Econometrics Commons^™

The Grid Bootstrap For Continuous Time Models, Yiu Lim Lui, Weilin Xiao, Jun Yu

Research Collection School Of Economics

This article proposes the new grid bootstrap to construct confidence intervals (CI) for the persistence parameter in a class of continuous-time models. It is different from the standard grid bootstrap of Hansen in dealing with the initial condition. The asymptotic validity of the CI is discussed under the in-fill scheme. The modified grid bootstrap leads to uniform inferences on the persistence parameter. Its improvement over in-fill asymptotics is achieved by expanding the coefficient-based statistic around its in-fill asymptotic distribution that is non-pivotal and depends on the initial condition. Monte Carlo studies show that the modified grid bootstrap performs better than …

Declining Discount Rates In Singapore's Market For Privately Developed Apartments, Eric Fesselmeyer, Haoming Liu, Alberto Salvo

Research Collection College of Integrative Studies

Singapore's market for new privately developed apartments exhibits wide quasi-experimental variation in ownership tenure. We develop an empirical model in which prices are decomposed into the utility of housing services and a factor that shifts with asset tenure and the discount rate schedule, which we discipline to vary smoothly over time. We estimate discount rates that decline over time and, to accommodate the observed price differences, fall to 0.5-1.5% p.a. by year 400. The finding that households making sizable transactions do not entirely discount benefits accruing centuries from today is relevant, with the appropriate risk adjustment, for evaluating climate-change investments.

Occupation Density Estimation For Noisy High-Frequency Data, Congshan Zhang, Jia Li, Tim Bollerslev

Research Collection School Of Economics

This paper studies the nonparametric estimation of occupation densities for semimartingale processes observed with noise. As leading examples we consider the stochastic volatility of a latent efficient price process, the volatility of the latent noise that separates the efficient price from the actually observed price, and nonlinear transformations of these processes. Our estimation methods are decidedly nonparametric and consist of two steps: the estimation of the spot price and noise volatility processes based on pre-averaging techniques and in-fill asymptotic arguments, followed by a kernel-type estimation of the occupation densities. Our spot volatility estimates attain the optimal rate of convergence, and …

A Posterior-Based Wald-Type Statistic For Hypothesis Testing, Yong Li, Xiaobin Liu, Tao Zeng, Jun Yu

Research Collection School Of Economics

A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions under the correct model specification. The new statistic can be explained as a posterior version of the Wald statistic and has several nice properties. First, it is well-defined under improper prior distributions. Second, it avoids Jeffreys–Lindley–Bartlett’s paradox. Third, under the null hypothesis and repeated sampling, it follows a χ2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">χ2 …

Conditional Superior Predictive Ability, Jia Li, Zhipeng Liao, Rogier Quaedvlieg

Research Collection School Of Economics

This article proposes a test for the conditional superior predictive ability (CSPA) of a family of forecasting methods with respect to a benchmark. The test is functional in nature: under the null hypothesis, the benchmark’s conditional expected loss is no more than those of the competitors, uniformly across all conditioning states. By inverting the CSPA tests for a set of benchmarks, we obtain confidence sets for the uniformly most superior method. The econometric inference pertains to testing conditional moment inequalities for time series data with general serial dependence, and we justify its asymptotic validity using a uniform non-parametric inference method …

Risk Price Variation: The Missing Half Of Empirical Asset Pricing, Andrew John Patton, Brian M. Weller

Research Collection School Of Economics

Equal compensation across assets for the same risk exposures is a bedrock of asset pricing theory and empirics. Yet real-world frictions can violate this equality and create apparently high Sharpe ratio opportunities. We develop new methods for asset pricing with cross-sectional heterogeneity in compensation for risk. We extend k-means clustering to group assets by risk prices and introduce a formal test for whether differences in risk premiums across market segments are too large to occur by chance. We find significant evidence of cross-sectional variation in risk prices for almost all combinations of test assets, factor models, and time periods considered.

