scholarly journals IV AND GMM INFERENCE IN ENDOGENOUS STOCHASTIC UNIT ROOT MODELS

2017 ◽  
Vol 34 (5) ◽  
pp. 1065-1100 ◽  
Author(s):  
Offer Lieberman ◽  
Peter C.B. Phillips
Keyword(s):  
Stock Returns ◽  
Unit Root ◽  
Instrumental Variable ◽  
Nonlinear Least Squares ◽  
Asymptotic Distributions ◽  
Small Samples ◽  
Time Varying ◽  
Limit Theory ◽  
The One ◽  
Unit Root Models

Lieberman and Phillips (2017; LP) introduced a multivariate stochastic unit root (STUR) model, which allows for random, time varying local departures from a unit root (UR) model, where nonlinear least squares (NLLS) may be used for estimation and inference on the STUR coefficient. In a structural version of this model where the driver variables of the STUR coefficient are endogenous, the NLLS estimate of the STUR parameter is inconsistent, as are the corresponding estimates of the associated covariance parameters. This paper develops a nonlinear instrumental variable (NLIV) as well as GMM estimators of the STUR parameter which conveniently addresses endogeneity. We derive the asymptotic distributions of the NLIV and GMM estimators and establish consistency under similar orthogonality and relevance conditions to those used in the linear model. An overidentification test and its asymptotic distribution are also developed. The results enable inference about structural STUR models and a mechanism for testing the local STUR model against a simple UR null, which complements usual UR tests. Simulations reveal that the asymptotic distributions of the NLIV and GMM estimators of the STUR parameter as well as the test for overidentifying restrictions perform well in small samples and that the distribution of the NLIV estimator is heavily leptokurtic with a limit theory which has Cauchy-like tails. Comparisons of STUR coefficient and standard UR coefficient tests show that the one-sided UR test performs poorly against the one-sided STUR coefficient test both as the sample size and departures from the null rise. The results are applied to study the relationships between stock returns and bond spread changes.

Small-Sample Accuracy of Approximate Distributions of Functions of Observed Probabilities From t Tests

1991 ◽  
Vol 16 (4) ◽  
pp. 345-369
Author(s):  
Betsy Jane Becker
Keyword(s):  
Small Sample ◽  
Distribution Functions ◽  
Asymptotic Distributions ◽  
Cumulative Distribution ◽  
Statistical Hypothesis ◽  
Small Samples ◽  
P Value ◽  
Natural Logarithm ◽  
Standard Normal ◽  
The One

The observed probability p is the social scientist’s primary tool for evaluating the outcomes of statistical hypothesis tests. Functions of p s are used in tests of “combined significance,” meta-analytic summaries based on sample probability values. This study examines the nonnull asymptotic distributions of several functions of one-tailed sample probability values (from t tests). Normal approximations were based on the asymptotic distributions of z(p), the standard normal deviate associated with the one-sided p value; of ln(p), the natural logarithm of the probability value; and of several modifications of ln(p). Two additional approximations, based on variance-stabilizing transformations of ln(p) and z(p), were derived. Approximate cumulative distribution functions (cdfs) were compared to the computed exact cdf of the p associated with the one-sample t test. Approximations to the distribution of z(p) appeared quite accurate even for very small samples, while other approximations were inaccurate unless sample sizes or effect sizes were very large. Approximations based on variance-stabilizing transformations were not much more accurate than those based on ln(p) and z(p). Generalizations of the results are discussed, and implications for use of the approximations conclude the article.

scholarly journals Limit Theory for Stationary Autoregression with Heavy-Tailed Augmented GARCH Innovations

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 816
Author(s):  
Eunju Hwang
Keyword(s):  
Unit Root ◽  
Stable Distribution ◽  
Asymptotic Properties ◽  
Tail Index ◽  
Asymptotic Distributions ◽  
Uniform Limit ◽  
Limit Theory ◽  
Heavy Tailed ◽  
Heteroscedastic Variance ◽  
Ar Models

This paper considers stationary autoregressive (AR) models with heavy-tailed, general GARCH (G-GARCH) or augmented GARCH noises. Limit theory for the least squares estimator (LSE) of autoregression coefficient ρ=ρn is derived uniformly over stationary values in [0,1), focusing on ρn→1 as sample size n tends to infinity. For tail index α∈(0,4) of G-GARCH innovations, asymptotic distributions of the LSEs are established, which are involved with the stable distribution. The convergence rate of the LSE depends on 1−ρn2, but no condition on the rate of ρn is required. It is shown that, for the tail index α∈(0,2), the LSE is inconsistent, for α=2, logn/(1−ρn2)-consistent, and for α∈(2,4), n1−2/α/(1−ρn2)-consistent. Proofs are based on the point process and the asymptotic properties in AR models with G-GARCH errors. However, this present work provides a bridge between pure stationary and unit-root processes. This paper extends the existing uniform limit theory with three issues: the errors have conditional heteroscedastic variance; the errors are heavy-tailed with tail index α∈(0,4); and no restriction on the rate of ρn is necessary.

