Comparisons of Tests for the Presence of Random Walk Coefficients in a Simple Linear Model

Nyblom, Jukka; Mäkeläinen, Timo

doi:10.1080/01621459.1983.10477032

Cited by 116 publications

(70 citation statements)

References 13 publications

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“…When seasonality is absent, unit root tests, see Dickey and Fuller (1979) and Phillips and Perron (1988), test the null of integration versus a stationary alternative see De Jong and Whiteman (1991), Koop (1992), Sims (1988), Sims and Uhlig (1991), Phillips (1991), Schotman and van Dijk (1991), Phillips and Perron (1994), among others, for the Bayesian approach to unit root testing; on the contrary, the tests proposed by Nyblom and Makelainen (1983) and Kwiatkowski et al (1992) test trend stationarity against the alternative of integration. Unit root tests were extended to the seasonal case by Hylleberg et al (1990), whereas the extension for stationarity tests was proposed by Canova and Hansen (1995), and Busetti and Harvey (2003).…”

Section: Bayesian Stochastic Specification Searchmentioning

confidence: 99%

Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search

Proietti

Grassi

2014

Empir Econ

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An important issue in modelling economic time series is whether key unobserved components representing trends, seasonality and calendar components, are deterministic or evolutive. We address it by applying a recently proposed Bayesian variable selection methodology to an encompassing linear mixed model that features, along with deterministic effects, additional random explanatory variables that account for the evolution of the underlying level, slope, seasonality and trading days. Variable selection is performed by estimating the posterior model probabilities using a suitable Gibbs sampling scheme.The paper conducts an extensive empirical application on a large and representative set of monthly time series concerning industrial production and retail turnover. We find strong support for the presence of stochastic trends in the series, either in the form of a time-varying level, or, less frequently, of a stochastic slope, or both. Seasonality is a more stable component: only in 70% of the cases we were able to select at least one stochastic trigonometric cycle out of the six possible cycles. Most frequently the time variation is found in correspondence with the fundamental and the first harmonic cycles.An interesting and intuitively plausible finding is that the probability of estimating time-varying components increases with the sample size available. However, even for very large sample sizes we were unable to find stochastically varying calendar effects. AbstractAn important issue in modelling economic time series is whether key unobserved components representing trends, seasonality and calendar components, are deterministic or evolutive. We address it by applying a recently proposed Bayesian variable selection methodology to an encompassing linear mixed model that features, along with deterministic effects, additional random explanatory variables that account for the evolution of the underlying level, slope, seasonality and trading days. Variable selection is performed by estimating the posterior model probabilities using a suitable Gibbs sampling scheme.The paper conducts an extensive empirical application on a large and representative set of monthly time series concerning industrial production and retail turnover. We find strong support for the presence of stochastic trends in the series, either in the form of a time-varying level, or, less frequently, of a stochastic slope, or both. Seasonality is a more stable component: only in 70% of the cases we were able to select at least one stochastic trigonometric cycle out of the six possible cycles. Most frequently the time variation is found in correspondence with the fundamental and the first harmonic cycles.An interesting and intuitively plausible finding is that the probability of estimating time-varying components increases with the sample size available. However, even for very large sample sizes we were unable to find stochastically varying calendar effects.

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Section: Bayesian Stochastic Specification Searchmentioning

confidence: 99%

Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search

Proietti

Grassi

2014

Empir Econ

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“…(ii) Under the sequence of alternatives H 2n , the limiting distribution of n(b 2 − k(k + 2)) 2 /(8k(k + 2)) is a noncentral chi-squared distribution with 1 degrees of freedom and noncentrality parameter Nyblom and Mäkeläinen (1983) extented the definition of Pitman efficiency in cases where the limiting distributions of test statistics are of different types. In our case, the asymptotic relative efficiency of U with respect to b 1 is then easily seen to be…”

Section: Limiting Efficienciesmentioning

confidence: 99%

Tests of multinormality based on location vectors and scatter matrices

Kankainen

Taskinen

Oja

2007

Stat. Meth. & Appl.

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“…One of the frequently used tests for parameter constancy against the general alternative is the CUSUM test based on recursive residuals proposed by Brown, Durbin, and Evans (1975), and this test was further developed based on OLS residuals by Ploberger and Krämer (1992). By specifying a random walk as the alternative, optimal tests for parameter constancy were investigated by Nyblom and Mäkeläinen (1983), Nyblom (1986Nyblom ( , 1989, and Nabeya and Tanaka (1988), among others, while the point optimal test for general regression models was studied by Elliott and Müller (2006). On the other hand, it is often the case that a one-time structural change with an unknown change point is considered as the alternative and the sup-type test by Andrews (1993) and the mean-and exponential-type tests developed by Andrews and Ploberger (1994) and Andrews, Lee, and Ploberger (1996) are widely used in practical analyses.…”

Section: Introductionmentioning

confidence: 99%

Improving the finite sample performance of tests for a shift in mean

Kurozumi

2015

Journal of Statistical Planning and Inference

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It is widely known that structural break tests based on the long-run variance estimator, which is estimated under the alternative, suffer from serious size distortion when the errors are serially correlated. In this paper, we propose bias-corrected tests for a shift in mean by correcting the bias of the long-run variance estimator up to O(1/T ). Simulation results show that the proposed tests have good size and high power. JEL classification: C12, C22

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Comparisons of Tests for the Presence of Random Walk Coefficients in a Simple Linear Model

Cited by 116 publications

References 13 publications

Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search

Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search

Tests of multinormality based on location vectors and scatter matrices

Improving the finite sample performance of tests for a shift in mean

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