Nonignorable Missing Data, Single Index Propensity Score And Profile Synthetic Distribution Function, Xuerong Chen, Denis H. Y. Leung, Jing Qin

Research Collection School Of Economics

In missing data problems, missing not at random is difficult to handle since the response probability or propensity score is confounded with the outcome data model in the likelihood. Existing works often assume the propensity score is known up to a finite dimensional parameter. We relax this assumption and consider an unspecified single index model for the propensity score. A pseudo-likelihood based on the complete data is constructed by profiling out a synthetic distribution function that involves the unknown propensity score. The pseudo-likelihood gives asymptotically normal estimates. Simulations show the method compares favorably with existing methods.

A Panel Clustering Approach To Analyzing Bubble Behavior, Yanbo Liu, Peter C. B. Phillips, Jun Yu

Research Collection School Of Economics

This study provides new mechanisms for identifying and estimating explosive bubbles in mixed-root panel autoregressions with a latent group structure. A post-clustering approach is employed that combines a recursive k-means clustering al-gorithm with panel-data test statistics for testing the presence of explosive roots in time series trajectories. Uniform consistency of the k-means clustering algorithm is established, showing that the post-clustering estimate is asymptotically equivalent to the oracle counterpart that uses the true group identities. Based on the estimated group membership, right-tailed self-normalized t-tests and coefficient-based J-tests, each with pivotal limit distributions, are introduced to detect the explosive roots. The usual …

Uniform Nonparametric Inference For Spatially Dependent Panel Data: The Xtnpsreg Command, Jia Li, Zhipeng Liao, Wenyu Zhou

Research Collection School Of Economics

In this article, we introduce a command, xtnpsreg, that implements a uniform nonparametric inference procedure for possibly unbalanced panel datasets with general forms of spatio-temporal dependence. We demonstrate how to apply this command in several use cases, including (i) the nonparametric estimation of conditional mean function and its marginal response; (ii) the construction of uniform confidence bands for these nonparametric functional parameters; (iii) specification tests for parametric model restrictions; and (iv) the estimation and uniform inference for functional coefficients in semi-nonparametric models.

Learning Before Testing: A Selective Nonparametric Test For Conditional Moment Restrictions, Jia Li, Zhipeng Liao, Wenyu Zhou

Research Collection School Of Economics

This paper develops a new test for conditional moment restrictions via nonparametric series regression, with approximating series terms selected by Lasso. Machine-learning the main features of the unknown conditional expectation function beforehand enables the test to seek power in a targeted fashion. The data-driven selection, however, also tends to distort the test’s size nontrivially, because it restricts the (growing-dimensional) score vector in the series regression on a random polytope, and hence, effectively alters the score’s asymptotic normality. A novel critical value is proposed to account for this truncation effect. We establish the size and local power properties of the proposed …

Forecasting Equity Index Volatility By Measuring The Linkage Among Component Stocks, Yue Qiu, Tian Xie, Jun Yu, Qiankun Zhou

Research Collection School Of Economics

The linkage among the realized volatilities of component stocks is important when modeling and forecasting the relevant index volatility. In this article, the linkage is measured via an extended Common Correlated Effects (CCEs) approach under a panel heterogeneous autoregression model where unobserved common factors in errors are assumed. Consistency of the CCE estimator is obtained. The common factors are extracted using the principal component analysis. Empirical studies show that realized volatility models exploiting the linkage effects lead to significantly better out-of-sample forecast performance, for example, an up to 32% increase in the pseudo R2. We also conduct various forecasting exercises …

Pitfalls In Bootstrapping Spurious Regression, Peter C. B. Phillips

Research Collection School Of Economics

The bootstrap is shown to be inconsistent in spurious regression. The failure of the bootstrap is spectacular in that the bootstrap effectively turns a spurious regression into a cointegrating regression. In particular, the serial correlation coefficient of the residuals in the bootstrap regression does not converge to unity, so the bootstrap is not even first order consistent. The block bootstrap serial correlation coefficient does converge to unity and is therefore first order consistent, but has a slower rate of convergence and a different limit distribution from that of the sample data serial correlation coefficient. The analysis covers spurious regressions involving …

