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Testing Density Forecasts, With Applications to Risk Management

密度预测检验及其在风险管理中的应用

The forecast evaluation literature has traditionally focused on methods of assessing point forecasts. However, in the context of many models of financial risk, interest centers on more than just a single point of the forecast distribution. For example, value-at-risk models that are currently in extremely wide use form interval forecasts. Many other important financial calculations also involve estimates not summarized by a point forecast. Although some techniques are…

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On a Mixture Autoregressive Conditional Heteroscedastic Model

混合自回归条件异方差模型

We propose a mixture autoregressive conditional heteroscedastic (MAR-ARCH) model for modeling nonlinear time series. The models consist of a mixture of K autoregressive components with autoregressive conditional heteroscedasticity; that is, the conditional mean of the process variable follows a mixture AR (MAR) process, whereas the conditional variance of the process variable follows a mixture ARCH process. In addition to the advantage of better description of the…

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Stochastic Neural Networks With Applications to Nonlinear Time Series

随机神经网络及其在非线性时间序列中的应用

We consider a variant of the conventional neural network model, called the stochastic neural network, that can be used to approximate complex nonlinear stochastic systems. We show how the expectation-maximization algorithm can be used to develop efficient estimation schemes that have much lower computational complexity than those for conventional neural networks. This enables us to carry out model selection procedures, such as the Bayesian information criterion, to choose…

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Any Inspection is Manipulable

任何检验都可被操纵

Abstract. A forecaster provides a probabilistic prediction regarding the following day’s state of nature. To examine the forecaster, an inspector employs calibration tests that compare the average prediction and the empirical frequency of pre-specified events. This paper shows that any mixed test can be manipulated in the sense that, independently of the state realizations, the difference between the average prediction and the past empirical frequency that corresponds to…

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Model uncertainty in cross‐country growth regressions

跨国增长回归中的模型不确定性

Abstract We investigate the issue of model uncertainty in cross‐country growth regressions using Bayesian Model Averaging (BMA). We find that the posterior probability is spread widely among many models, suggesting the superiority of BMA over choosing any single model. Out‐of‐sample predictive results support this claim. In contrast to Levine and Renelt ( 1992 ), our results broadly support the more ‘optimistic’ conclusion of Sala‐i‐Martin ( 1997b ), namely that some…

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Improving Federal-Funds Rate Forecasts in VAR Models Used for Policy Analysis

改进政策分析用VAR模型的联邦基金利率预测

Federal-funds rate-forecast errors from vector autoregressive (VAR) models used for monetary policy analysis and fitted by ordinary least squares (OLS) are large relative to those from the futures market. Using three different structural VAR models, we show that forecasts based on a shrinkage estimator dominate the OLS-based forecasts--even after restricting the lag length and/or imposing exact unit-root restrictions--and are broadly comparable to the futures-market…

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To Aggregate, Pool, or Neither

预测数据应聚合、合并,还是两者都不采用?

It is well known that, even if all forecasters are rational, unbiasedness tests using consensus forecasts are inconsistent because forecasters have private information. However, if all forecasters face a common realization, pooled estimators are also inconsistent. In contrast, we show that when predictions and realizations are integrated and cointegrated, microhomogeneity ensures that consensus and pooled estimators are consistent. Therefore, contrary to claims in the…

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On the Nonlinear Predictability of Stock Returns Using Financial and Economic Variables

利用金融与经济变量预测股票收益的非线性可预测性

In a recent article by Qi, neural networks trained by Bayesian regularization were used to predict excess returns on the S&P 500. The article concluded that the switching portfolio based on the recursive neural-network forecasts generates higher accumulated wealth with lower risks than that based on linear regression. Unfortunately, attempts to replicate the results were unsuccessful. Replicated results using the same software, approach and data detailed by Qi indicate that,…

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The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series

使用巴特沃斯滤波器估计经济时间序列的趋势与周期

Long-term trends and business cycles are usually estimated by applying the Hodrick and Prescott (HP) filter to X-11 seasonally adjusted data. A two-stage procedure is proposed in this article to improve this methodology. The improvement is based on (a) using Butterworth or band-pass filters specifically designed for the problem at hand as an alternative to the HP filter, (b) applying the selected filter to estimated trend cycles instead of to seasonally adjusted series, and…

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Monetary policy analysis and inflation targeting in a small open economy: a VAR approach*

小型开放经济中的货币政策分析与通胀目标制:VAR 方法

Abstract Empirical monetary policy research has increased in the last decade, possibly because deregulation and explicit monetary targets have made monetary policy issues more interesting. In particular, within the inflation targeting framework it has been argued that inflation forecasts can be used as optimal intermediate targets for monetary policy, and the development of empirical models that have good forecasting properties is therefore important. This paper shows that a…

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Uniform convergence of sample second moments of families of time series arrays

时间序列数组族样本二阶矩的一致收敛

We consider abstractly defined time series arrays y t(T), 1 \le t\le T, requiring only that their sample lagged second moments converge and that their end values y1+j(T) and yT-j(T) be of order less than T½ for each j \ge 0. We show that,under quite general assumptions, various types of arrays that arise naturally in time series analysis have these properties,including regression residuals from a time series regression, seasonal adjustments and infinite variance processes…