scholarly journals FUNCTIONAL FORM MISSPECIFICATION IN REGRESSIONS WITH A UNIT ROOT

2010 ◽  
Vol 27 (2) ◽  
pp. 285-311 ◽  
Author(s):  
Ioannis Kasparis
Keyword(s):  
Limit Distribution ◽  
Unit Root ◽  
Functional Form ◽  
Convergence Rates ◽  
Nonlinear Least Squares ◽  
Rates Of Convergence ◽  
Limit Theory ◽  
True Value ◽  
Stochastic Trends ◽  
Order Of Magnitude

We examine the limit properties of the nonlinear least squares (NLS) estimator under functional form misspecification in regression models with a unit root. Our theoretical framework is the same as that of Park and Phillips (2001, Econometrica 69, 117–161). We show that the limit behavior of the NLS estimator is largely determined by the relative orders of magnitude of the true and fitted models. If the estimated model is of different order of magnitude than the true model, the estimator converges to boundary points. When the pseudo-true value is on a boundary, standard methods for obtaining rates of convergence and limit distribution results are not applicable. We provide convergence rates and limit theory when the pseudo-true value is an interior point. If functional form misspecification is committed in the presence of stochastic trends, the convergence rates can be slower and the limit distribution different than that obtained under correct specification.

scholarly journals COVID-19 Outbreak and CO2 Emissions: Macro-Financial Linkages

2020 ◽  
Vol 14 (1) ◽  
pp. 12
Author(s):  
Julien Chevallier
Keyword(s):  
Co2 Emissions ◽  
Fossil Fuels ◽  
Mixed Data ◽  
Energy Information Administration ◽  
Time Varying ◽  
Data Sampling ◽  
Quantitative Finance ◽  
Financial Variables ◽  
Mixed Data Sampling ◽  
The One

In the Dynamic Conditional Correlation with Mixed Data Sampling (DCC-MIDAS) framework, we scrutinize the correlations between the macro-financial environment and CO2 emissions in the aftermath of the COVID-19 diffusion. The main original idea is that the economy’s lock-down will alleviate part of the greenhouse gases’ burden that human activity induces on the environment. We capture the time-varying correlations between U.S. COVID-19 confirmed cases, deaths, and recovered cases that were recorded by the Johns Hopkins Coronavirus Center, on the one hand; U.S. Total Industrial Production Index and Total Fossil Fuels CO2 emissions from the U.S. Energy Information Administration on the other hand. High-frequency data for U.S. stock markets are included with five-minute realized volatility from the Oxford-Man Institute of Quantitative Finance. The DCC-MIDAS approach indicates that COVID-19 confirmed cases and deaths negatively influence the macro-financial variables and CO2 emissions. We quantify the time-varying correlations of CO2 emissions with either COVID-19 confirmed cases or COVID-19 deaths to sharply decrease by −15% to −30%. The main takeaway is that we track correlations and reveal a recessionary outlook against the background of the pandemic.

scholarly journals Bayesian analysis of time-varying interactions between stock returns and foreign equity flows

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Boubekeur Baba ◽  
Güven Sevil
Keyword(s):  
Stock Returns ◽  
Negative Feedback ◽  
Positive Feedback ◽  
Positive Response ◽  
Time Varying ◽  
Economic Uncertainty ◽  
Foreign Investors ◽  
New Findings ◽  
Net Flows ◽  
Feedback Trading

AbstractThis study discusses the trading behavior of foreign investors with respect to economic uncertainty in the South Korean stock market from a time-varying perspective. We employ a news-based measure of economic uncertainty along with the model of time-varying parameter vector autoregression with stochastic volatility. The empirical analysis reveals several new findings about foreign investors’ trading behaviors. First, we find evidence that positive feedback trading often appears during periods of high economic uncertainty, whereas negative feedback trading is exclusively observable during periods of low economic uncertainty. Second, the foreign investors’ feedback trading appears mostly to be well-timed and often leads the time-varying economic uncertainty except in periods of global crises. Third, lagged negative (positive) response of net flows to economic uncertainty is found to be coupled with lagged positive (negative) feedback trading. Fourth, the study documents an asymmetric response of foreign investors with regard to negative and positive shocks of economic uncertainty. Specifically, we find that they instantly turn to positive feedback trading after a negative contemporaneous response of net flows to shocks of economic uncertainty. In contrast, they move slowly toward negative feedback trading after a positive response of net flows to uncertainty shocks.

scholarly journals The time-varying effects of oil prices on oil–gas stock returns of the fragile five countries

