An empirical investigation of direct and iterated multistep conditional forecasts

When constructing unconditional point forecasts, both direct and iterated multistep (DMS and IMS) approaches are common. However, in the context of producing conditional forecasts, IMS approaches based on vector autoregressions are far more common than simpler DMS models. This is despite the fact that there are theoretical reasons to believe that DMS models are more robust to misspecification than are IMS models. In the context of unconditional forecasts, Marcellino et al. (Journal of Econometrics, 2006, 135, 499–526) investigate the empirical relevance of these theories. In this paper, we extend that work to conditional forecasts. We do so based on linear bivariate and trivariate models estimated using a large dataset of macroeconomic time series. Over comparable samples, our results reinforce those in Marcellino et al.: the IMS approach is typically a bit better than DMS with significant improvements only at longer horizons. In contrast, when we focus on the Great Moderation sample we find a marked improvement in the DMS approach relative to IMS. The distinction is particularly clear when we forecast nominal rather than real variables where the relative gains can be substantial.     

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.     

Bayesian VARs: Specification Choices and Forecast Accuracy

In this paper we discuss how the point and density forecasting performance of Bayesian vector autoregressions (BVARs) is affected by a number of specification choices. We adopt as a benchmark a common specification in the literature, a BVAR with variables entering in levels and a prior modeled along the lines of Sims and Zha (International Economic Review 1998; 39 : 949–968). We then consider optimal choice of the tightness, of the lag length and of both; evaluate the relative merits of modeling in levels or growth rates; compare alternative approaches to h‐step‐ahead forecasting (direct, iterated and pseudo‐iterated); discuss the treatment of the error variance and of cross‐variable shrinkage; and assess rolling versus recursive estimation. Finally, we analyze the robustness of the results to the VAR size and composition (using also data for France, Canada and the UK, while the main analysis is for the USA). We obtain a large set of empirical results, but the overall message is that we find very small losses (and sometimes even gains) from the adoption of specification choices that make BVAR modeling quick and easy, in particular for point forecasting. This finding could therefore further enhance the diffusion of the BVAR as an econometric tool for a vast range of applications. Copyright © 2013 John Wiley & Sons, Ltd.     

The performance of alternative forecasting methods for SETAR models

We compare a number of methods that have been proposed in the literature for obtaining h-step ahead minimum mean square error forecasts for self-exciting threshold autoregressive (SETAR) models. These forecasts are compared to those from an AR model. The comparison of forecasting methods is made using Monte Carlo simulation. The Monte-Carlo method of calculating SETAR forecasts is generally at least as good as that of the other methods we consider. An exception is when the disturbances in the SETAR model come from a highly asymmetric distribution, when a Bootstrap method is to be preferred.An empirical application calculates multi-period forecasts from a SETAR model of US gross national product using a number of the forecasting methods. We find that whether there are improvements in forecast performance relative to a linear AR model depends on the historical epoch we select, and whether forecasts are evaluated conditional on the regime the process was in at the time the forecast was made.     

Forecasting a long memory process subject to structural breaks

We develop an easy-to-implement method for forecasting a stationary autoregressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an autoregressive (AR) model and suggest using an information criterion (AIC or Mallows’ _Cp$C_p$) to choose the order of the approximate AR model. Our method avoids the issue of estimation inaccuracy of the long memory parameter and the issue of spurious breaks in finite sample. Insights from our theoretical analysis are confirmed by Monte Carlo experiments, through which we also find that our method provides a substantial improvement over existing prediction methods. An empirical application to the realized volatility of three exchange rates illustrates the usefulness of our forecasting procedure. The empirical success of the HAR-RV model can be explained, from an econometric perspective, by our theoretical and simulation results.     

Epidemic forecasting with a new fuzzy regression equation

The traditional fuzzy regression model involves two solving processes. First, the extension principle is used to derive the membership function of extrapolated values, and then, attempts are made to include every collected value with a membership degree of at least h in the fuzzy regression interval. However, the membership function of extrapolated values is sometimes highly complex, and it is difficult to determine the h value, i.e., the degree of fit between the input values and the extrapolative fuzzy output values, when the information obtained from the collected data is insufficient. To solve this problem, we proposed a simplified fuzzy regression equation based on Carlsson and Fullér’s possibilistic mean and variance method and used it for modeling the constraints and objective function of a fuzzy regression model without determining the membership function of extrapolative values and the value of h. Finally, we demonstrated the application of our model in forecasting pneumonia mortality. Thus, we verified the effectiveness of the proposed model and confirmed the potential benefits of our approach, in which the forecasting error is very small.     

