Measuring predictability: theory and macroeconomic applications

We propose a measure of predictability based on the ratio of the expected loss of a short‐run forecast to the expected loss of a long‐run forecast. This predictability measure can be tailored to the forecast horizons of interest, and it allows for general loss functions, univariate or multivariate information sets, and covariance stationary or difference stationary processes. We propose a simple estimator, and we suggest resampling methods for inference. We then provide several macroeconomic applications. First, we illustrate the implementation of predictability measures based on fitted parametric models for several US macroeconomic time series. Second, we analyze the internal propagation mechanism of a standard dynamic macroeconomic model by comparing the predictability of model inputs and model outputs. Third, we use predictability as a metric for assessing the similarity of data simulated from the model and actual data. Finally, we outline several non‐parametric extensions of our approach. Copyright © 2001 John Wiley & Sons, Ltd.     

Understanding survey-based inflation expectations

This paper examines the behavior of inflation expectations in the United States. After documenting deviations from rationality in survey-based inflation expectations, I apply a model selection algorithm, boosting, to the inflation expectations of households and professionals. The algorithm builds a regression-like model of expected inflation using a large panel of macroeconomic data as possible covariates. The algorithm achieves a very strong fit in-sample, and finds that the inflation expectations of households correlate with different macroeconomic variables from the expectations of professionals. However, it is difficult to exploit the predictability of inflation expectations in order to improve forecasts of the realized inflation.     

On economic uncertainty,stock market predictability and nonlinear spillover effects

This paper uses a k-th order nonparametric Granger causality test to analyze whether firm-level, economic policy and macroeconomic uncertainty indicators predict movements in real stock returns and their volatility. Linear Granger causality tests show that whilst economic policy and macroeconomic uncertainty indices can predict stock returns, firm-level uncertainty measures possess no predictability. However, given the existence of structural breaks and inherent nonlinearities in the series, we employ a nonparametric causality methodology, as linear modeling leads to misspecifications thus the results cannot be considered reliable. The nonparametric test reveals that in fact no predictability can be observed for the various measures of uncertainty i.e., firm-level, macroeconomic and economic policy uncertainty, vis-à-vis real stock returns. In turn, a profound causal predictability is demonstrated for the volatility series, with the exception of firm-level uncertainty. Overall our results not only emphasize the role of economic and firm-level uncertainty measures in predicting the volatility of stock returns, but also presage against using linear models which are likely to suffer from misspecification in the presence of parameter instability and nonlinear spillover effects.     

Forecasting aggregates using panels of nonlinear time series

Macroeconomic time series such as total unemployment or total industrial production concern data which are aggregated across regions, sectors, or age categories. In this paper we examine whether forecasts for these aggregates can be improved by considering panel models for the disaggregate series. As many macroeconomic variables have nonlinear properties, we specifically focus on panels of nonlinear time series. We discuss the representation of such models, parameter estimation and a method for generating forecasts. We illustrate the usefulness of our approach for simulated data and for the US coincident index, making use of state-specific component series.     

Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A re-examination

In this paper, we examine the forecast accuracy of linear autoregressive, smooth transition autoregressive (STAR), and neural network (NN) time series models for 47 monthly macroeconomic variables of the G7 economies. Unlike previous studies that typically consider multiple but fixed model specifications, we use a single but dynamic specification for each model class. The point forecast results indicate that the STAR model generally outperforms linear autoregressive models. It also improves upon several fixed STAR models, demonstrating that careful specification of nonlinear time series models is of crucial importance. The results for neural network models are mixed in the sense that at long forecast horizons, an NN model obtained using Bayesian regularization produces more accurate forecasts than a corresponding model specified using the specific-to-general approach. Reasons for this outcome are discussed.     

Forecasting the US term structure of interest rates using a macroeconomic smooth dynamic factor model

We extend the class of dynamic factor yield curve models in order to include macroeconomic factors. Our work benefits from recent developments in the dynamic factor literature related to the extraction of the common factors from a large panel of macroeconomic series and the estimation of the parameters in the model. We include these factors in a dynamic factor model for the yield curve, in which we model the salient structure of the yield curve by imposing smoothness restrictions on the yield factor loadings via cubic spline functions. We carry out a likelihood-based analysis in which we jointly consider a factor model for the yield curve, a factor model for the macroeconomic series, and their dynamic interactions with the latent dynamic factors. We illustrate the methodology by forecasting the U.S. term structure of interest rates. For this empirical study, we use a monthly time series panel of unsmoothed Fama–Bliss zero yields for treasuries of different maturities between 1970 and 2009, which we combine with a macro panel of 110 series over the same sample period. We show that the relationship between the macroeconomic factors and the yield curve data has an intuitive interpretation, and that there is interdependence between the yield and macroeconomic factors. Finally, we perform an extensive out-of-sample forecasting study. Our main conclusion is that macroeconomic variables can lead to more accurate yield curve forecasts.     

