mean squares prediction error. Copyright © 2008 John Wiley & Sons, Ltd.     

Break Detectability and Mean Square Forecast Error Ratios for Selecting Estimation Windows

It has been suggested that a major problem for window selection when we estimate models for forecasting is to empirically determine the timing of the break. However, if the window choice between post‐break or full sample is based on mean square forecast error ratios, it is difficult to understand why such a problem arises since break detectability and these ratios seem to have the same determinants. This paper analyses this issue first for the expected values in conditional models and then by Monte Carlo simulations for more general cases. Results show similar behaviour between rejection frequencies and the ratios but only for break tests that do not take into account forecasting error covariances, as is the case with mean square forecast error measures. Moreover, the asymmetric shape of the frequency distribution of the ratios could help us to better grasp empirical problems. An illustration using actual data is given. Copyright © 2011 John Wiley & Sons, Ltd.     

Forecasts of power-transformed series

Consider a time series transformed by an instantaneous power function of the Box-Cox type. For a wide range of fractional powers, this paper gives the relative bias in original metric forecasts due to use of the simple inverse retransformation when minimum mean squared error (conditional mean) forecasts are optimal. This bias varies widely according to the characteristics of the data. A fast algorithm is given to find this bias, or to find minimum mean squared error forecasts in the original metric. The results depend on the assumption that the forecast errors in the transformed metric are Gaussian. An example using real data is given.     

Forecasting US employment growth using forecast combining methods

We examine different approaches to forecasting monthly US employment growth in the presence of many potentially relevant predictors. We first generate simulated out‐of‐sample forecasts of US employment growth at multiple horizons using individual autoregressive distributed lag (ARDL) models based on 30 potential predictors. We then consider different methods from the extant literature for combining the forecasts generated by the individual ARDL models. Using the mean square forecast error (MSFE) metric, we investigate the performance of the forecast combining methods over the last decade, as well as five periods centered on the last five US recessions. Overall, our results show that a number of combining methods outperform a benchmark autoregressive model. Combining methods based on principal components exhibit the best overall performance, while methods based on simple averaging, clusters, and discount MSFE also perform well. On a cautionary note, some combining methods, such as those based on ordinary least squares, often perform quite poorly. Copyright © 2008 John Wiley & Sons, Ltd.     

Finite sample forecast results for vector autoregressive moving average models

Using the 'standard' approach to forecasting in the vector autoregressive moving average model, we establish basic general results on exact finite sample forecasts and their mean squared error matrices. Comparison between the exact and conditional methods of initiating the finite sample forecast calculations is presented, and a few illustrative cases are given.     

Backtesting Value‐at‐Risk: A Generalized Markov Test

Testing the validity of value‐at‐risk (VaR) forecasts, or backtesting, is an integral part of modern market risk management and regulation. This is often done by applying independence and coverage tests developed by Christoffersen (International Economic Review, 1998; 39(4), 841–862) to so‐called hit‐sequences derived from VaR forecasts and realized losses. However, as pointed out in the literature, these aforementioned tests suffer from low rejection frequencies, or (empirical) power when applied to hit‐sequences derived from simulations matching empirical stylized characteristics of return data. One key observation of the studies is that higher‐order dependence in the hit‐sequences may cause the observed lower power performance. We propose to generalize the backtest framework for VaR forecasts, by extending the original first‐order dependence of Christoffersen to allow for a higher‐ or kth‐order dependence. We provide closed‐form expressions for the tests as well as asymptotic theory. Not only do the generalized tests have power against kth‐order dependence by definition, but also included simulations indicate improved power performance when replicating the aforementioned studies. Further, included simulations show much improved size properties of one of the suggested tests. Copyright © 2017 John Wiley & Sons, Ltd.     

Forecasting an aggregate of cointegrated disaggregates

This study examines the problem of forecasting an aggregate of cointegrated disaggregates. It first establishes conditions under which forecasts of an aggregate variable obtained from a disaggregate VECM will be equal to those from an aggregate, univariate time series model, and develops a simple procedure for testing those conditions. The paper then uses Monte Carlo simulations to show, for a finite sample, that the proposed test has good size and power properties and that whether a model satisfies the aggregation conditions is closely related to out‐of‐sample forecast performance. The paper then shows that ignoring cointegration and specifying the disaggregate model as a VAR in differences can significantly affect analyses of aggregation, with the VAR‐based test for aggregation possibly leading to faulty inference and the differenced VAR forecasts potentially understating the benefits of disaggregate information. Finally, analysis of an empirical problem confirms the basic results. Copyright © 2000 John Wiley & Sons, Ltd.     