A Practical Guide To Harnessing The Har Volatility Model, Adam Clements, Daniel P. A. Preve

Research Collection School Of Economics

The standard heterogeneous autoregressive (HAR) model is perhaps the most popular benchmark model for forecasting return volatility. It is often estimated using raw realized variance (RV) and ordinary least squares (OLS). However, given the stylized facts of RV and well-known properties of OLS, this combination should be far from ideal. The aim of this paper is to investigate how the predictive accuracy of the HAR model depends on the choice of estimator, transformation, or combination scheme made by the market practitioner. In an out-of-sample study, covering the S&P 500 index and 26 frequently traded NYSE stocks, it is found that …

Economic Forecasting In An Epidemic: A Break From The Past?, Hwee Kwan Chow, Keen Meng Choy

Research Collection School Of Economics

This paper aims to investigate whether the predictive ability and behaviour of professional forecasters are different during the Covid-19 epidemic as compared with the global financial crisis of 2008 and normal times. To this end, we utilise a survey of professional forecasters in Singapore collated by the central bank to analyse the forecasting record for GDP growth and CPI inflation. We first examine the point forecasts to document the extent of forecast failure in the pandemic crisis and test for behavioural explanations of the possible sources of forecast errors such as leader following and herding behaviour. Using percentile-based summary measures …

Fixed-K Inference For Volatility, Tim Bollerslev, Jia Li, Zhipeng Liao

Research Collection School Of Economics

We present a new theory for the conduct of nonparametric inference about the latent spot volatility of a semimartingale asset price process. In contrast to existing theories based on the asymptotic notion of an increasing number of observations in local estimation blocks, our theory treats the estimation block size k as fixed. While the resulting spot volatility estimator is no longer consistent, the new theory permits the construction of asymptotically valid and easy-to-calculate pointwise confidence intervals for the volatility at any given point in time. Extending the theory to a high-dimensional inference setting with a growing number of estimation blocks …

Spatial Dynamic Models With Short Panels: Evaluating The Impact Of Home Purchase Restrictions On Housing Prices, Naqun Huang, Zhenlin Yang

Research Collection School Of Economics

Since the 2007 housing crisis in the United States, many countries have begun implementing various macroprudential policies to curb the ongoing rise in housing prices. As there is no clear consensus in the literature on the efficacy of these interventions, understanding their short-term impacts is crucial in informing future policy designs. Adapting a new econometric technique, we examine the short-term impact of home purchase restrictions in Singapore, accounting for the short panel nature of the data and the existence of dynamic, spatial, spatiotemporal, and unit-specific effects. Using quarterly housing data over 2012Q4-2014Q2, we find that public housing prices decrease by …

Rationalizable Implementation In Finite Mechanisms, Y-C Chen, Takashi Kunimoto, Y Sun, S. Xiong

Research Collection School Of Economics

We prove that the Maskin monotonicity condition (proposed by Bergemann et al. (2011)) fully characterizes exact rationalizable implementation in an environment with lotteries and transfers. Different from previous papers, our approach possesses many appealing features simultaneously, e.g., finite mechanisms with no integer game or modulo game are used; no transfers are made in any rationalizable profile; the message space is small; the implementation is robust to information perturbations in the sense of Oury and Tercieux (2012).

Singapore As A Sustainable City: Past, Present And The Future, Tomoki Fujii, Rohan Ray

Research Collection School Of Economics

Singapore has achieved impressive economic growth over the last half-century. This chapter provides an overview of the major sustainability challenges Singapore has experienced and the policies that have been adopted to address them, particularly in the areas of land use, transportation, waste management, water, and energy. It argues that Singapore has been successful in addressing these challenges owing to sound long-term vision and planning as well as flexibility in the implementation of the policies to tackle them. The chapter provides some discussion on policy options, challenges, and opportunities for making Singapore more sustainable and liveable. Leaders of Singapore have recognised …

