Bootstrap methods for stationary functional time series

Shang, Han Lin

doi:10.1007/s11222-016-9712-8

Cited by 49 publications

(38 citation statements)

References 42 publications

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“…bootstrap method by sampling with replacement from historical errors

({}, ê_{K}^{l} true(normalt true), ⋯, ê_{n}^{l} true(normalt true))

. The bootstrapped

{\overset{β}{true}}^{b} true(normals, normalt true)

can be obtained by bootstrapping the original functional time series expressed as

X_{i}^{b} (t) = μ (t) + \sum_{k = 1}^{\min (n, \infty)} β_{i, k}^{b} ϕ_{k} (t), i = 1, ⋯, n,

where

((), β_{1, k}^{b}, ⋯, β_{n, k}^{b})

represents the k th bootstrapped principal component scores via maximum entropy (see also Shang, ). Using a set of bootstrapped data

false{{scriptX}_{1}^{b} true(t true), ⋯, {scriptX}_{n}^{b} true(t true) false}

, we applied the functional linear regression in Equation to obtain bootstrapped estimates of regression coefficient function.…”

Section: Interval Forecast Methodsmentioning

confidence: 99%

“…represents the kth bootstrapped principal component scores via maximum entropy (see also Shang, 2017). Using a set of bootstrapped data {X b 1 (t), … , X b n (t)}, we applied the functional linear regression in Equation 7 to obtain bootstrapped estimates of regression coefficient function.…”

Section: Functional Linear Regressionmentioning

confidence: 99%

“…Klepsch, Klüppelberg, and Wei () extended the FAR and FMA processes to a functional autoregressive moving average (FARMA). Recently, Li, Robinson, and Shang () considered long‐range dependent functional time series, and developed a functional autoregressive integrated moving average process. Adopting a nonparametric perspective, Besse, Cardot, and Stephenson () suggested that functional kernel regression be used to measure the temporal dependence by a similarity measure characterized by notions of neighborhood distance and bandwidth.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Forecasting intraday S&P 500 index returns: A functional time series approach

Shang

2017

Journal of Forecasting

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Financial data often take the form of a collection of curves that can be observed sequentially over time; for example, intraday stock price curves and intraday volatility curves. These curves can be viewed as a time series of functions that can be observed on equally spaced and dense grids. Owing to the so‐called curse of dimensionality, the nature of high‐dimensional data poses challenges from a statistical perspective; however, it also provides opportunities to analyze a rich source of information, so that the dynamic changes of short time intervals can be better understood. In this paper, we consider forecasting a time series of functions and propose a number of statistical methods that can be used to forecast 1‐day‐ahead intraday stock returns. As we sequentially observe new data, we also consider the use of dynamic updating in updating point and interval forecasts for achieving improved accuracy. The forecasting methods were validated through an empirical study of 5‐minute intraday S&P 500 index returns.

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“…bootstrap method by sampling with replacement from historical errors

({}, ê_{K}^{l} true(normalt true), ⋯, ê_{n}^{l} true(normalt true))

. The bootstrapped

{\overset{β}{true}}^{b} true(normals, normalt true)

can be obtained by bootstrapping the original functional time series expressed as

X_{i}^{b} (t) = μ (t) + \sum_{k = 1}^{\min (n, \infty)} β_{i, k}^{b} ϕ_{k} (t), i = 1, ⋯, n,

where

((), β_{1, k}^{b}, ⋯, β_{n, k}^{b})

represents the k th bootstrapped principal component scores via maximum entropy (see also Shang, ). Using a set of bootstrapped data

false{{scriptX}_{1}^{b} true(t true), ⋯, {scriptX}_{n}^{b} true(t true) false}

, we applied the functional linear regression in Equation to obtain bootstrapped estimates of regression coefficient function.…”

Section: Interval Forecast Methodsmentioning

confidence: 99%

Section: Functional Linear Regressionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Forecasting intraday S&P 500 index returns: A functional time series approach

Shang

2017

Journal of Forecasting

Self Cite

View full text Add to dashboard Cite

show abstract

“…where β b 1,k , · · · , β b n,k denote the k th bootstrapped principal component scores via maximum entropy (see also Shang 2018). With a set of bootstrapped data {X b 1 (t), · · · , X b n (t)} available, we apply the functional linear regression of Equation (9) to obtain bootstrapped estimates of regression coefficient function.…”

Section: Functional Linear Regressionmentioning

confidence: 99%

Intraday forecasts of a volatility index: functional time series methods with dynamic updating

2018

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As a forward-looking measure of future equity market volatility, the VIX index has gained immense popularity in recent years to become a key measure of risk for market analysts and academics. We consider discrete reported intraday VIX tick values as realisations of a collection of curves observed sequentially on equally spaced and dense grids over time and utilise functional data analysis techniques to produce one-day-ahead forecasts of these curves.The proposed method facilitates the investigation of dynamic changes in the index over very short time intervals as showcased using the 15-second high-frequency VIX index values. With the help of dynamic updating techniques, our point and interval forecasts are shown to enjoy improved accuracy over conventional time series models.

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“…In order to obtain sample distribution of the test statistic and in consequence the necessary p-values we propose to use a maximal entropy bootstrap methodology proposed by Vinod and de Lacalle (2009) and implemented in meboot R package. Note that in the time series setting due to the temporal dependence between observations, resampling and especially bootstrap seem to be the only solution to conduct statistical inference (see Shang (2016)). Having empirical time series under our study we generate bootstrap samples using meboot R package, and then we calculate our sample Wilcoxon statistic distribution to obtain appropriate p-values.…”

Section: Local Wilcoxon Test For Testing Homogeneitymentioning

confidence: 99%

Detecting a structural change in functional time series using local Wilcoxon statistic

2017

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Functional data analysis (FDA) (Ramsay et al. (2009);Ramsay and Silverman (2005)) is a part of modern multivariate statistics that analyses data providing information about curves, surfaces or anything else varying over a certain continuum. In economics and empirical finance we often have to deal with time series of functional data, where we cannot easily decide, whether they are to be considered as homogeneous or heterogeneous. At present a discussion on adequate tests of homogenity for functional data is carried (see e.g. Flores et al. (2015)). We propose a novel statistic for detetecting a structural change in functional time series based on a local Wilcoxon statistic induced by a local depth function proposed in Paindaveine and Van Bever (2013).

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Bootstrap methods for stationary functional time series

Cited by 49 publications

References 42 publications

Forecasting intraday S&P 500 index returns: A functional time series approach

Forecasting intraday S&P 500 index returns: A functional time series approach

Intraday forecasts of a volatility index: functional time series methods with dynamic updating

Detecting a structural change in functional time series using local Wilcoxon statistic

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