Panel Stationarity Test with Structural Breaks*

In this paper, we extend the heterogeneous panel data stationarity test of Hadri [Econometrics Journal, Vol. 3 (2000) pp. 148–161] to the cases where breaks are taken into account. Four models with different patterns of breaks under the null hypothesis are specified. Two of the models have been already proposed by Carrion‐i‐Silvestre et al. [Econometrics Journal, Vol. 8 (2005) pp. 159–175]. The moments of the statistics corresponding to the four models are derived in closed form via characteristic functions. We also provide the exact moments of a modified statistic that do not asymptotically depend on the location of the break point under the null hypothesis. The cases where the break point is unknown are also considered. For the model with breaks in the level and no time trend and for the model with breaks in the level and in the time trend, Carrion‐i‐Silvestre et al. [Econometrics Journal, Vol. 8 (2005) pp. 159–175] showed that the number of breaks and their positions may be allowed to differ across individuals for cases with known and unknown breaks. Their results can easily be extended to the proposed modified statistic. The asymptotic distributions of all the statistics proposed are derived under the null hypothesis and are shown to be normally distributed. We show by simulations that our suggested tests have in general good performance in finite samples except the modified test. In an empirical application to the consumer prices of 22 OECD countries during the period from 1953 to 2003, we found evidence of stationarity once a structural break and cross‐sectional dependence are accommodated.     

A general class of univariate skew distributions considering Stein’s lemma and infinite divisibility

In this article, we consider a general form of univariate skewed distributions. We denote this form by GUS(λ; h(x)) or GUS with density s(x|λ, h(x)) = 2f(x)G(λ h(x)), where f is a symmetric density, G is a symmetric differentiable distribution, and h(x) is an odd function. A special case of this general form, normal case, is derived and denoted by GUSN(λ; h(x)). Some representations and some main properties of GUS(λ; h(x)) are studied. The moments of GUSN(λ; h(x)) and SN(λ), the known skew normal distribution of Azzalini (1985), are compared and the relationship between them is given. As an application, we use it to construct a new form for skew t-distribution and skew Cauchy distribution. In addition, we extend Stein’s lemma and study infinite divisibility of GUSN(λ; h(x)).     

Mining the past to determine the future: Comments

In forecasting, data mining is frequently perceived as a distinct technological discipline without immediate relevance to the challenges of time series prediction. However, Hand (2009) postulates that when the large cross-sectional datasets of data mining and the high-frequency time series of forecasting converge, common problems and opportunities are created for the two disciplines. This commentary attempts to establish the relationship between data mining and forecasting via the dataset properties of aggregate and disaggregate modelling, in order to identify areas where research in data mining may contribute to current forecasting challenges, and vice versa. To forecasting, data mining offers insights on how to handle large, sparse datasets with many binary variables, in feature and instance selection. Furthermore data mining and related disciplines may stimulate research into how to overcome selectivity bias using reject inference on observational datasets and, through the use of experimental time series data, how to extend the utility and costs of errors beyond measuring performance, and how to find suitable time series benchmarks to evaluate computer intensive algorithms. Equally, data mining can profit from forecasting’s expertise in handling nonstationary data to counter the out-of-date-data problem, and how to develop empirical evidence beyond the fine tuning of algorithms, leading to a number of potential synergies and stimulating research in both data mining and forecasting.     