Entrepreneurship In Singapore, Jungho Lee

Research Collection School Of Economics

Singapore has completed its catch-up growth phase and needs to find a new growth engine. Entrepreneurship can contribute to a nation’s productivity growth. The purpose of this chapter is twofold. First, a theoretical framework is presented, along with empirical evidence, to understand government interventions aimed at boosting entrepreneurship. Second, using the framework, the chapter discusses whether Singapore’s current policies are suitable for helping entrepreneurship. The theory demonstrates four reasons why government intervention is needed: (1) resource misallocation, (2) positive externality, (3) entrepreneurial human capital, and (4) tax and default policies. Singapore’s government has implemented various policies that potentially fix market …

Different Strokes For Different Folks: Long Memory And Roughness, Shuping Shi, Jun Yu

SMU Economics and Statistics Working Paper Series

The log realized volatility of financial assets is often modeled as an autoregressive fractionally integrated moving average model (ARFIMA) process, denoted by ARFIMA(p, d, q), with p = 1 and q = 0. Two conflicting results have been found in the literature regarding the dynamics. One stream shows that the data series has a long memory (i.e., the fractional parameter d > 0) with strong mean reversion (i.e., the autoregressive coefficient |α1| ≈ 0). The other stream suggests that the volatil-ity is rough (i.e., d < 0) with highly persistent dynamic (i.e., α1 → 1). To consolidate the findings, this paper first examines the finite sample properties of alternative estimation methods employed in the literature for the ARFIMA(1, d, 0) model and then applies the outperforming techniques to a wide range of financial assets. The candidate methods include two parametric maximum likeli-hood (ML) methods (the maximum time-domain modified profile likelihood (MPL) and maximum frequency-domain likelihood) and two semiparametric methods (the local Whittle method and log periodogram estimation method). The two parametric methods work well across all parameter set-tings, with the MPL method outperforming. In contrast, the two semiparametric methods have a very large upward bias for d and an equally large downward bias for α1 when α1 is close to unity. The poor performance of the semiparametric methods in the presence of a highly persistent dynamic might lead to a false conclusion of long memory. In the empirical applications, we find that the log realized volatilities of exchange rate futures over the past decade have a long memory, where the point estimate of d is between 0.4 and 0.5 and the estimate of α1 is near zero. For other finan-cial assets considered (including stock indices and industry indices), we find that they have rough volatility, with the point estimate of d being negative and the point estimates of α1 close to unity.

Wild Bootstrap For Instrumental Variable Regressions With Weak And Few Clusters, Wenjie Wang, Yichong Zhang

Research Collection School Of Economics

We study the wild bootstrap inference for instrumental variable (quantile) regressions in the framework of a small number of large clusters, in which the number of clusters is viewed as fixed and the number of observations for each cluster diverges to infinity. For subvector inference, we show that the wild bootstrap Wald test with or without using the cluster-robust covariance matrix controls size asymptotically up to a small error as long as the parameters of endogenous variables are strongly identified in at least one of the clusters. We further develop a wild bootstrap Anderson-Rubin (AR) test for full-vector inference and …

Glivenko-Cantelli Theorems For Integrated Functionals Of Stochastic Processes, Jia Li, Congshan Zhang, Yunxiao Liu

Research Collection School Of Economics

We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Hölder classes as special cases. The general Glivenko-Cantelli theorem is then applied in more concrete high-frequency statistical settings to establish uniform convergence results for general integrated functionals of the volatility of efficient price and local moments of microstructure noise.

Volatility Coupling, Jean Jacod, Jia Li, Zhipeng Liao

Research Collection School Of Economics

This paper provides a strong approximation, or coupling, theory for spot volatility estimators formed using high-frequency data. We show that the t-statistic process associated with the nonparametric spot volatility estimator can be strongly approximated by a growing-dimensional vector of independent variables defined as functions of Brownian increments. We use this coupling theory to study the uniform inference for the volatility process in an infill asymptotic setting. Specifically, we propose uniform confidence bands for spot volatility, beta, idiosyncratic variance processes, and their nonlinear transforms. The theory is also applied to address an open question concerning the inference of monotone nonsmooth integrated …

Efficient Estimation Of Integrated Volatility Functionals Under General Volatility Dynamics, Jia Li, Yunxiao Liu

Research Collection School Of Economics

We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.

