Estimation of a flexible simple linear model for interval data based on set arithmetic

A novel way for addressing one-sided hypothesis tests for the mean of unable to observe real random variables from which we have information provided in terms of interval data is proposed. For this purpose, a measure of similarity between intervals is considered and the classical one-sided hypothesis test to check whether the similarity between the expectation of a random interval and a subset of an specific unbounded interval is high enough. Asymptotic and bootstrap techniques are applied in order to study the limit distribution of the proposed test statistic. Some simulations have been carried out in order to show the empirical behavior of the test.

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“…This characterization has been shown to be a valuable tool for different statistical purposes (see, e.g., [2,5]). …”

Section: Random Intervalsmentioning

confidence: 99%

Similarity based one-sided tests for the expected value and interval data

Grzegorzewski¹,

Ramos-Guajardo²

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…Nonetheless, intervals can alternatively be expressed by means of the so-called canonical decomposition [2] given by…”

Section: Preliminariesmentioning

confidence: 99%

“…Hence, they can lead to ill-defined estimated models. On the other hand, the models proposed in [2,3,5] are formalized according to the natural interval arithmetic and their estimators lead to models that are always well-defined over the sample range.…”

Section: Introductionmentioning

confidence: 99%

“…The statistical study of regression models for interval data has been extensively addressed lately in the literature [2][3][4][5]7], deriving into several alternatives to tackle this problem. On one hand, the estimators proposed in [4,7] account the non-negativity constraints satisfied by the spread variables, but do not assure the existence of the residuals.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, intervals also model some features which are inherently interval-valued. For instance, the range of variation of the blood preasure of a patient along a day [2] or the tidal fluctuation [9].…”

Section: Introductionmentioning

confidence: 99%

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Strengthening Links Between Data Analysis and Soft Computing

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Abstract. A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried out by transforming a quadratic optimization problem with inequality constraints into a linear complementary problem and using Lemke's algorithm to solve it. Due to the irrelevance of certain cross-relationships, an alternative estimation process, the Lasso, is developed. A comparative study showing the differences between the proposed estimators is provided.

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Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?

Fischer

Blanco-Fernández

Winker

2015

Journal of Forecasting

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We study the performance of recently developed linear regression models for interval data when it comes to forecasting the uncertainty surrounding future stock returns. These interval data models use easy-to-compute daily return intervals during the modeling, estimation and forecasting stage. They have to stand up to comparable point-data models of the well-known capital asset pricing model type-which employ single daily returns based on successive closing prices and might allow for GARCH effects-in a comprehensive out-of-sample forecasting competition. The latter comprises roughly 1000 daily observations on all 30 stocks that constitute the DAX, Germany's main stock index, for a period covering both the calm market phase before and the more turbulent times during the recent financial crisis. The interval data models clearly outperform simple random walk benchmarks as well as the point-data competitors in the great majority of cases. This result does not only hold when one-day-ahead forecasts of the conditional variance are considered, but is even more evident when the focus is on forecasting the width or the exact location of the next day's return interval. Regression models based on interval arithmetic thus prove to be a promising alternative to established point-data volatility forecasting tools.

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Estimation of a flexible simple linear model for interval data based on set arithmetic

Cited by 81 publications

References 21 publications

Similarity based one-sided tests for the expected value and interval data

Similarity based one-sided tests for the expected value and interval data

Lasso Estimation of an Interval-Valued Multiple Regression Model

Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?

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