Functional regression of continuous state distributions

Park, Joon‐Young; Qian, Junhui

doi:10.1016/j.jeconom.2011.09.024

Cited by 32 publications

(32 citation statements)

References 5 publications

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“…It is well expected that the replacement of the original centered density (w t ) with the demeaned density estimate (ŵ t ) does not affect the asymptotic theory as long as the number of cross-sectional or high frequency observations available in each time period to estimate (f t ) is large enough relative to the number T of time series observations. This was indeed shown by Park and Qian (2012) for a stationary functional regression model. In this section, we show that our asymptotic theories developed in the previous section continue to hold even when we use (ŵ t ) in the place of (w t ).…”

Section: Models With Estimated Densitiessupporting

confidence: 65%

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Nonstationarity in time series of state densities

Chang

Kim

Park

2016

Journal of Econometrics

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124

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JEL classification: C13 C32Keywords: Time series of cross-sectional and intra-period distributions State density Nonstationarity Unit root Functional principal component analysis a b s t r a c t This paper proposes a new framework to analyze the nonstationarity in the time series of state densities, representing either cross-sectional or intra-period distributions of some underlying economic variables. We regard each state density as a realization of Hilbertian random variable, and use a functional time series model to fit a given time series of state densities. This allows us to explore various sources of the nonstationarity of such time series. The potential unit roots are identified through functional principal component analysis, and subsequently tested by the generalized eigenvalues of leading components of normalized estimated variance operator. The asymptotic null distribution of the test statistic is obtained and tabulated. We use the methodology developed in the paper to investigate the state densities given by the cross-sectional distributions of individual earnings and the intra-month distributions of stock returns. We find some clear evidence for the presence of strong persistency in their time series.

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Section: Models With Estimated Densitiessupporting

confidence: 65%

“…See, e.g., Bosq (2000) for a detailed introduction to the subject. The reader is also referred to Park and Qian (2012) for the statistical theory of stationary regression with state densities defined similarly as in our paper.…”

Section: Introductionmentioning

confidence: 99%

Nonstationarity in time series of state densities

Chang

Kim

Park

2016

Journal of Econometrics

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124

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“…Bowsher and Meeks () and Kargin and Onatski () applied it to forecast a yield curve as the function of maturity. See also Park and Qian (, ) for forecasting the non‐parametric density function of intraday stock returns.…”

Section: Functional Auto‐regressive Distributionmentioning

confidence: 99%

“…Specifically, we follow Bosq (), Cardot et al . (, ), Mas () and Park and Qian (, ), and develop a semiparametric functional auto‐regressive (FAR) modelling strategy for forecasting the time varying cross‐sectional density. In particular, the cross‐sectional densities are treated as time series of the functional data and their dynamic nature is estimated via an AR model in the functional space.…”

Section: Introductionmentioning

confidence: 99%

Forecasting Distributions of Inflation Rates: the Functional Auto-Regressive Approach

Chaudhuri

Kim

Shin

2015

Journal of the Royal Statistical Society Series A: Statistics in Society

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In line with the recent developments on the statistical analysis of functional data, we develop the semiparametric functional autoregressive (FAR) modeling approach to the density forecasting analysis of national inflation rates using sectoral inflation rates in the UK over the period January 1997-September 2013. The pseudo out-of-sample forecasting evaluation and test results provide an overall support to superior performance of our proposed models over the aggregate autoregressive models and their statistical validity. The fan-chart analysis and the probability event forecasting exercise provide a further support for our approach in a qualitative sense, revealing that the modified FAR models can provide a complementary tool for generating the density forecast of inflation, and analyse the performance of the central bank in achieving announced inflation target. As inflation targeting monetary policies are usually set with recourse to the medium-term forecasts, our proposed work may provide policymakers with an invaluably enriched information set.JEL Classification: C14, C53, E31.

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“…This can easily be done using methodology presented in the subsequent sections. Testing the hypothesis for the general case can also be developed as in Park and Qian (2008). For this, we may define g κ as in (6) and standardize the Wald statistic for the hypothesis H 0 : α κi = 0 for i = 1, .…”

Section: The Model and Assumptionsmentioning

confidence: 99%