Leading Indicators for Euro‐area Inflation and GDP Growth*

In this paper, we evaluate the role of a set of variables as leading indicators for Euro‐area inflation and GDP growth. Our leading indicators are taken from the variables in the European Central Bank's (ECB) Euro‐area‐wide model database, plus a set of similar variables for the US. We compare the forecasting performance of each indicator ex post with that of purely autoregressive models. We also analyse three different approaches to combining the information from several indicators. First, ex post, we discuss the use as indicators of the estimated factors from a dynamic factor model for all the indicators. Secondly, within an ex ante framework, an automated model selection procedure is applied to models with a large set of indicators. No future information is used, future values of the regressors are forecast, and the choice of the indicators is based on their past forecasting records. Finally, we consider the forecasting performance of groups of indicators and factors and methods of pooling the ex ante single‐indicator or factor‐based forecasts. Some sensitivity analyses are also undertaken for different forecasting horizons and weighting schemes of forecasts to assess the robustness of the results.     

Forecasting by factors,by variables,by both or neither?

We consider forecasting with factors, variables and both, modeling in-sample using Autometrics so all principal components and variables can be included jointly, while tackling multiple breaks by impulse-indicator saturation. A forecast-error taxonomy for factor models highlights the impacts of location shifts on forecast-error biases. Forecasting US GDP over 1-, 4- and 8-step horizons using the dataset from Stock and Watson (2009) updated to 2011:2 shows factor models are more useful for nowcasting or short-term forecasting, but their relative performance declines as the forecast horizon increases. Forecasts for GDP levels highlight the need for robust strategies, such as intercept corrections or differencing, when location shifts occur as in the recent financial crisis.     

Forecasting financial crises for an enterprise by using the Grey Markov forecasting model

The business environment is rapidly changing and some enterprises have announced unexpected restructurings, leading to stagnating stock prices and declines in their business performance. To prepare for calamity, it is becoming increasingly important for enterprise managers to use current financial data for short-term financial forecasting. Managers and investors are increasingly concerned with immediately and accurately forecasting firm financial crises using a limited amount of financial data. This work employs Z-Score value, which can be used to measure multinomial financial crisis index for forecasting, and utilizes Grey Markov forecasting for valuation. Based on the research results, the accuracy of the Grey Markov forecasting model is as expected, with excellent Z-Score, and the model can rapidly forecast the likelihood of firm financial crises. The study results can provide a good reference for government and financial institutions in examining financial risk, and for investors in selecting investment targets.     

Modelling and forecasting value at risk and expected shortfall for GCC stock markets: Do long memory,structural breaks,asymmetry, and fat-tails matter?

This paper addresses the question whether dual long memory (LM), asymmetry and structural breaks in stock market returns matter when forecasting the value at risk (VaR) and expected shortfall (ES) for short and long trading positions. We answer this question for the Gulf Cooperation Council (GCC) stock markets. Empirically, we test the occurrence of structural breaks in the GCC return data using the Inclan and Tiao (1994)’s algorithm and we check the relevance of LM using Shimotsu (2006) procedure before estimating the ARFIMA-FIGARCH and ARFIMA-FIAPARCH models with different innovations’ distributions and computing VaR and ES. Our results show that all the GCC market's volatilities exhibit significant structural breaks matching mainly with the 2008–2009 global financial crises and the Arab spring. Also, they are governed by LM process either in the mean or in the conditional variance which cannot be due to the occurrence of structural breaks. Furthermore, the forecasting ability analysis shows that the FIAPARCH model under skewed Student-t distribution turn out to improve substantially the VaR and the ES forecasts.     

Does global inflation help forecast inflation in industrialized countries?

Ciccarelli and Mojon (CM; Review of Economics and Statistics, 2010, 92(3), 524–535) propose an inflation forecasting model incorporating a global inflation factor and show that it consistently beats several standard forecasting benchmarks. We show that CM's global inflation model does not improve upon the Atkeson and Ohanian (AO; Federal Reserve Bank of Minneapolis Quarterly Review, 2001, 25(1), 2–11) naive benchmark. However, we find that augmenting the AO model with a global inflation factor improves forecast accuracy at longer horizons, supporting CM's claim about the usefulness of global inflation.     

Optimal extended complete block designs for dependent observations

Optimal designs under general dependence structures are usually difficult to specify theoretically or find algorithmically. However, they can sometimes be found for a specific dependence structure and a particular parameter value. In this paper, a class of generalized binary block designs with t treatments and b blocks of size k>t is considered. Each block consists of h consecutive complete blocks and, at the end, an incomplete block of size k−ht (if k > ht). For a suitable number of blocks, a universally optimal design is found for a first-order stationary autoregressive process with positive correlations. Optimal generalized binary designs and balanced block designs are also considered. Some constructions for a universally optimal design are described. A negative dependence parameter, and some other dependence structures, are also considered.     

