Least Squares Estimation of Large Dimensional Threshold Factor Models

Massacci, Daniele

doi:10.2139/ssrn.2636801

Cited by 12 publications

(23 citation statements)

References 57 publications

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“…Most results in this paper hold for the following diffusion index threshold forecasting model

\begin{matrix} x_{t} & = I (g_{t} \leq φ_{x}) {boldΛ}_{1} {boldf}_{t} + I (g_{t} > φ_{x}) {boldΛ}_{2} {boldf}_{t} + {bolde}_{t}, t = 1, \dots, T, \\ y_{t + h} & = I (g_{t} \leq φ_{y}) (γ_{1}^{'} f_{t} + β_{1}^{'} w_{t}) + I (g_{t} > φ_{y}) (γ_{2}^{'} f_{t} + β_{2}^{'} w_{t}) + ε_{t + h}, t = 1, \dots, T, h \geq 0, \end{matrix}

where

g_{t} \in R

is the common observable threshold random variable, and φ x and φ y are the unknown threshold values. The model lets y t + h depend upon f t , the vector of latent factors driving the comovement in x t according to the threshold factor model of Massacci (). Let

{\overset{false^}{φ}}_{x}

and

{\overset{false^}{φ}}_{y}

be the least squares estimators for

φ_{boldx}^{0}

and

φ_{y}^{0}

, respectively, namely for the true values of φ x and φ y respectively.…”

Section: Extensions and Modificationsmentioning

confidence: 99%

“…where g t ∈ R is the common observable threshold random variable, and x and y are the unknown threshold values. The model lets y t+h depend upon f t , the vector of latent factors driving the comovement in x t according to the threshold factor model of Massacci (2017). Letˆ x andˆ y be the least squares estimators for 0 x and 0 y , respectively, namely for the true values of x and y respectively.…”

Section: Diffusion Index Threshold Forecasting Modelmentioning

confidence: 99%

“…Let N and T denote the cross‐sectional and time series dimensions respectively. We estimate the model by least squares by minimizing the sum of squared residuals (Baltagi et al ., ; Massacci, ): the resulting principal components estimator for factors and loadings has the same convergence rate

C_{NT} = min false{\sqrt{N}, \sqrt{T} false}

as in the linear case (Bai and Ng, ). We then turn to the single break factor augmented regression.…”

Section: Introductionmentioning

confidence: 99%

“…Baltagi, Kao and Wang (2016), Ma and Su (2016) and Barigozzi, Cho and Fryzlewicz (2018) allow for multiple breaks. Massacci (2017) studies large dimensional threshold factor models with regime shifts in the loadings driven by a covariate. These contributions do not consider the whole diffusion index forecasting model.…”

Section: Introductionmentioning

confidence: 99%

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Unstable Diffusion Indexes: With an Application to Bond Risk Premia

Massacci

2019

Oxf Bull Econ Stat

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This paper studies the empirically relevant problem of estimation and inference in diffusion index forecasting models with structural instability. Factor model and factor augmented regression both experience a structural change with different unknown break dates. In the factor model, we estimate factors and loadings by principal components. We consider least squares estimation of the factor augmented regression and propose a break test. The empirical application uncovers instabilities in the linkages between bond risk premia and macroeconomic factors.

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“…Most results in this paper hold for the following diffusion index threshold forecasting model

\begin{matrix} x_{t} & = I (g_{t} \leq φ_{x}) {boldΛ}_{1} {boldf}_{t} + I (g_{t} > φ_{x}) {boldΛ}_{2} {boldf}_{t} + {bolde}_{t}, t = 1, \dots, T, \\ y_{t + h} & = I (g_{t} \leq φ_{y}) (γ_{1}^{'} f_{t} + β_{1}^{'} w_{t}) + I (g_{t} > φ_{y}) (γ_{2}^{'} f_{t} + β_{2}^{'} w_{t}) + ε_{t + h}, t = 1, \dots, T, h \geq 0, \end{matrix}

where

g_{t} \in R

{\overset{false^}{φ}}_{x}

and

{\overset{false^}{φ}}_{y}

be the least squares estimators for

φ_{boldx}^{0}

and

φ_{y}^{0}

, respectively, namely for the true values of φ x and φ y respectively.…”

Section: Extensions and Modificationsmentioning

confidence: 99%

Section: Diffusion Index Threshold Forecasting Modelmentioning

confidence: 99%

C_{NT} = min false{\sqrt{N}, \sqrt{T} false}

as in the linear case (Bai and Ng, ). We then turn to the single break factor augmented regression.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Unstable Diffusion Indexes: With an Application to Bond Risk Premia

Massacci

2019

Oxf Bull Econ Stat

Self Cite

View full text Add to dashboard Cite

show abstract

“…Bhushal and Sipakar [6] estimated the threshold point of growth and inflation in Nepal. Massacci [7] estimated unknown thresholds using large-dimensional threshold factor models. The impact of missing thresholds was investigated by Riley et al [8] in a meta-analysis context.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inferences Related to the Threshold Values of Uniform and Exponential Distributions

2016

International Journal of Scientific and Innovative Mathematical

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The estimation of threshold values by various statistical approaches has been intensively studied since 2002. However, confidence intervals and hypothesis testing procedures for the threshold parameters of uniform and exponential distributions have been neglected in threshold value-related inferential studies. The thresholds of random variables with assumed distributions are not always known, and must sometimes be inferred. In this work, the unknown threshold values of uniform and exponential distributions are inferred from unbiased maximum likelihood estimators and their probability density functions. Procedures for constructing confidence intervals and tests of hypotheses related to the unknown threshold values are established. Simulated data are generated from a uniform and an exponential distribution, both with unknown threshold parameters, using the statistical software MINITAB. Based on the simulated data, confidence intervals are constructed and hypotheses are tested on the unknown threshold values. The simulation results almost perfectly agree with the theoretical analysis. Using the proposed procedures, researchers could estimate the threshold parameters of other distributions in future inference-making studies.

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Simultaneous multiple change-point and factor analysis for high-dimensional time series

Barigozzi

Cho

Fryźlewicz

2018

Journal of Econometrics

101

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We propose the first comprehensive treatment of high-dimensional time series factor models with multiple change-points in their second-order structure. We operate under the most flexible definition of piecewise stationarity, and estimate the number and locations of change-points consistently as well as identifying whether they originate in the common or idiosyncratic components. Through the use of wavelets, we transform the problem of change-point detection in the second-order structure of a high-dimensional time series, into the (relatively easier) problem of change-point detection in the means of high-dimensional panel data. Also, our methodology circumvents the difficult issue of the accurate estimation of the true number of factors in the presence of multiple change-points by adopting a screening procedure. We further show that consistent factor analysis is achieved over each segment defined by the change-points estimated by the proposed methodology. In extensive simulation studies, we observe that factor analysis prior to change-point detection improves the detectability of change-points, and identify and describe an interesting 'spillover' effect in which substantial breaks in the idiosyncratic components get, naturally enough, identified as change-points in the common components, which prompts us to regard the corresponding change-points as also acting as a form of 'factors'. Our methodology is implemented in the R package factorcpt, available from CRAN.

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Least Squares Estimation of Large Dimensional Threshold Factor Models

Cited by 12 publications

References 57 publications

Unstable Diffusion Indexes: With an Application to Bond Risk Premia

Unstable Diffusion Indexes: With an Application to Bond Risk Premia

Statistical Inferences Related to the Threshold Values of Uniform and Exponential Distributions

Simultaneous multiple change-point and factor analysis for high-dimensional time series

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