Bootstrap prediction intervals in state–space models

Rodríguez, Alejandro; Ruiz, Esther

doi:10.1111/j.1467-9892.2008.00604.x

Cited by 41 publications

(29 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…. , V * T }, from the empirical distribution of the standardized innovations, Vt/ Ft; see, Stoffer and Wall (1991) and Rodriguez and Ruiz (2009) for its practical implementation. This non-parametric bootstrap does not assume any particular distribution of the errors.…”

Section: Bootstrap Proceduresmentioning

confidence: 99%

Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Rodríguez

Ruiz

2012

Computational Statistics & Data Analysis

Self Cite

View full text Add to dashboard Cite

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) January 2010 AbstractIn the context of linear state space models with Gaussian errors and known parameters, the Kalman filter generates best linear unbiased predictions of the underlying components together with their corresponding prediction mean squared errors (PMSE). However, in practice, the filter is run by substituting some parameters of the model by consistent estimates. In these circumstances, the PMSEs given by the Kalman filter do not take into account the parameter uncertainty and, consequently, they underestimate the true PMSEs. In this paper, we propose two new bootstrap procedures to obtain PMSE of the unobserved states based on obtaining replicates of the underlying states conditional on the information available at each moment of time. By conditioning on the available information, we simplify the procedure with respect to alternative bootstrap proposals previously available in the literature. Furthermore, we show that the new procedures proposed in this paper have better finite sample properties than the alternatives. We implement the proposed procedures for estimating the PMSE of several key unobservable US macroeconomic variables as the output gap, the non accelerating inflation rate of unemployment (NAIRU), the long-run investment rate and the core inflation. We show how taking into account the parameter uncertainty may change the prediction intervals constructed for those unobservable macroeconomic variables and, in particular, change the conclusions about the utility of the NAIRU as a macroeconomic indicator for expansions and recessions.

show abstract

Section: Bootstrap Proceduresmentioning

confidence: 99%

Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Rodríguez

Ruiz

2012

Computational Statistics & Data Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

“…Unfortunately fairly complicated expressions appear already in rather simple models. Bootstrap solutions are given by several authors; see for example Beran (1990), Masarotto (1990), Grigoletto (1998), Kim (2004), Pascual, Romo, and Ruiz (2004), Clements and Kim (2007), Kabaila and Syuhada (2008), and Rodriguez and Ruiz (2009).…”

Section: Introductionmentioning

confidence: 99%

Improved frequentist prediction intervals for autoregressive models by simulation

Helske¹,

Nyblom²

2015

Unobserved Components and Time Series Econometrics

View full text Add to dashboard Cite

It is well known that the so called plug-in prediction intervals for autoregressive processes, with Gaussian disturbances, are too narrow, i.e. the coverage probabilities fall below the nominal ones. However, simulation experiments show that the formulas borrowed from the ordinary linear regression theory yield one-step prediction intervals, which have coverage probabilities very close to what is claimed. From a Bayesian point of view the resulting intervals are posterior predictive intervals when uniform priors are assumed for both autoregressive coefficients and logarithm of the disturbance variance. This finding opens the path how to treat multi-step prediction intervals which are obtained easily by simulation either directly from the posterior distribution or using importance sampling. A notable improvement is gained in frequentist coverage probabilities. An application of the method to forecasting the annual gross domestic product growth in the United Kingdom and Spain is given for the period 2002-2011 using the estimation period 1962-2001.

show abstract

“…Tmax−1 t=T in This procedure borrows from Rodriguez and Ruiz (2009), who show how to to compute nonparametric bootstrap prediction intervals in state space models, while taking into account the uncertainty linked to parameter estimation and not resorting to parametric assumptions for the shock distribution in the model. 38 We start our out-of-sample computations in 1985, which means that the first estimation is done using T in = 40 years of data, and the length of the full sample in our case is T max = 65 years.…”

Section: E Bootstrap Distribution Of Out-of-sample R-squaresmentioning

confidence: 99%

Dividend Growth Predictability and the Price-Dividend Ratio

Piatti

Trojani

2012

SSRN Journal

View full text Add to dashboard Cite

Conventional tests of present-value models tend to over-reject the null of no predictability, concluding that price-dividend ratio variations are due to both cash flow and discount rate shocks. We propose a nonparametric Monte Carlo testing method, which does not rely on distributional assumptions to aggregate the information from the time series of price-dividend ratios and dividend growth. We find evidence of return predictability, but no apparent evidence of dividend growth predictability, thus reconciling the diverging conclusions in the literature. Our findings are robust to the specification of the predictive information set and account for the intrinsic probability of detecting predictive relations by chance alone.

show abstract

Bootstrap prediction intervals in state–space models

Cited by 41 publications

References 8 publications

Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Improved frequentist prediction intervals for autoregressive models by simulation

Dividend Growth Predictability and the Price-Dividend Ratio

Contact Info

Product

Resources

About