Forecasting Limit Order Book Liquidity Supply-Demand Curves with Functional Autoregressive Dynamics

Chen, Ying; Chua, Wee Song; Härdle, Wolfgang Karl

doi:10.2139/ssrn.2818409

Cited by 1 publication

(6 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using the B‐spline expansions, we can represent the FAR model of order 1 in terms of the B‐spline coefficient relations:

\begin{matrix} lefttrue \\ a_{t, k} = η_{k} + {normalɛ}_{t, k} + {false\sum}_{i = 1}^{\infty} \times \{{false\sum}_{j = 1}^{\infty} (\frac{w_{j + m} - w_{j + 1}}{w_{j + m} - w_{j}} - \frac{w_{j + m + 1} - w_{j + 2}}{w_{j + m + 1} - w_{j + 1}}) c_{j} - c_{k}\} \times \frac{w_{i + m} - w_{i}}{m} a_{t - 1, i}, \end{matrix}

for all k = 1, …, ∞. The FAR model ) can be solved by estimating the B‐spline coefficients, see Chen, Chua, and Härdle (2019).…”

Section: Modelsmentioning

confidence: 99%

“…Denote the bivariate series of curves by

Y_{t}^{(1)} ((), τ)

and

Y_{t}^{(2)} ((), τ)

at t = 1, …, n . Chen, Chua, and Härdle (2019) proposed the vector FAR (VFAR) model of order p for the bivariate time series defined as:

([], \begin{array}{c} Y_{t}^{(1)} - μ_{1} \\ Y_{t}^{(2)} - μ_{2} \end{array}) = \sum_{k = 1}^{p} ([], \begin{array}{c} ρ^{11, k} & ρ^{12, k} \\ ρ^{21, k} & ρ^{22, k} \end{array}) ([], \begin{array}{c} Y_{t - k}^{(1)} - μ_{1} \\ Y_{t - k}^{(2)} - μ_{2} \end{array}) + ([], \begin{array}{c} ε_{t}^{(1)} \\ ε_{t}^{(2)} \end{array})

where ρ 11, k , ρ 12, k , ρ 21, k , ρ 22, k are the operators that show the serial cross‐dependence among the curves on their k th lagged values. Again, the operators are bounded linear operator from ℋ to ℋ.…”

Section: Modelsmentioning

confidence: 99%

“…As before, every ρ is written in the form of a convolution kernel Hilbert–Schmidt operator as ϕ 11 , ϕ 12 , ϕ 21 and ϕ 22 respectively with ϕ xy ∈ L 2 ([0, 1]) and ‖ ϕ xy ‖ 2 < 1 for xy = 11,12,21 and 22. Following the similar expansion as in the classic univariate model under sieve

Θ_{m_{n}},

for example, the B‐spline expansion as in Chen, Chua, and Härdle (2019), the relationship of the B‐spline coefficients are derived for the VFAR. We refer to Chen, Chua, and Härdle (2019) for the detailed procedure for the VFAR estimator and its asymptotic properties.…”

Section: Modelsmentioning

confidence: 99%

“…To investigate the effect of large‐dimensional functional and scalar covariates on the serially dependent functional time series, Chen, Koch, and Xu (2019) proposed a partial FAR (pFAR) model. Beyond the univariate FAR models, Chen, Chua, and Härdle (2019) proposed the vector FAR (VFAR) model describing the joint dynamics of the multiple functional time series with serial cross‐dependence in a unified framework. When the dimension becomes too large, the VFAR model faces an overparametrization problem.…”

Section: Introductionmentioning

confidence: 99%

“…While the classical FAR models only consider the dependence of curves on their own lagged values, the FARX and pFAR models by incorporating exogenous information can facilitate richer dynamics and also causal interpretation. Next, we will discuss the vector FAR (VFAR) model for multiple‐dimensional functional time series that exhibit lead–lag cross dependence by Chen, Chua, and Härdle (2019). When the dimension of functional time series increases, we will show how to build up factors via the common functional principal component (CFPC) analysis, see Zhang et al (2017).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A review study of functional autoregressive models with application to energy forecasting

Chen

Koch

Lim

et al. 2020

WIREs Computational Stats

Self Cite

View full text Add to dashboard Cite

In this data‐rich era, it is essential to develop advanced techniques to analyze and understand large amounts of data and extract the underlying information in a flexible way. We provide a review study on the state‐of‐the‐art statistical time series models for univariate and multivariate functional data with serial dependence. In particular, we review functional autoregressive (FAR) models and their variations under different scenarios. The models include the classic FAR model under stationarity; the FARX and pFAR model dealing with multiple exogenous functional variables and large‐scale mixed‐type exogenous variables; the vector FAR model and common functional principal component technique to handle multiple dimensional functional time series; and the warping FAR, varying coefficient‐FAR and adaptive FAR models to handle seasonal variations, slow varying effects and the more challenging cases of structural changes or breaks respectively. We present the models’ setup and detail the estimation procedure. We discuss the models’ applicability and illustrate the numerical performance using real‐world data of high‐resolution natural gas flows in the high‐pressure gas pipeline network of Germany. We conduct 1‐day and 14‐days‐ahead out‐of‐sample forecasts of the daily gas flow curves. We observe that the functional time series models generally produce stable out‐of‐sample forecast accuracy. This article is categorized under: Statistical Models > Semiparametric Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

show abstract

“…Using the B‐spline expansions, we can represent the FAR model of order 1 in terms of the B‐spline coefficient relations: