Three Essays on Estimation and Testing of Nonparametric Models

In this dissertation, I focus on the development and application of nonparametric methods in econometrics. First, a constrained nonparametric regression method is developed to estimate a function and its derivatives subject to shape restrictions implied by economic theory. The constrained estimators...

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Main Author: Ma, Guangyi
Other Authors: Xu, Ke-Li
Format: Others
Language:en_US
Published: 2012
Subjects:
Online Access:http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11768
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spelling ndltd-tamu.edu-oai-repository.tamu.edu-1969.1-ETD-TAMU-2012-08-117682013-01-08T10:44:37ZThree Essays on Estimation and Testing of Nonparametric ModelsMa, GuangyiConstrained nonparametric regressionCUSUM of squares testderivative estimationempirical likelihoodfunctional-coefficient cointegrationnonparametric alternativeoption pricingpurchasing power paritystate-price densitystructural changetime-varying coefficient modelvolatility break.In this dissertation, I focus on the development and application of nonparametric methods in econometrics. First, a constrained nonparametric regression method is developed to estimate a function and its derivatives subject to shape restrictions implied by economic theory. The constrained estimators can be viewed as a set of empirical likelihood-based reweighted local polynomial estimators. They are shown to be weakly consistent and have the same first order asymptotic distribution as the unconstrained estimators. When the shape restrictions are correctly specified, the constrained estimators can achieve a large degree of finite sample bias reduction and thus outperform the unconstrained estimators. The constrained nonparametric regression method is applied on the estimation of daily option pricing function and state-price density function. Second, a modified Cumulative Sum of Squares (CUSQ) test is proposed to test structural changes in the unconditional volatility in a time-varying coefficient model. The proposed test is based on nonparametric residuals from local linear estimation of the time-varying coefficients. Asymptotic theory is provided to show that the new CUSQ test has standard null distribution and diverges at standard rate under the alternatives. Compared with a test based on least squares residuals, the new test enjoys correct size and good power properties. This is because, by estimating the model nonparametrically, one can circumvent the size distortion from potential structural changes in the mean. Empirical results from both simulation experiments and real data applications are presented to demonstrate the test's size and power properties. Third, an empirical study of testing the Purchasing Power Parity (PPP) hypothesis is conducted in a functional-coefficient cointegration model, which is consistent with equilibrium models of exchange rate determination with the presence of trans- actions costs in international trade. Supporting evidence of PPP is found in the recent float exchange rate era. The cointegration relation of nominal exchange rate and price levels varies conditioning on the real exchange rate volatility. The cointegration coefficients are more stable and numerically near the value implied by PPP theory when the real exchange rate volatility is relatively lower.Xu, Ke-Li2012-10-19T15:30:51Z2012-10-22T18:03:11Z2012-10-19T15:30:51Z2012-082012-10-19August 2012thesistextapplication/pdfhttp://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11768en_US
collection NDLTD
language en_US
format Others
sources NDLTD
topic Constrained nonparametric regression
CUSUM of squares test
derivative estimation
empirical likelihood
functional-coefficient cointegration
nonparametric alternative
option pricing
purchasing power parity
state-price density
structural change
time-varying coefficient model
volatility break.
spellingShingle Constrained nonparametric regression
CUSUM of squares test
derivative estimation
empirical likelihood
functional-coefficient cointegration
nonparametric alternative
option pricing
purchasing power parity
state-price density
structural change
time-varying coefficient model
volatility break.
Ma, Guangyi
Three Essays on Estimation and Testing of Nonparametric Models
description In this dissertation, I focus on the development and application of nonparametric methods in econometrics. First, a constrained nonparametric regression method is developed to estimate a function and its derivatives subject to shape restrictions implied by economic theory. The constrained estimators can be viewed as a set of empirical likelihood-based reweighted local polynomial estimators. They are shown to be weakly consistent and have the same first order asymptotic distribution as the unconstrained estimators. When the shape restrictions are correctly specified, the constrained estimators can achieve a large degree of finite sample bias reduction and thus outperform the unconstrained estimators. The constrained nonparametric regression method is applied on the estimation of daily option pricing function and state-price density function. Second, a modified Cumulative Sum of Squares (CUSQ) test is proposed to test structural changes in the unconditional volatility in a time-varying coefficient model. The proposed test is based on nonparametric residuals from local linear estimation of the time-varying coefficients. Asymptotic theory is provided to show that the new CUSQ test has standard null distribution and diverges at standard rate under the alternatives. Compared with a test based on least squares residuals, the new test enjoys correct size and good power properties. This is because, by estimating the model nonparametrically, one can circumvent the size distortion from potential structural changes in the mean. Empirical results from both simulation experiments and real data applications are presented to demonstrate the test's size and power properties. Third, an empirical study of testing the Purchasing Power Parity (PPP) hypothesis is conducted in a functional-coefficient cointegration model, which is consistent with equilibrium models of exchange rate determination with the presence of trans- actions costs in international trade. Supporting evidence of PPP is found in the recent float exchange rate era. The cointegration relation of nominal exchange rate and price levels varies conditioning on the real exchange rate volatility. The cointegration coefficients are more stable and numerically near the value implied by PPP theory when the real exchange rate volatility is relatively lower.
author2 Xu, Ke-Li
author_facet Xu, Ke-Li
Ma, Guangyi
author Ma, Guangyi
author_sort Ma, Guangyi
title Three Essays on Estimation and Testing of Nonparametric Models
title_short Three Essays on Estimation and Testing of Nonparametric Models
title_full Three Essays on Estimation and Testing of Nonparametric Models
title_fullStr Three Essays on Estimation and Testing of Nonparametric Models
title_full_unstemmed Three Essays on Estimation and Testing of Nonparametric Models
title_sort three essays on estimation and testing of nonparametric models
publishDate 2012
url http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11768
work_keys_str_mv AT maguangyi threeessaysonestimationandtestingofnonparametricmodels
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