Stock market volatility and the forecasting performance of stock index futures

This study attempts to apply the general equilibrium model of stock index futures with both stochastic market volatility and stochastic interest rates to the TAIFEX and the SGX Taiwan stock index futures data, and compares the predictive power of the cost of carry and the general equilibrium models. This study also represents the first attempt to investigate which of the five volatility estimators can enhance the forecasting performance of the general equilibrium model. Additionally, the impact of the up‐tick rule and other various explanatory factors on mispricing is also tested using a regression framework. Overall, the general equilibrium model outperforms the cost of carry model in forecasting prices of the TAIFEX and the SGX futures. This finding indicates that in the higher volatility of the Taiwan stock market incorporating stochastic market volatility into the pricing model helps in predicting the prices of these two futures. Furthermore, the comparison results of different volatility estimators support the conclusion that the power EWMA and the GARCH(1,1) estimators can enhance the forecasting performance of the general equilibrium model compared to the other estimators. Additionally, the relaxation of the up‐tick rule helps reduce the degree of mispricing. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting with preliminary data

This paper examines several methods to forecast revised US trade balance figures by incorporating preliminary data. Two benchmark forecasts are considered: one ignoring the preliminary data and the other applying a combination approach; with the second outperforming the first. Competing models include a bivariate AR error-correction model and a bivariate AR error-correction model with GARCH effects. The forecasts from the latter model outperforms the combination benchmark for the one-step forecast case only. A restricted AR error-correction model with GARCH effects is discovered to provide the best forecasts. © 1997 John Wiley & Sons, Ltd.     

Bias‐corrected bootstrap prediction regions for vector autoregression

This paper examines small sample properties of alternative bias‐corrected bootstrap prediction regions for the vector autoregressive (VAR) model. Bias‐corrected bootstrap prediction regions are constructed by combining bias‐correction of VAR parameter estimators with the bootstrap procedure. The backward VAR model is used to bootstrap VAR forecasts conditionally on past observations. Bootstrap prediction regions based on asymptotic bias‐correction are compared with those based on bootstrap bias‐correction. Monte Carlo simulation results indicate that bootstrap prediction regions based on asymptotic bias‐correction show better small sample properties than those based on bootstrap bias‐correction for nearly all cases considered. The former provide accurate coverage properties in most cases, while the latter over‐estimate the future uncertainty. Overall, the percentile‐t bootstrap prediction region based on asymptotic bias‐correction is found to provide highly desirable small sample properties, outperforming its alternatives in nearly all cases. Copyright © 2004 John Wiley & Sons, Ltd.     

Asymmetry in the link between the yield spread and industrial production: threshold effects and forecasting

We analyse the nonlinear behaviour of the information content in the spread for future real economic activity. The spread linearly predicts one‐year‐ahead real growth in nine industrial production sectors of the USA and four of the UK over the last 40 years. However, recent investigations on the spread–real activity relation have questioned both its linear nature and its time‐invariant framework. Our in‐sample empirical evidence suggests that the spread–real activity relationship exhibits asymmetries that allow for different predictive power of the spread when past spread values were above or below some threshold value. We then measure the out‐of‐sample forecast performance of the nonlinear model using predictive accuracy tests. The results show that significant improvement in forecasting accuracy, at least for one‐step‐ahead forecasts, can be obtained over the linear model. Copyright © 2004 John Wiley & Sons, Ltd.     

The impact of measurement errors on ARMA prediction

Measurement errors can have dramatic impact on the outcome of empirical analysis. In this article we quantify the effects that they can have on predictions generated from ARMA processes. Lower and upper bounds are derived for differences in minimum mean squared prediction errors (MMSE) for forecasts generated from data with and without errors. The impact that measurement errors have on MMSE and other relative measures of forecast accuracy are presented for a variety of model structures and parameterizations. Based on these results the need to set up the models in state space form to extract the signal component appears to depend upon whether processes are nearly non‐invertible or non‐stationary or whether the noise‐to‐signal ratio is very high. Copyright © 1999 John Wiley & Sons, Ltd.     

Forecast evaluation tests in the presence of ARCH

We consider tests for the equality of prediction mean squared errors and for forecast encompassing. It is shown that, if forecast errors exhibit ARCH, size distortions are induced in the usual tests. Adjusted test statistics are suggested to alleviate this problem. Copyright © 1999 John Wiley & Sons, Ltd.     

On the Modelling and Forecasting of Multivariate Realized Volatility: Generalized Heterogeneous Autoregressive (GHAR) Model

Recent multivariate extensions of the popular heterogeneous autoregressive model (HAR) for realized volatility leave substantial information unmodelled in residuals. We propose to employ a system of seemingly unrelated regressions to model and forecast a realized covariance matrix to capture this information. We find that the newly proposed generalized heterogeneous autoregressive (GHAR) model outperforms competing approaches in terms of economic gains, providing better mean–variance trade‐off, while, in terms of statistical precision, GHAR is not substantially dominated by any other model. Our results provide a comprehensive comparison of the performance when realized covariance, subsampled realized covariance and multivariate realized kernel estimators are used. We study the contribution of the estimators across different sampling frequencies, and show that the multivariate realized kernel and subsampled realized covariance estimators deliver further gains compared to realized covariance estimated on a 5‐minute frequency. In order to show economic and statistical gains, a portfolio of various sizes is used. Copyright © 2016 John Wiley & Sons, Ltd.