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Interval forecasts and parameter uncertainty

区间预测与参数不确定性

Forecast intervals generalize point forecasts to represent and incorporate uncertainty. Forecast intervals calculated from dynamic models typically sidestep the issue of parameter estimation. This paper shows how to construct asymptotic forecast intervals which incorporate the uncertainty due to parameter estimation. Our proposed solution is a simple proportional adjustment to the interval endpoints, the adjustment factor depending on the asymptotic variance of the interval…

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A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series

宏观时间序列多步预测:直接法与迭代 AR 方法的比较

“Iterated” multiperiod ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas “direct” forecasts are made using a horizon-specific estimated model, where the dependent variable is the multi-period ahead value being forecasted. Which approach is better is an empirical matter: in theory, iterated forecasts are more efficient if correctly specified, but direct forecasts are more robust to model…

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A regime switching long memory model for electricity prices

电价的状态转换长记忆模型

In this paper we develop a regime switching model which can generate long memory (fractional integration) in each of the regime states. This property is relevant in a number of cases. For instance, the deregulated market for electricity power in the Nordic countries is characterized by electricity spot prices with a high degree of long memory. It occurs that in some time periods bilateral prices are identical whereas in other periods the prices differ. The latter occurs when…

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Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models

VAR 模型中协整秩检验与选择的自助法算法

In this paper a bootstrap algorithm for a reduced rank vector autoregressive model with a restricted linear trend and independent, identically distributed errors is analyzed. For testing the cointegration rank, the asymptotic distribution under the hypothesis is the same as for the usual likelihood ratio test, so that the bootstrap is consistent. It is furthermore shown that a bootstrap procedure for determining the rank is asymptotically consistent in the sense that the…

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Tests of Conditional Predictive Ability

条件预测能力检验

We propose a framework for out-of-sample predictive ability testing and forecast selection designed for use in the realistic situation in which the forecasting model is possibly misspecified, due to unmodeled dynamics, unmodeled heterogeneity, incorrect functional form, or any combination of these. Relative to the existing literature (Diebold and Mariano (1995) and West (1996)), we introduce two main innovations: (i) We derive our tests in an environment where the finite…

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Efficient prediction for linear and nonlinear autoregressive models

线性与非线性自回归模型的有效预测

Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better parametric rates and are asymptotically efficient. The proof is based on a…

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Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: A stochastic recurrence equations approach

条件异方差时间序列的准极大似然估计:随机递推方程方法

This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form Xt=σtZt, where the unobservable volatility σt is a parametric function of (Xt−1, …, Xt−p, σt−1, …, σt−q) for some p, q≥0, and (Zt) is standardized i.i.d. noise. We assume that these models are solutions to stochastic recurrence equations which satisfy a contraction (random Lipschitz coefficient) property. These assumptions are…

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Efficient Tests for General Persistent Time Variation in Regression Coefficients

回归系数一般持续性时变的有效检验

There are a large number of tests for instability or breaks in coefficients in regression models designed for different possible departures from the stable model. We make two contributions to this literature. First, we consider a large class of persistent breaking processes that lead to asymptotically equivalent efficient tests. Our class allows for many or relatively few breaks, clustered breaks, regularly occurring breaks, or smooth transitions to changes in the regression…

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Tests for Cointegration Breakdown Over a Short Time Period

短时段内协整关系失效的检验

This article introduces tests for cointegration breakdown that may occur over a relatively short time period, such as at the end of the sample. The breakdown may be due to a shift in the cointegrating vector or due to a shift in the errors from being I(0) to being I(1). Tests are introduced based on the postbreakdown sum of squared residuals and sum of squared reverse partial sums of residuals. Critical values are provided using a subsampling method. Asymptotic results take…

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Modeling Purchases as Repeated Events

将购买行为建模为重复事件

We put forward a statistical model for interpurchase times that incorporates all current and past information available for all purchases as time runs along the calendar time scale. It delivers forecasts for the number of purchases in the next period, as well as for the timing of subsequent and consecutive purchases. Purchase occasions are viewed as a counting process that counts the recurrent purchases for each house-hold as they evolve over time. We illustrate our model…

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Simulation Methods for Lévy-Driven Continuous-Time Autoregressive Moving Average (CARMA) Stochastic Volatility Models

Lévy 驱动的连续时间 CARMA 随机波动率模型模拟方法

We develop simulation schemes for the new classes of non-Gaussian pure jump Lévy processes for stochastic volatility. We write the price and volatility processes as integrals against a vector Lévy process, which makes series approximation methods directly applicable. These methods entail simulation of the Lévy increments and formation of weighted sums of the increments; they do not require a closed-form expression for a tail mass function or specification of a copula…

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Volatility Forecasting With Range-Based EGARCH Models

基于价格极差的 EGARCH 模型与波动率预测

We provide a simple, yet highly effective framework for forecasting return volatility by combining exponential generalized autoregressive conditional heteroscedasticity models with data on the range. Using Standard and Poor's 500 index data for 1983–2004, we demonstrate the importance of a long-memory specification, based on either a two-factor structure or fractional integration, that allows for some asymmetry between market returns and volatility innovations. Out-of-sample…

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A NECESSARY AND SUFFICIENT CONDITION FOR THE STRICT STATIONARITY OF A FAMILY OF GARCH PROCESSES

一类 GARCH 过程严格平稳的充要条件

We consider a family of GARCH(1,1) processes introduced in He and Teräsvirta (1999a, Journal of Econometrics 92, 173–192). This family contains various popular generalized autoregressive conditional heteroskedasticity (GARCH) models as special cases. A necessary and sufficient condition for the existence of a strictly stationary solution is given.This research was financially supported by the Jan Wallander's and Tom Hedelius' Foundation, Grant J03–41. The author thanks the…

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RANDOM EFFECTS AND SPATIAL AUTOCORRELATION WITH EQUAL WEIGHTS

等权重下的随机效应与空间自相关

This note considers a panel data regression model with spatial autoregressive disturbances and random effects where the weight matrix is normalized and has equal elements. This is motivated by Kelejian, Prucha, and Yuzefovich (2005, Journal of Regional Science, forthcoming), who argue that such a weighting matrix, having blocks of equal elements, might be considered when units are equally distant within certain neighborhoods but unrelated between neighborhoods. We derive a…

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UNBALANCED COINTEGRATION

不平衡协整

Recently, increasing interest in the issue of fractional cointegration has emerged from theoretical and empirical viewpoints. Here, as opposed to the traditional prescription of unit root observables with weak dependent cointegrating errors, the orders of integration of these series are allowed to take real values, but, as in the traditional framework, equality of the orders of at least two observable series is necessary for cointegration. This assumption, in view of the…

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BIAS-REDUCED LOG-PERIODOGRAM AND WHITTLE ESTIMATION OF THE LONG-MEMORY PARAMETER WITHOUT VARIANCE INFLATION

不增加方差的长记忆参数偏差缩减对数周期图与 Whittle 估计

The bias-reduced log-periodogram estimator of Andrews and Guggenberger (2003, Econometrica 71, 675–712) for the long-memory parameter d in a stationary long-memory time series reduces the asymptotic bias of the original log-periodogram estimator of Geweke and Porter-Hudak (1983) by an order of magnitude but inflates the asymptotic variance by a multiplicative constant cr, for example, c1 = 2.25 and c2 = 3.52. In this paper, we introduce a new, computationally attractive…

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