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An automatic leading indicator of economic activity: forecasting GDP growth for European countries*

经济活动的自动先行指标:欧洲国家GDP增长预测

In the construction of a leading indicator model of economic activity, economists must select among a pool of variables which lead output growth. Usually the pool of variables is large and a selection of a subset must be carried out. This paper proposes an automatic leading indicator model which, rather than preselection, uses a dynamic factor model to summarize the information content of a pool of variables. Results using quarterly data for France, Germany, Italy and the…

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Forecasting with difference-stationary and trend-stationary models

Although difference-stationary (DS) and trend-stationary (TS) processes have been subject to considerable analysis, there are no direct comparisons for each being the datageneration process (DGP).We examine incorrect choice between these models for forecasting for both known and estimated parameters. Three sets of Monte Carlo simulations illustrate the analysis, to evaluate the biases in conventional standard errors when each model is misspecified, compute the relative…

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Analysis of a panel of UK macroeconomic forecasts

英国宏观经济预测面板分析

This paper looks at unobserved components models and examines the implied weighting patterns for signal extraction. There are four main themes. The first concerns the implications of correlated disturbances driving the components, especially those cases in which the correlation is perfect. The second is about the way in which ARIMA-based methods for trend extraction relate to those based on unobserved components. The third explores the impact of heteroscedasticity and…

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Fiscal forecasting: The track record of the IMF, OECD and EC

财政预测:国际货币基金组织、经合组织与欧委会的历史表现

We analyse the relative performance of the IMF, OECD and EC in forecasting the government deficit, as a ratio to GDP, for the G7 countries. Interesting differences across countries emerge, sometimes supporting the hypothesis of an asymmetric loss function (i.e. of a preference for underprediction or overprediction), and potential benefits from forecast pooling.

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A Parametric Approach to Flexible Nonlinear Inference

灵活非线性推断的参数化方法

This paper proposes a new framework for determining whether a given relationship is nonlinear, what the nonlinearity looks like, and whether it is adequately described by a particular parametric model. The paper studies a regression or forecasting model of the form yt=μ(xt)+εt where the functional form of μ(⋅) is unknown. We propose viewing μ(⋅) itself as the outcome of a random process. The paper introduces a new stationary random field m(⋅) that generalizes…

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Nonasymptotic bounds for autoregressive time series modeling

自回归时间序列建模的非渐近界

The subject of this paper is autoregressive (AR) modeling of a stationary, Gaussian discrete time process, based on a finite sequence of observations. The process is assumed to admit an AR($\infty$) representation with exponentially decaying coefficients. We adopt the nonparametric minimax framework and study how well the process can be approximated by a finite­order AR model. A lower bound on the accuracy of AR approximations is derived, and a nonasymptotic upper bound on…

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Prediction Intervals for ARIMA Models

ARIMA 模型的预测区间

The problem of constructing prediction intervals for linear time series (ARIMA) models is examined. The aim is to find prediction intervals that incorporate an allowance for sampling error associated with parameter estimates. The effect of constraints on parameters arising from stationarity and invertibility conditions is also incorporated. Two new methods, based on varying degrees of first-order Taylor approximations, are proposed. These are compared in a simulation study…

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Modelling the conditional volatility of commodity index futures as a regime switching process

商品指数期货条件波动率的状态转换建模

Abstract Commodity index futures offer a versatile tool for gaining different forms of exposure to commodity markets. Volatility is a critical input in many of these applications. This paper examines issues in modelling the conditional variance of futures returns based on the Goldman Sachs Commodity Index (GSCI). Given that commodity markets tend to be ‘choppy’ (Webb, 1987 ), a general econometric model is proposed that allows for abrupt changes or regime shifts in…

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Long-Horizon Exchange Rate Predictability?

汇率存在长期可预测性吗?

Several authors have recently investigated the predictability of exchange rates by fitting a sequence of long-horizon error-correction equations. We show by means of a simulation study that, in small to medium samples, inference from this regression procedure depends on the null hypothesis that is used to generate empirical critical values. The standard assumption of a stationary error-correction term between exchange rates and fundamentals biases the results in favor of…

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Bootstrap-After-Bootstrap Prediction Intervals for Autoregressive Models

自回归模型的自助法后再自助法预测区间

The use of the Bonferroni prediction interval based on the bootstrap-after-bootstrap is proposed for autoregressive (AR) models. Monte Carlo simulations are conducted using a number of AR models including stationary, unit-root, and near-unit-root processes. The major finding is that the bootstrap-after-bootstrap provides a superior small-sample alternative to asymptotic and standard bootstrap prediction intervals. The latter are often too narrow, substantially…

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Forecasting an Accumulated Series Based on Partial Accumulation

基于部分累计数据预测累计总量

We present a Bayesian solution to forecasting a time series when few observations are available. The quantity to predict is the accumulated value of a positive, continuous variable when partially accumulated data are observed. These conditions appear naturally in predicting sales of style goods and coupon redemption. A simple model describes the relation between partial and total values, assuming stable seasonality. Exact analytic results are obtained for point forecasts and…

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