On persistence of shocks to economic variables

Lippi, Marco; Reichlin, Lucrezia

doi:10.1016/0304-3932(92)90024-v

Cited by 48 publications

(5 citation statements)

References 7 publications

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“…The sign of ρ wv is related to ψ(1) 2 computed from the reduced form ARIMA model. For example, Lippi and Reichlin (1992) showed that if ρ wv = 0 then it must be the case that ψ(1) 2 < 1, i.e. if the series is persistent then the series cannot be decomposed into uncorrelated components.…”

Section: I(1) Modelsmentioning

confidence: 98%

The relationship between the Beveridge–Nelson decomposition and other permanent–transitory decompositions that are popular in economics

Zivot

Creal

2008

Journal of Econometrics

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Section: I(1) Modelsmentioning

confidence: 98%

The relationship between the Beveridge–Nelson decomposition and other permanent–transitory decompositions that are popular in economics

Zivot

Creal

2008

Journal of Econometrics

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“…Subsequently, many studies have dealt with issues in analytic identification, empirical estimation, and interpretation of the IND assumption (e.g. Nelson, 1988; Lippi and Reichlin, 1992; Joo and Jun, 1997; Proietti and Harvey, 2000; Morley et al , 2003; Proietti, 2006; Nagakura and Zivot, 2007; Nagakura, 2008a,b; Oh et al , 2008).…”

Section: Introductionmentioning

confidence: 99%

“…Nelson (1988) and Joo and Jun (1997) showed that the IND assumption restricts the parameter space of the equivalent autoregressive integrated moving average (ARIMA)(1, 1, 1) model and results in the spuriously decomposed trend and cycle. Lippi and Reichlin (1992) analytically proved that state space trend–cycle decomposition under the IND assumption (hereafter, we refer to this as the UC decomposition)1 does not exist if the persistence measure calculated from ARIMA( p , 1, q ) parameters is higher than unity. Morley et al (2003) analytically and empirically showed that the IND assumption causes the empirical difference between the Beveridge–Nelson decomposition (Beveridge and Nelson, 1981; hereafter, the BN decomposition) and UC decomposition for the ARIMA(2, 1, 2) model.…”

Section: Introductionmentioning

confidence: 99%

Parameter Space Restrictions in State Space Models

Jun

Kim

Park

et al. 2011

Journal of Forecasting

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The state space model is widely used to handle time series data driven by related latent processes in many fi elds. In this article, we suggest a framework to examine the relationship between state space models and autoregressive integrated moving average (ARIMA) models by examining the existence and positive-defi niteness conditions implied by auto-covariance structures. This study covers broad types of state space models frequently used in previous studies. We also suggest a simple statistical test to check whether a certain state space model is appropriate for the specifi c data. For illustration, we apply the suggested procedure in the analysis of the United States real gross domestic product data. showed that the IND assumption restricts the parameter space of the equivalent autoregressive integrated moving average (ARIMA)(1, 1, 1) model and results in the spuriously decomposed trend and cycle. Lippi and Reichlin (1992) analytically proved that state space trend-cycle decomposition under the IND assumption (hereafter, we refer to this as the UC decomposition) 1 does not exist if the persistence measure calculated from ARIMA(p, 1, q) parameters is higher than unity. Morley et al. (2003) analytically and empirically showed that the IND assumption causes the empirical difference between the Beveridge-Nelson decomposition (Beveridge and Nelson, 1981; hereafter, the BN decomposition) and UC decomposition for the ARIMA(2, 1, 2) model. They also proved that relaxing the IND assumption leads to a result identical to that of the BN decomposition. ) models, respectively.All these studies emphasize that the IND assumption restricts the parameter space of the corresponding ARIMA model. In this study, we generalize this point by showing that the latent structure, including the IND assumption, of any state space model restricts the parameter space of the corresponding ARIMA model. We provide a general framework to study the relationship between state space models and ARIMA models. We derive the restricted parameter spaces for frequently used state space models as special cases of our general framework. We also suggest an easy statistical test to determine whether data can be modeled as a state space model or not. For illustration, we use the proposed framework and test procedure in the analysis of the US real gross domestic product (GDP) data. THE EXISTENCE AND POSITIVE-DEFINITENESS CONDITIONSConsider the following state space model: y t t t t t t n Parameter Space Restrictions in State Space Models 111 φ θ ε B y B t t (7) 112 D. B. Jun et al.where each noise e i,t is distributed by N(0, λ i σ 2 ε ) and ϕ p is not zero. The fi rst element of x t is the I(1) trend and the second element is the AR(p) cycle. Eliminating x t , we have Parameter Space Restrictions in State Space Models 117 between parameters of the state space model and those of the corresponding ARIMA model 4 can be derived as follows: DOI: 10.1002/for Figure 1. The relationship between ρ and λ given the ARIMA parameters: (a) θ > ϕ (ϕ = −0.3, θ = 0.0383); (b)...

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“…This components model, however, implied a persistence estimate of 64-a highly implausible value under the usual interpretation of the Campbell-Mankiw point estimate and standard error. H n fact, Lippi and Reichlin (1992) showed that every unobserved-components model in which the generating model is the sum of a random walk and any uncorrelated stationary process necessarily restricts persistence to be less than 1. This suggests that the unobserved-components approach is unsatisfactory for the estimation of persistence.…”

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confidence: 98%