The historical functional linear model

Malfait, Nicole; Ramsay, J. O.

doi:10.2307/3316063

Cited by 123 publications

(185 citation statements)

References 7 publications

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“…It is possible to obtain estimators of causal functional linear models via finite elements methods as done in (Malfait & Ramsay, 2003) for the case of historical functional linear models.…”

Section: Y(t) = α(T) + Xβ(t) + E(t)mentioning

confidence: 99%

Estimation of Causal Functional Linear Regression Models

Miranda¹

2017

JMR

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We present a methodology for estimating causal functional linear models using orthonormal tensor product expansions. More precisely, we estimate the functional parameters α and β that appear in the causal functional linear regression model:where supp β ⊂ T, and T is the closed triangular region whose vertexes are (a, a), (b, a) and (b, b). We assume we have an independent sample {(Y k , X k ) : 1 ≤ k ≤ N, k ∈ N} of observations where the X k 's are functional covariates, the Y k 's are time order preserving functional responses and E k , 1 ≤ k ≤ N, is i.i.d. zero mean functional noise.

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“…It is possible to obtain estimators of causal functional linear models via finite elements methods as done in (Malfait & Ramsay, 2003) for the case of historical functional linear models.…”

Section: Y(t) = α(T) + Xβ(t) + E(t)mentioning

confidence: 99%

Estimation of Causal Functional Linear Regression Models

Miranda¹

2017

JMR

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“…Often one is interested in predicting the value of an unobserved process Y (t) only from past observations of a related process, i.e., only from data generated by X(s), s ≤ t, up to time t. As time t increases, the prediction needs to be continuously updated. Models which relate the entire functional history of the process X up to time s to a real-valued outcome that is observed later (such as Y (t) or some other outcome which will be observed after time s and the distribution of which will change as s increases) have been studied in Malfait and Ramsay (2003) and Müller and Zhang (2005).…”

Section: Dynamics Of Multivariate Processesmentioning

confidence: 99%

Dynamic relations for sparsely sampled Gaussian processes

Müller

Yang

2009

TEST

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In longitudinal studies, it is common to observe repeated measurements data from a sample of subjects where noisy measurements are made at irregular times, with a random number of measurements per subject. Often a reasonable assumption is that the data are generated by the trajectories of a smooth underlying stochastic process. In some cases one observes multivariate time courses generated by a multivariate stochastic process. To understand the nature of the underlying processes, it is then of interest to relate the values of a process at one time with the value it assumes at another time, and also to relate the values assumed by different components of a multivariate trajectory at the same time or at a specific times selected for each trajectory. In addition, an assessment of these relationships will allow to predict future values of an individual's trajectories.Derivatives of the trajectories are frequently more informative than the time courses themselves, for instance in the case of growth curves. It is then of great interest to study the estimation of derivatives from sparse data. Such estimation procedures permit the study of time-dynamic relationships between derivatives and trajectory levels within the same trajectory and between the components of multivariate trajectories. Reviewing and extending recent work, we demonstrate the estimation of corresponding empirical dynamical systems and demonstrate asymptotic consistency of predictions and dynamic transfer functions. We illustrate the resulting prediction procedures and empirical first order differential equations with a study of the dynamics of longitudinal functional data for the relationship of blood pressure and body mass index.

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“…Background on FDA can be found in Ramsay and Silverman (2005). For other applications of FDA to economic time series, we refer to Malfait and Ramsay (2003) and Ramsay and Ramsey (2001).…”

Section: Introductionmentioning

confidence: 99%

Functional data analysis for volatility

Müller

Sen

Stadtmüller

2011

Journal of Econometrics

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We introduce a functional volatility process for modeling volatility trajectories for high frequency observations in financial markets and describe functional representations and data-based recovery of the process from repeated observations. A study of its asymptotic properties, as the frequency of observed trades increases, is complemented by simulations and an application to the analysis of intra-day volatility patterns of the S&P 500 index. The proposed volatility model is found to be useful to identify recurring patterns of volatility and for successful prediction of future volatility, through the application of functional regression and prediction techniques.

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The historical functional linear model

Cited by 123 publications

References 7 publications

Estimation of Causal Functional Linear Regression Models

Estimation of Causal Functional Linear Regression Models

Dynamic relations for sparsely sampled Gaussian processes

Functional data analysis for volatility

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