Forecast on silver futures linked with structural breaks and day-of-the-week effect

Silver future is crucial to global financial markets. However, the existing literature rarely considers the impacts of structural breaks and day-of-the-week effect simultaneously on the volatility of silver future price. Based on heterogeneous autoregressive (HAR) theory, we establish six new type heterogeneous autoregressive (HAR) models by incorporating structural breaks and day-of-the-week effect to forecast the volatility. The empirical results indicate that new models’ accuracy is better than the original HAR model. We find that structural breaks and the day-of-the-week effect contain much forecasting information on silver forecasting. In addition, structural breaks have a positive effect on the silver futures’ volatility. Day-of-the-week effect has a significantly negative influence on silver futures’ price volatility, especially in the mid-term and the long-term. Our works is the first to combine the structural breaks and day-of-the-week effect to identify more market information. This paper provides a better forecasting method to predict silver future volatility.     

The problem of optimum stratification and allocation withq=n/N>0

Summary Dalenius/Gurney [1951] published necessary conditions for the stratum boundaries, so that with Neyman's optimal allocation of the sample sizen the variance of the sample mean will become a minimum. They introduced in the variance of the sample mean for the sample sizesn _h the opti mal values according to Neyman and differentiated this variance with respect to the stratum boundaries. Because Neyman's allocation formula yields only feasible solutions forn _h N _h , the conditions ofDalenius result in wrong, i.e. nonfeasible solutions, if one of the restrictionsn _h N _h (h=1 (1) L) is violated.By the example of a logarithmic normal distribution with =0, =1,5 forL=2 the behaviour of the Dalenius-Neyman-minimum and that of the feasible minimum will be shown in dependence on the sampling fractionq=n/N and a critical valueq _c will be given. For valuesq>q _c the Dalenius-Neyman-minimum is no longer feasible.For the same logarithmic normal distribution andL=2 (1) 10 this critical sampling fractionq _c will be given (section 5).For different values of andq the optimal stratum boundaries and sampling fractions are listed in section 6 forL=2;3;4.     

Some notes on discount factor restrictions for dynamic optimization problems

We consider dynamic optimization problems on one-dimensional state spaces. Under standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation between the size of the discount factor of the dynamic optimization problem on the one hand and the properties of the dynamical system x_t+1=h(x_t) on the other hand. The purpose of this paper is to survey some of the most important contributions of this literature and to modify or improve them in various directions. We deal in particular with the topological entropy of the dynamical system, with its Lyapunov exponents, and with its periodic orbits.     

Further Evidence on the Statistical Properties of Real GNP*

The well‐known lack of power of unit‐root tests has often been attributed to the short length of macroeconomic variables and also to data‐generating processes (DGPs) departing from the I(1)–I(0) models. This paper shows that by using long spans of annual real gross national product (GNP) and GNP per capita (133 years), high power can be achieved, leading to the rejection of both the unit‐root and the trend‐stationary hypothesis. More flexible representations are then considered, namely, processes containing structural breaks (SB) and fractional orders of integration (FI). Economic justification for the presence of these features in GNP is provided. It is shown that both FI and SB formulations are in general preferred to the autoregressive integrated moving average (ARIMA) [I(1) or I(0)] formulations. As a novelty in this literature, new techniques are applied to discriminate between FI and SB. It turns out that the FI specification is preferred, implying that GNP and GNP per capita are non‐stationary, highly persistent but mean‐reverting series. Finally, it is shown that the results are robust when breaks in the deterministic component are allowed for in the FI model. Some macroeconomic implications of these findings are also discussed.     

Quality & Quantity journal: a bibliometric snapshot

This article analyzes the Quality & Quantity journal from the point of view of some bibliometric indicators: the Hirsch (h) and the g-index for journals, the total number of citations, the h- and the g-spectrum. Journal time evolution is also studied and discussed in detail. As a final point, an interesting issue about how to objectively evaluate the journal popularity in the professional world—rather than the scientific/academic—is presented and left open.