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Begüm Yurteri Kösedağlı ◽  
Gül Huyugüzel Kışla ◽  
A. Nazif Çatık
Keyword(s):  
Stock Returns ◽  
Positive Impact ◽  
Structural Break ◽  
Oil Prices ◽  
Time Varying ◽  
Asset Pricing Model ◽  
Daily Data ◽  
Structural Break Test ◽  
The Impact ◽  
Oil Gas

AbstractThis study analyzes oil price exposure of the oil–gas sector stock returns for the fragile five countries based on a multi-factor asset pricing model using daily data from 29 May 1996 to 27 January 2020. The endogenous structural break test suggests the presence of serious parameter instabilities due to fluctuations in the oil and stock markets over the period under study. Moreover, the time-varying estimates indicate that the oil–gas sectors of these countries are riskier than the overall stock market. The results further suggest that, except for Indonesia, oil prices have a positive impact on the sectoral returns of all markets, whereas the impact of the exchange rates on the oil–gas sector returns varies across time and countries.

scholarly journals Time-varying inflation risk and stock returns

2020 ◽  
Vol 136 (2) ◽  
pp. 444-470 ◽  
Author(s):  
Martijn Boons ◽  
Fernando Duarte ◽  
Frans de Roon ◽  
Marta Szymanowska
Keyword(s):  
Stock Returns ◽  
Time Varying ◽  
Inflation Risk

scholarly journals Optimisation of Time-Varying Asset Pricing Models with Penetration of Value at Risk and Expected Shortfall

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 394
Author(s):  
Adeel Nasir ◽  
Kanwal Iqbal Khan ◽  
Mário Nuno Mata ◽  
Pedro Neves Mata ◽  
Jéssica Nunes Martins
Keyword(s):  
At Risk ◽  
Asset Pricing ◽  
Stock Returns ◽  
Value At Risk ◽  
Expected Shortfall ◽  
Time Varying ◽  
Pricing Models ◽  
Asset Pricing Model ◽  
Asset Pricing Models ◽  
Market Beta

This study aims to apply value at risk (VaR) and expected shortfall (ES) as time-varying systematic and idiosyncratic risk factors to address the downside risk anomaly of various asset pricing models currently existing in the Pakistan stock exchange. The study analyses the significance of high minus low VaR and ES portfolios as a systematic risk factor in one factor, three-factor, and five-factor asset pricing model. Furthermore, the study introduced the six-factor model, deploying VaR and ES as the idiosyncratic risk factor. The theoretical and empirical alteration of traditional asset pricing models is the study’s contributions. This study reported a strong positive relationship of traditional market beta, value at risk, and expected shortfall. Market beta pertains its superiority in estimating the time-varying stock returns. Furthermore, value at risk and expected shortfall strengthen the effects of traditional beta impact on stock returns, signifying the proposed six-factor asset pricing model. Investment and profitability factors are redundant in conventional asset pricing models.

Market reaction to scheduled and unscheduled news announcements under varying economic conditions

2020 ◽  
Author(s):  
◽  
Parveshsingh Seeballack
Keyword(s):  
Stock Returns ◽  
Risk Premium ◽  
Implied Volatility ◽  
Equity Market ◽  
Economic Conditions ◽  
Time Varying ◽  
Equity Risk Premium ◽  
Macroeconomic News ◽  
Equity Risk ◽  
News Announcements

The unifying theme of this dissertation is the study of the role of macroeconomic news announcements in the context of the equity market. We focus on two important areas of the asset pricing theory, namely price discovery and equity risk premium forecasting. Chapter 2 investigates the time-varying sensitivity of stock returns to scheduled macroeconomic news announcements (MNAs) using high-frequency data. We present new insights into how efficiently stock returns incorporate the informational content of MNAs. We further provide evidence that the stock market response to MNAs is cyclical, and finally we conclude Chapter 2 with an investigation into the factors driving the time-varying sensitivity of stock return to MNAs. Chapter 3 investigates the time-varying sensitivity of stock returns in the context of unscheduled macroeconomic news announcements using high-frequency data. We investigate the speed and persistence in stock returns’ response to unscheduled macro-news announcements, and whether the reactions are dependent on the state of the economy, or general investor sentiment level. Combined, Chapters 2 and 3 provide interesting insights into how equity market participants react to the arrival of scheduled and unscheduled macro-announcements, under varying economic conditions. Chapter 4 focuses on equity risk premium forecasting. We investigate the predictive ability of option-implied volatility variables at monthly horizon, under varying economic conditions. We innovate by constructing monthly announcement and non-announcement option-implied volatility predictors and assess whether the monthly announcement option-implied volatility predictors contain additional information for better out-of-sample predictions of the monthly equity risk premium. Each of the three empirical chapters explores a unique aspect of the asset pricing theory in the context of the U.S. equity market.

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