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Shrinkage estimators for periodic autoregressions

周期自回归模型的收缩估计

A periodic autoregression [PAR] is a seasonal time series model where the autoregressive parameters vary over the seasons. A drawback of PAR models is that the number of parameters increases dramatically when the number of seasons gets large. Hence, one needs many periods with intra-seasonal data to be able to get reliable parameter estimates. Therefore, these models are rarely applied for weekly or daily observations. In this paper we propose shrinkage estimators which…

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To pool or not to pool: What is a good strategy for parameter estimation and forecasting in panel regressions?

合并还是不合并:面板回归参数估计与预测的策略

Summary This paper considers estimating the slope parameters and forecasting in potentially heterogeneous panel data regressions with a long time dimension. We propose a novel optimal pooling averaging estimator that makes an explicit trade‐off between efficiency gains from pooling and bias due to heterogeneity. By theoretically and numerically comparing various estimators, we find that a uniformly best estimator does not exist and that our new estimator is superior in…

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Real-Time Inflation Forecasting in a Changing World

变化环境下的实时通胀预测

This article revisits the accuracy of inflation forecasting using activity and expectations variables. We apply Bayesian model averaging across different regression specifications selected from a set of potential predictors that includes lagged values of inflation, a host of real activity data, term structure data, (relative) price data, and surveys. In this model average, we can entertain different channels of structural instability, by either incorporating stochastic…

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A RANK‐ORDERED LOGIT MODEL WITH UNOBSERVED HETEROGENEITY IN RANKING CAPABILITIES

考虑排序能力不可观测异质性的排序 Logit 模型

Abstract To study preferences, respondents to a survey are usually asked to select their most preferred option from a set. Preferences can be estimated more efficiently if respondents are asked to rank all alternatives. When some respondents are unable to perform the ranking task, using the complete ranking may lead to a substantial bias. We introduce a model which endogenously describes the ranking capabilities of individuals. Estimated preferences based on this model are…

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Do Leading Indicators Lead Peaks More Than Troughs?

领先指标对经济周期峰值的领先时间是否长于谷值?

We develop a novel Markov switching vector autoregressive model to investigate the possibility that leading indicators have different lead times at business cycle peaks and at troughs. In this model, coincident and leading indicators share a common Markov state process, but their cycles are nonsynchronous, with the nonsynchronicity varying across regimes. An application shows that on average the Conference Board’s Composite Leading Index leads the Composite Coincident Index…

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Modeling category‐level purchase timing with brand‐level marketing variables

利用品牌层面营销变量建模品类层面的购买时点

Abstract Purchase timing of households is usually modeled at the category level. However, many potential explanatory variables are observed at the brand level. To explain interpurchase times one has to either construct category‐level measures of marketing efforts, or integrate the model with a model for brand choice. In this paper we pursue the latter where we use latent brand preferences to capture the relevance of the marketing mix of an individual brand. We compare our…

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Explaining individual response using aggregated data

利用汇总数据解释个体响应

Empirical analysis of individual response behavior is sometimes limited due to the lack of explanatory variables at the individual level. In this paper we put forward a new approach to estimate the effects of covariates on individual response, where the covariates are unknown at the individual level but observed at some aggregated level. This situation may, for example, occur when the response variable is available at the household level but covariates only at the zip-code…

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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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Generalized reduced rank tests using the singular value decomposition

基于奇异值分解的广义降秩检验

We propose a novel statistic to test the rank of a matrix. The rank statistic overcomes deficiencies of existing rank statistics, like: necessity of a Kronecker covariance matrix for the canonical correlation rank statistic of Anderson (1951), sensitivity to the ordering of the variables for the LDU rank statistic of Cragg and Donald (1996) and Gill and Lewbel (1992), a limiting distribution that is not a standard chi-squared distribution for the rank statistic of Robin and…

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Deriving target selection rules from endogenously selected samples

从内生选择样本推导目标客户选择规则

Abstract The selection of the most profitable customers in a customer database for targeted activities is often done based on observed behaviour in the past. Consequently, databases arising from the responses to, for example, direct mailings in the past are not random samples. When not all heterogeneity across customers is observed, target selection will be based on unobserved heterogeneity and hence it is endogenous. We develop a method to adjust the likelihood function of…

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Bayes Estimates of Markov Trends in Possibly Cointegrated Series

可能协整序列中马尔可夫趋势的贝叶斯估计

Stylized facts show that average growth rates of U.S. per capita consumption and income differ in recession and expansion periods. Because a linear combination of such series does not have to be a constant mean process, standard cointegration analysis between the variables to examine the permanent income hypothesis may not be valid. To model the changing growth rates in both series, we introduce a multivariate Markov trend model that accounts for different growth rates in…

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Modelling and forecasting level shifts in absolute returns

绝对收益水平跳变的建模与预测

Abstract Due to high and low volatility periods, time series of absolute returns experience temporary level shifts which differ in length and size. In this paper we modify the basic Censored Latent Effects Autoregressive [CLEAR] model, such that it can describe and forecast the location and size of such level shifts. For our particular application, we assume that technical trading variables may have explanatory value for future level shifts, where these effects may differ…

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Censored latent effects autoregression, with an application to US unemployment

删失潜在效应自回归模型及其美国失业应用

Abstract A model is proposed to describe observed asymmetries in postwar unemployment time series data. We assume that recession periods, when unemployment increases rapidly, correspond with unobserved positive shocks. The generating mechanism of these latent shocks is a censored regression model, where linear combinations of lagged explanatory variables lead to positive shocks, while otherwise shocks are equal to zero. We apply this censored latent effects autoregression to…

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A dynamic multinomial probit model for brand choice with different long‐run and short‐run effects of marketing‐mix variables

营销组合变量具有不同长期与短期效应的动态多项 Probit 品牌选择模型

Abstract In this paper we propose a dynamic multinomial probit model in order to estimate the long‐run and short‐ run effects of marketing mix variables on brand choice. The latent variables, which contain the unobserved perceived utilities, follow a first‐order vector error correction autoregressive process of order 1 with current and lagged explanatory variables. The unrestricted autoregressive parameter matrix concerns the intertemporal correlation in perceived utilities…

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Bayesian analysis of seasonal unit roots and seasonal mean shifts

季节单位根与季节均值变动的贝叶斯分析

In this paper we propose a Bayesian analysis of seasonal unit roots in quarterly observed time series. Seasonal unit root processes are useful to describe economic series with changing seasonal fluctuations. A natural alternative model for similar purposes contains deterministic seasonal mean shifts instead of seasonal stochastic trends. This leads to analysing seasonal unit roots in the presence of mean shifts using Bayesian techniques. Our method is illustrated using…

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