Estimation of latent factors for high-dimensional time series

Lam, Clifford; Yao, Qiwei; Bathia, Neil

doi:10.1093/biomet/asr048

Cited by 177 publications

(315 citation statements)

References 24 publications

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“…The theoretical properties of the estimators are investigated. As in Lam, Yao, and Bathia (2011), whose model is essentially a oneregime model in our case, the convergence rate of estimated loading space depends on the 'strength' of the state. We find that, with multiple states of different 'strength', the convergence rate of the loading space estimator for strong states is the same as the one-regime case, while the rate improves for weak states, gaining extra information from the strong states.…”

Section: Introductionmentioning

confidence: 99%

“…Peña and Box (1987) and Pan and Yao (2008) decomposed the time series into two parts, a latent factor process and a vector white noise process, in which strong cross-sectional dependence is allowed. Lam, Yao, and Bathia (2011) and Lam and Yao (2012) developed an approach that takes advantage of information from autocovariance matrices at nonzero lags via eigendecomposition to estimate the factor loading space, and they established the asymptotic properties as the dimension goes to infinity with sample size. This innovative method is applicable to nonstationary processes and processes with uncorrelated or endogenous regressors Chang, Guo, and Yao (2013).…”

Section: Introductionmentioning

confidence: 99%

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Regime-switching factor models for high-dimensional time series

Liu

Chen²

2017

STAT SINICA

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Abstract:We consider a factor model for high-dimensional time series with regimeswitching dynamics. The switching is assumed to be driven by an unobserved Markov chain; the mean, factor loading matrix, and covariance matrix of the noise process are different among the regimes. The model is an extension of the traditional factor models for time series and provides flexibility in dealing with applications in which underlying states may be changing over time. We propose an iterative approach to estimating the loading space of each regime and clustering the data points, combining eigenanalysis and the Viterbi algorithm. The theoretical properties of the procedure are investigated. Simulation results and the analysis of a data example are presented.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Regime-switching factor models for high-dimensional time series

Liu

Chen²

2017

STAT SINICA

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“…In Lam et al (2011), they consider {x i } being a stationary time series and {ǫ i } being a white noise. In this paper, we assume that {x i } has independent and identically distributed vectors, and the same goes for {ǫ i }.…”

Section: Extension To Data From a Factor Modelmentioning

confidence: 99%

“…We can easily see that with the low dimensionality of x i , if some of the factors in x i are strong factors (that is, the corresponding columns in A have the majority of coefficients being non-zero; see Lam et al (2011) and Lam and Yao (2012) for the formal definitions of strong and weak factors), we cannot really write…”

Section: Extension To Data From a Factor Modelmentioning

confidence: 99%

Nonparametric eigenvalue-regularized precision or covariance matrix estimator

Lam¹

2016

Ann. Statist.

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We introduce nonparametric regularization of the eigenvalues of a sample covariance matrix through splitting of the data (NERCOME), and prove that NERCOME enjoys asymptotic optimal nonlinear shrinkage of eigenvalues with respect to the Frobenius norm. One advantage of NERCOME is its computational speed when the dimension is not too large. We prove that NERCOME is positive definite almost surely, as long as the true covariance matrix is so, even when the dimension is larger than the sample size. With respect to the Stein's loss function, the inverse of our estimator is asymptotically the optimal precision matrix estimator. Asymptotic efficiency loss is defined through comparison with an ideal estimator, which assumed the knowledge of the true covariance matrix. We show that the asymptotic efficiency loss of NERCOME is almost surely 0 with a suitable split location of the data.We also show that all the aforementioned optimality holds for data with a factor structure. Our method avoids the need to first estimate any unknowns from a factor model, and directly gives the covariance or precision matrix estimator, which can be useful when factor analysis is not the ultimate goal. We compare the performance of our estimators with other methods through extensive simulations and real data analysis.MSC classification : 62G20, 15B52

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“…We shall denote this type of fms by L1FM in the forecasting exercise. This model was extended to the non-stationary case by Poncela (2004 y 2006) and Lam, Yao and Bathia (2011), while seasonal dynamic fms were analysed in Alonso and others (2011).…”

Section: Factor Modelsmentioning

confidence: 99%

Mexico : Combining monthly inflation predictions from surveys

Poncela¹,

Guerrero²,

Islas³

et al. 2014

CEPAL Review

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We examine the problem of combining Mexican inflation predictions or projections provided by a biweekly survey of professional forecasters. Consumer price inflation in Mexico is measured twice a month. We consider several combining methods and advocate the use of dimension reduction techniques whose performance is compared with different benchmark methods, including the simplest average prediction. Missing values in the database are imputed by two different databased methods. The results obtained are basically robust to the choice of the imputation method. A preliminary analysis of the data was based on its panel data structure and showed the potential usefulness of using dimension reduction techniques to combine the experts' predictions. The main findings are: the first monthly predictions are best combined by way of the first principal component of the predictions available; the best second monthly prediction is obtained by calculating the median prediction and is more accurate than the first one. KEYWORDS

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Estimation of latent factors for high-dimensional time series

Cited by 177 publications

References 24 publications

Regime-switching factor models for high-dimensional time series

Regime-switching factor models for high-dimensional time series

Nonparametric eigenvalue-regularized precision or covariance matrix estimator

Mexico : Combining monthly inflation predictions from surveys

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