Cumulated Sum of Squares Statistics for Nonlinear and Nonstationary Regressions

Berenguer-Rico, Vanessa; Nielsen, Bent

doi:10.1017/s0266466618000476

Cited by 8 publications

(4 citation statements)

References 45 publications

(78 reference statements)

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“…In Deng and Perron (,b), the authors developed a comprehensive analysis of the power properties of CUSUM and related statistics in the context of detecting parameter shifts in regression models under stationarity. Kasparis () and more recently Berenguer‐Rico and Nielsen () introduced a CUSUM‐based approach for detecting misspecification in nonlinear models with non‐stationary regressors. The idea behind a test statistic such as equations or is that any omitted time variation within the predictive regression will contaminate the standard least squares residuals and their squares and hence should be detectable by analysing how

{\overset{false^}{u}}_{t}

and

{\overset{false^}{u}}_{t}^{2}

fluctuate.…”

Section: Cumulative Squared Residuals‐based Testsmentioning

confidence: 99%

A Simple Approach for Diagnosing Instabilities in Predictive Regressions

Pitarakis

2017

Oxf Bull Econ Stat

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We introduce a method for detecting the presence of time variation and instabilities in the parameters of predictive regressions linking noisy variables such as stock returns to highly persistent predictors such as stock market valuation ratios. Our proposed approach relies on the least squares based squared residuals of the predictive regression and is trivial to implement. More importantly the distribution of our test statistic is shown to be free of nuisance parameters, is already tabulated in the literature and is robust to the degree of persistence of the chosen predictor. Our proposed method is subsequently applied to the predictability of monthly US stock returns with the dividend yield, dividend payout, earnings-price, dividend-price and book-to-market value ratios. Our results strongly support the presence of instabilities over the 1927-2013 period but also clearly point to the disappearance of these after the mid 50s.

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{\overset{false^}{u}}_{t}

and

{\overset{false^}{u}}_{t}^{2}

fluctuate.…”

Section: Cumulative Squared Residuals‐based Testsmentioning

confidence: 99%

A Simple Approach for Diagnosing Instabilities in Predictive Regressions

Pitarakis

2017

Oxf Bull Econ Stat

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“…For example, certain non-linear functions 6 of I(1) processes can wrongly behave like stationary long memory processes (see, e.g., Kasparis et al (2014)). A recent approach which considers structural breaks under such conditions is presented by Berenguer-Rico and Nielsen (2020). In this paper, we consider the weak dependence assumption.…”

Section: Asymptotic Distributions Of Test Statisticsmentioning

confidence: 99%

Partial Sum Processes of Residual-Based and Wald-type Break-Point Statistics in Time Series Regression Models

Katsouris¹

2022

Preprint

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We revisit classical asymptotics when testing for a structural break in linear regression models by obtaining the limit theory of residual-based and Wald-type processes. First, we establish the Brownian bridge limiting distribution of these test statistics. Second, we study the asymptotic behaviour of the partial-sum processes in nonstationary (linear) time series regression models. Although, the particular comparisons of these two different modelling environments is done from the perspective of the partial-sum processes, it emphasizes that the presence of nuisance parameters can change the asymptotic behaviour of the functionals under consideration. Simulation experiments verify size distortions when testing for a break in nonstationary time series regressions which indicates that the normalized Brownian bridge limit cannot provide a suitable asymptotic approximation in this case. Further research is required to establish the cause of size distortions under the null hypothesis of parameter stability.

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“…Statisticians and econometricians have also often served as its Warden including Sir David Cox, 1988−1994, Sir Tony Atkinson, 1995−2005 Ingrid Harbo, Søren Johansen, Nielsen andAnders Rahbek, 1998, andNielsen, 2009) in addition to those mentioned elsewhere. Nielsen has collaborated with many other Oxford faculty (see e.g., Nielsen, 2007, andVanessa Berenguer-Rico andNielsen, 2019) and contributed to a wide range of econometric theory developments as well as to teaching.…”

Section: Nuffield Collegementioning

confidence: 99%

Oxford’s Contributions to Econometrics

Hendry

Nielsen

2021

The Palgrave Companion to Oxford Economics

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Faculty and graduates of Oxford University have played a significant role in the history of econometrics from an early date. The term econometrics was only formulated by Ragnar Frisch in the 1930s, but in the 17 th Century, William Petty created a discipline that he called Political Arithmetick, a forerunner of quantitative economics that led to the more specialized statistical approach of econometrics. During the first half of the 20 th Century, Oxford scholars like Colin Clark made major advances in creating aggregate economic measurements. From the late 1970s, the focus was primarily on macro-econometrics for the remainder of that century, buttressed by research on methods for analyzing dynamic panels. In the 21 st century, micro-econometrics was added to the portfolio. The most recent addition is Climate Econometrics, developing and applying econometric tools for analyzing climate data, which is driven by human economic behavior so faces much the same slew of problems as macroeconomic time series.

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Cumulated Sum of Squares Statistics for Nonlinear and Nonstationary Regressions

Cited by 8 publications

References 45 publications

A Simple Approach for Diagnosing Instabilities in Predictive Regressions

A Simple Approach for Diagnosing Instabilities in Predictive Regressions

Partial Sum Processes of Residual-Based and Wald-type Break-Point Statistics in Time Series Regression Models

Oxford’s Contributions to Econometrics

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