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2021

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Articles 31 - 60 of 138

Full-Text Articles in Econometrics

Different Strokes For Different Folks: Long Memory And Roughness, Shuping Shi, Jun Yu Aug 2021

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.


Data For "Uncertainty And Reputation Effects In Credence Goods Markets", Eric Schniter, J. Dustin Tracy, Vojtěch Zíka Aug 2021

Data For "Uncertainty And Reputation Effects In Credence Goods Markets", Eric Schniter, J. Dustin Tracy, Vojtěch Zíka

ESI Data Sets

Credence-goods experiments have focused on stylized settings in which experts can perfectly identify the buyer’s best option and that option works without fail. However, in nature credence goods involve uncertainties that complicate assessing the quality of service and advice. We introduce two sources of uncertainty into a credence goods experiment. The first is diagnostic uncertainty; experts receive a noisy signal of buyer type so might make an ‘honest’ mistake when advising what is in buyers’ best interests. The second is service uncertainty; the services available to the buyer do not always work. Both sources of uncertainty make detection of expert …


Government Expenditure And Economic Dimensions: Determinants Of Fiscal Policy, Jay Pee A. Maalihan Aug 2021

Government Expenditure And Economic Dimensions: Determinants Of Fiscal Policy, Jay Pee A. Maalihan

Angelo King Institute for Economic and Business Studies (AKI)

Government expenditure is a known tool of fiscal policy. For a fiscal policy to fit the economic needs of a country, nuances regarding government expenditure such as economic dimensions must be considered as determinants of fiscal policy. This study assessed an econometric model of the significance of economic dimensions to government expenditure by utilizing data from 50 countries throughout 1999–2019. Hence, statistical tests and econometric methods such as fixed effects regression are executed to determine objectives of interest. This study contributes to the economic undertakings of various countries to plan and implement their strategic economic directions.


Wild Bootstrap For Instrumental Variable Regressions With Weak And Few Clusters, Wenjie Wang, Yichong Zhang Aug 2021

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 Aug 2021

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 Aug 2021

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 Aug 2021

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.


Keeping A Clean Reputation: More Evidence On The Perverse Effects Of Disclosure, Cary Deck, J. Dustin Tracy Jul 2021

Keeping A Clean Reputation: More Evidence On The Perverse Effects Of Disclosure, Cary Deck, J. Dustin Tracy

ESI Working Papers

When a principal relies on an agent, a conflict of interest can encourage the agent to provide biased advice. Conventional wisdom suggests that such behavior can be reduced through disclosure requirements. However, disclosure has been shown to exacerbate self-serving bias and can actually lead to greater harm for the principal in one-shot interactions. But in many naturally occurring settings, agents form reputations, a mechanism that could diminish the incentive to provide biased advice. We test for bias in the advice agents provide when faced with reputation concerns, and examine the impact of disclosure in such an environment. In controlled laboratory …


The Economic Impact Of Lockdowns: A Theoretical Assessment, Gabriele Camera, Alessandro Gioffré Jul 2021

The Economic Impact Of Lockdowns: A Theoretical Assessment, Gabriele Camera, Alessandro Gioffré

ESI Working Papers

The sudden appearance of the SARS-CoV-2 virus and the onset of the COVID-19 pandemic triggered extreme and open-ended “lockdowns” to manage the disease. Should these drastic interventions be the blueprint for future epidemics? We construct an analytical framework, based on the theory of random matching, which makes explicit how epidemics spread through economic activity. Imposing lockdowns by assumption prevents contagion and reduces healthcare costs, but also disrupts income-generation processes. We characterize how lockdowns impact the contagion process and social welfare. Numerical analysis suggests that protracted, open-ended lockdowns are generally suboptimal, bringing into question the policy responses seen in many countries.


Forecast Pooling Or Information Pooling During Crises? Midas Forecasting Of Gdp In A Small Open Economy, Hwee Kwan Chow-Tan, Daniel Han Jul 2021

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 …


Understanding And Contextualizing Foraging Among Recreational Opportunities In The North Central United States, Iris I. Mcfarlin Jul 2021

Understanding And Contextualizing Foraging Among Recreational Opportunities In The North Central United States, Iris I. Mcfarlin

School of Natural Resources: Dissertations, Theses, and Student Research

Over the past few decades, there has been a resurgence in popularity and recognition of foraging for wild products and foods. Despite the cultural importance and ubiquity of foraging, there have been relatively few scientific investigations (as compared to other consumptive outdoor activities such as hunting and fishing) of the social factors influencing foraging behavior, landscape preferences, and the types of materials foraged in the United States. As such, there is a fundamental need to understand more about the practice and about those who participate. We conducted two surveys to gather information on foragers’ motivations and demographic characteristics and to …


Essays On Spatial Econometrics Application In Study Of Conflict And Economic Activity, Ahmed Sadek Yousuf Jul 2021

Essays On Spatial Econometrics Application In Study Of Conflict And Economic Activity, Ahmed Sadek Yousuf

Graduate Theses and Dissertations

Spatial interaction and the locational structure between observations as well as availability of satellite derived data has meant a richer and more exhaustive exploration of topics relevant in development topics, particularly in areas of subnational economic activity and conflict. This research leverages thus spatial econometric techniques to dynamically decompose impacts from socio-economic determinants on conflict incidence (with setting in Sub-Saharan Africa). Later I also present a statistical framework (based on extension of Henderson’s approach (2012)) to augment official income figures at district / county level with multiple satellite derived signals, with specific context given to developing countries.