Forecasting macroeconomic variables using collapsed dynamic factor analysis

We explore a new approach to the forecasting of macroeconomic variables based on a dynamic factor state space analysis. Key economic variables are modeled jointly with principal components from a large time series panel of macroeconomic indicators using a multivariate unobserved components time series model. When the key economic variables are observed at a low frequency and the panel of macroeconomic variables is at a high frequency, we can use our approach for both nowcasting and forecasting purposes. Given a dynamic factor model as the data generation process, we provide Monte Carlo evidence of the finite-sample justification of our parsimonious and feasible approach. We also provide empirical evidence for a US macroeconomic dataset. The unbalanced panel contains quarterly and monthly variables. The forecasting accuracy is measured against a set of benchmark models. We conclude that our dynamic factor state space analysis can lead to higher levels of forecasting precision when the panel size and time series dimensions are moderate.     

Forecasting commodity price indexes using macroeconomic and financial predictors

Using a long sample of commodity spot price indexes over the period 1947–2010, we examine the out-of-sample predictability of commodity prices by means of macroeconomic and financial variables. Commodity currencies are found to have some predictive power at short (monthly and quarterly) forecast horizons, while growth in industrial production and the investment–capital ratio have some predictive power at longer (yearly) horizons. Commodity price predictability is strongest when based on multivariate approaches that account for parameter estimation error. Commodity price predictability varies substantially across economic states, being strongest during economic recessions.     

Real‐time detection of regimes of predictability in the US equity premium

We propose new real‐time monitoring procedures for the emergence of end‐of‐sample predictive regimes using sequential implementations of standard (heteroskedasticity‐robust) regression t‐statistics for predictability applied over relatively short time periods. The procedures we develop can also be used for detecting historical regimes of temporary predictability. Our proposed methods are robust to both the degree of persistence and endogeneity of the regressors in the predictive regression and to certain forms of heteroskedasticity in the shocks. We discuss how the monitoring procedures can be designed such that their false positive rate can be set by the practitioner at the start of the monitoring period using detection rules based on information obtained from the data in a training period. We use these new monitoring procedures to investigate the presence of regime changes in the predictability of the US equity premium at the 1‐month horizon by traditional macroeconomic and financial variables, and by binary technical analysis indicators. Our results suggest that the 1‐month‐ahead equity premium has temporarily been predictable, displaying so‐called “pockets of predictability,” and that these episodes of predictability could have been detected in real time by practitioners using our proposed methodology.     

Learning,forecasting and structural breaks

We provide a general methodology for forecasting in the presence of structural breaks induced by unpredictable changes to model parameters. Bayesian methods of learning and model comparison are used to derive a predictive density that takes into account the possibility that a break will occur before the next observation. Estimates for the posterior distribution of the most recent break are generated as a by‐product of our procedure. We discuss the importance of using priors that accurately reflect the econometrician's opinions as to what constitutes a plausible forecast. Several applications to macroeconomic time‐series data demonstrate the usefulness of our procedure. Copyright © 2008 John Wiley & Sons, Ltd.     

Bayesian International Evidence on Heavy Tails, Non-Stationarity and Asymmetry over the Business Cycle

Although leptokurtosis is fairly common in macroeconomic time series, agreement over what non-normal distributions are plausible, is rare. The paper proposes a linear model that allows for trend versus difference stationarity and asymmetric behavior over the business cycle along with several distributional alternatives for the disturbance terms. It proposes computationally feasible Markov Chain Monte Carlo methods to perform Bayesian computations, applies the model to industrial production data of seven industrialized countries, and relies on prior predictive densities to compare models with Student- t , symmetric stable, EGARCH, exponential power family and finite-mixture-of-normals errors. The relationship between unit root inference, asymmetry and leptokurtosis is examined in detail using the exact, finite-sample posteriors corresponding to the different models.     

The quantilogram: With an application to evaluating directional predictability

We propose a new diagnostic tool for time series called the quantilogram. The tool can be used formally and we provide the inference tools to do this under general conditions, and it can also be used as a simple graphical device. We apply our method to measure directional predictability and to test the hypothesis that a given time series has no directional predictability. The test is based on comparing the correlogram of quantile hits to a pointwise confidence interval or on comparing the cumulated squared autocorrelations with the corresponding critical value. We provide the distribution theory needed to conduct inference, propose some model free upper bound critical values, and apply our methods to S&P500 stock index return data. The empirical results suggest some directional predictability in returns. The evidence is strongest in mid range quantiles like 5–10% and for daily data. The evidence for predictability at the median is of comparable strength to the evidence around the mean, and is strongest at the daily frequency.     

NONLINEAR TIME SERIES MODELS IN ECONOMICS

Abstract. In recent years there has been great interest in developing nonlinear extensions to the basic Autoregressive Integrated Moving Average model popularised by Box and Jenkins. Many of these have been in response to observed nonlinear behaviour in scientific areas such as electronic engineering, geology and oceanography and, as a consequence, have found little application in economics. Economic time series have features peculiar to themselves, and thus often require models to be developed in response to their own special nonlinear character. This paper therefore surveys those nonlinear time series models that have been developed in other disciplines and which have found to be useful for analysing economic time series, such as power transformations, fractional integration and deterministic chaos, and those that have been developed directly in response to nonlinear economic behaviour: for example, logistic transformations, asymmetric models, Markov models for business cycles and time deformation models. Also discussed are various tests for the presence of nonlinearity in time series and the evidence concerning the prevalence of such nonlinearity in economic time series is surveyed.     