Forecast Pooling Or Information Pooling During Crises? Midas Forecasting Of Gdp In A Small Open Economy, Hwee Kwan Chow-Tan, Daniel Han

SMU Economics and Statistics Working Paper Series

This study compares two distinct approaches, pooling forecasts from single indicator MIDAS models versus pooling information from indicators into factor MIDAS models, for short-term Singapore GDP growth forecasting with a large ragged-edge mixed frequency dataset. We investigate their relative predictive performance in a pseudo-out-of-sample forecasting exercise from 2007Q4 to 2020Q3. In the stable growth non-crisis period, no substantial difference in predictive performance is found across forecast models. We find factor MIDAS models dominate both the quarterly benchmark model and the forecast pooling strategy by wide margins in the Global Financial Crisis and the Covid-19 crisis. Reflecting the small open nature …

Generalized Local-To-Unity Models, Liyu Dou, Ulrich K. Müller

Research Collection School Of Economics

We introduce a generalization of the popular local‐to‐unity model of time series persistence by allowing for p autoregressive (AR) roots and p − 1 moving average (MA) roots close to unity. This generalized local‐to‐unity model, GLTU(p), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA(p,p − 1) process on the unit interval. Our main theoretical result establishes the richness of this model class, in the sense that it can well approximate a large class of processes with stationary Gaussian limits that are not entirely distinct from the unit root benchmark. We show that Campbell and …

Latent Local-To-Unity Models, Jun Yu

SMU Economics and Statistics Working Paper Series

This paper proposes a class of state-space models where the state equation is a local-to-unity process. The large sample theory is obtained for the least squares (LS) estimator of the autoregressive (AR) parameter in the AR representation of the model under two sets of conditions. In the first set of conditions, the error term in the observation equation is independent and identically distributed (iid), and the error term in the state equation is stationary and fractionally integrated with memory parameter H ϵ 2 (0; 1). It is shown that both the rate of convergence and the asymptotic distribution of the …

In-Fill Asymptotic Theory For Structural Break Point In Autoregression, Liang Jiang, Xiaohu Wang, Jun Yu

Research Collection School Of Economics

This article obtains the exact distribution of the maximum likelihood estimator of structural break point in the Ornstein–Uhlenbeck process when a continuous record is available. The exact distribution is asymmetric, trimodal, dependent on the initial condition. These three properties are also found in the finite sample distribution of the least squares (LS) estimator of structural break point in autoregressive (AR) models. Motivated by these observations, the article then develops an in-fill asymptotic theory for the LS estimator of structural break point in the AR(1) coefficient. The in-fill asymptotic distribution is also asymmetric, tri-modal, dependent on the initial condition, and delivers …

Three Essays On Nonstationary Financial Econometrics, Yajie Zhang

Dissertations and Theses Collection (Open Access)

This dissertation consists of three essays that contribute to the theory of nonstationary time-series analysis.

The first chapter explores the inference procedures for predictive regressions with time-varying characteristics. We extend the self-generated instrumentation, called IVX, to incorporate persistent regressors of functional local-to-unity, functional mildly explosive, and functional mildly stationary roots. The asymptotic distributions of IVX estimators under time-varying parameters are novel and nonpivotal but lead to pivotal distributions of the corresponding Wald statistics that are robust across various roots. The numerical experiments justify the robustness of IVX testing procedures in finite samples. We also verify the existence of time-varying coefficients …

On Factor Models With Random Missing: Em Estimation, Inference, And Cross Validation, Sainan Jin, Ke Miao, Liangjun Su

Research Collection School Of Economics

We consider the estimation and inference in approximate factor models with random missing values. We show that with the low rank structure of the common component, we can estimate the factors and factor loadings consistently with the missing values replaced by zeros. We establish the asymptotic distributions of the resulting estimators and those based on the EM algorithm. We also propose a cross validation-based method to determine the number of factors in factor models with or without missing values and justify its consistency. Simulations demonstrate that our cross validation method is robust to fat tails in the error distribution and …