货币供应量对价格体系的传导效应分析

货币作为中间目标变量存在于经济生活中的任何一部分。国民经济的健康运转离不开货币,而货币政策作为重要工具在宏观经济调控中起着举足轻重的作用。本文选用2004年1月-2014年3月货币供应量与价格指数的季度时间序列数据,通过非线性平滑转换模型,实证研究了货币供应量与价格体系之间的动态关系,得出我国货币供应量对价格体系具有较强的传导效应。在基于以上研究结果的基础上对我国货币政策提出了相关的政策建议。     

Forecasting with vector autoregressive (VAR) models subject to business cycle restrictions

In the last decade VAR models have become a widely-used tool for forecasting macroeconomic time series. To improve the out-of-sample forecasting accuracy of these models, Bayesian random-walk prior restrictions are often imposed on VAR model parameters. This paper focuses on whether placing an alternative type of restriction on the parameters of unrestricted VAR models improves the out-of-sample forecasting performance of these models. The type of restriction analyzed here is based on the business cycle characteristics of U.S. macroeconomic data, and in particular, requires that the dynamic behavior of the restricted VAR model mimic the business cycle characteristics of historical data. The question posed in this paper is: would a VAR model, estimated subject to the restriction that the cyclical characteristics of simulated data from the model “match up” with the business cycle characteristics of U.S. data, generate more accurate out-of-sample forecasts than unrestricted or Bayesian VAR models?     

基于BP神经网络的西安市宏观经济预测

宏观经济系统是一个复杂的非线性系统,对宏观经济进行预测应采用非线性的工具进行建模。采用BP神经网络对西安市宏观经济指标进行预测,此预测模型只需少量训练样本就可以确定网络的权值和阈值。实验表明模型预测精度高,能够对西安市宏观经济系统中的非线性关系进行描述,使建立的非线性模型与实际系统更加接近。     

Economic uncertainty and growth performance: a macroeconomic modeling analysis for Pakistan

This paper investigates the effects of economic uncertainty on growth performance of Pakistan through developing a small macroeconomic model. The GARCH method has been used for construction of economic uncertainty variables related to macroeconomic policies. The structural outcomes clearly indicate that economic policy uncertainty affects negatively on real and nominal sectors of Pakistan. The forecasting of model and different policy uncertainty simulation shocks also indicated that an adjustment in economic policies due to change of policy objectives create uncertain environment in country, which not only deteriorates the investment climate of country, it also affects the economic growth. Our study concludes that economic uncertainty not only reduces the current investment and economic growth, it also affects the future decision of investment and economic growth. This study suggests that sustainable and steady economic policies always reduce economic uncertainty and promote the confidence of economic agents, which help in achieving the targets of investment, trade and economic growth. Our study also maintains the predictability and reliability of government policies for the accomplishment of macroeconomic goals and economic development of country.     

CPI指数对我国宏观经济走势的影响

基于CPI指数与宏观经济走势关系的理论基础,侧重于从实证角度,运用时间序列分析工具来解析CPI指数与宏观经济走势之间的关系。研究结果表明,我国CPI指数与宏观经济走势之间存在着长期相关关系,长期来看CPI指数可以作为一个重要指标来预判宏观经济走势,决定财政政策;在短期来看,CPI指数属于滞后指标,只能用来反映之前的宏观经济状况。因此基于CPI指数的正确性及它对宏观经济的反应程度,采取合理的货币政策和经济政策的建议。     

Forecasting cryptocurrencies under model and parameter instability

This paper studies the predictability of cryptocurrency time series. We compare several alternative univariate and multivariate models for point and density forecasting of four of the most capitalized series: Bitcoin, Litecoin, Ripple and Ethereum. We apply a set of crypto-predictors and rely on dynamic model averaging to combine a large set of univariate dynamic linear models and several multivariate vector autoregressive models with different forms of time variation. We find statistically significant improvements in point forecasting when using combinations of univariate models, and in density forecasting when relying on the selection of multivariate models. Both schemes deliver sizable directional predictability.     

Semiparametric quantile averaging in the presence of high-dimensional predictors

The paper proposes a method for forecasting conditional quantiles. In practice, one often does not know the “true” structure of the underlying conditional quantile function, and in addition, we may have a large number of predictors. Focusing on such cases, we introduce a flexible and practical framework based on penalized high-dimensional quantile averaging. In addition to prediction, we show that the proposed method can also serve as a predictor selector. We conduct extensive simulation experiments to asses its prediction and variable selection performances for nonlinear and linear time series model designs. In terms of predictor selection, the approach tends to select the true set of predictors with minimal false positives. With respect to prediction accuracy, the method competes well even with the benchmark/oracle methods that know one or more aspects of the underlying quantile regression model. We further illustrate the merit of the proposed method by providing an application to the out-of-sample forecasting of U.S. core inflation using a large set of monthly macroeconomic variables based on FRED-MD database. The application offers several empirical findings.