In the first …


Making It Public: The Effect Of (Private And Public) Wage Proposals On Efficiency And Income Distribution, Lara Ezquerra, Joaquín Gómez-Miñambres, Natalia Jiminez, Praveen Kujal Jul 2021

Making It Public: The Effect Of (Private And Public) Wage Proposals On Efficiency And Income Distribution, Lara Ezquerra, Joaquín Gómez-Miñambres, Natalia Jiminez, Praveen Kujal

ESI Working Papers

The implications of (public or private) pre-play communication and information revelation in a labour relationship is not well understood. We address these implications theoretically and experimentally. In our baseline experiments, the employer offers a wage to the worker who may then accept or reject it. In the public and private treatment, workers, moving first, make a non-binding private or public wage proposal. Our theoretical model assumes that wage proposals convey information about a worker’s minimum acceptable wage and are misreported with a certain probability. It predicts that, on average, wage proposals lead to higher wage offers and acceptance rates, with …


An Experimental Study Of Within- And Cross-Cultural Cooperation: Chinese And American Play In The Prisoner’S Dilemma Game, Michael Kuroda, Jieran Li, Jason Shachat, Lijia Wei, Bochen Zhu Jul 2021

An Experimental Study Of Within- And Cross-Cultural Cooperation: Chinese And American Play In The Prisoner’S Dilemma Game, Michael Kuroda, Jieran Li, Jason Shachat, Lijia Wei, Bochen Zhu

ESI Working Papers

We study whether cross- and within-culture groups have different cooperation rates in the Prisoner’s Dilemma Game. In an experiment, university students in China and America engage in a single iteration of the game, complete belief elicitation tasks regarding their opponents’ play and take a survey including attitudinal measurements regarding their in- and out-group attitudes. Cooperation rates are higher across the two countries are higher in both cross-culture and in within-culture interactions, although not significantly. We also find that Chinese participants cooperate less than American ones. Further, female Chinese participants are more cooperative than Chinese male ones. In the cross-culture treatment, …


Generalized Local-To-Unity Models, Liyu Dou, Ulrich K. Müller Jul 2021

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 …


Economics Of Majoritarian Identity Politics, Rohit Ticku, Raghul S. Venkatesh Jun 2021

Economics Of Majoritarian Identity Politics, Rohit Ticku, Raghul S. Venkatesh

ESI Working Papers

Majoritarian identity politics has become salient in representative democracies. Why do parties engage in identity politics and what are its consequences? We present a model of electoral competition in which parties capture voter groups based on their identity, and compete over an economic policy platform for the support of non-partisan voters. In addition, the party that caters to majoritarian interests makes a costly investment in polarizing identity. The investment provides subsequent payoffs to voters who have a preference for identity. When voter preferences over policy platforms are idiosyncratic in nature, greater investment in polarizing identity (i) increases both parties’ rents …


Is Egypt On A Sustainable Path Of Debt Repayment: Evidence From Imf Framework And Fiscal Reaction Function, Maha Rashied Jun 2021

Is Egypt On A Sustainable Path Of Debt Repayment: Evidence From Imf Framework And Fiscal Reaction Function, Maha Rashied

Theses and Dissertations

Fiscal policy is the starting point for an economy to achieve solid economic and social objectives through macroeconomic stability. Risks associated with excessive borrowing and the required fiscal adjustments are threatening especially to developing countries whose debt to GDP ratios are on the rise. Those countries’ fiscal policies’ sustainability is questioned; hence this research aims at testing for Egypt public debt sustainability and assessing the method capitalized on by the Egyptian authorities; the IMF Approach. By comparing the IMF Debt Sustainability Analysis Approach to the fiscal reaction function with ARDL and VAR as estimation methods, the results of both methods …


The Contribution Of Mining Sector To Sustainable Development In Saudi Arabia, Mourad Zmami, Ousama Ben-Salha, Sultan O. Almarshad, Houyem Chekki Jun 2021

The Contribution Of Mining Sector To Sustainable Development In Saudi Arabia, Mourad Zmami, Ousama Ben-Salha, Sultan O. Almarshad, Houyem Chekki

Journal of Sustainable Mining

The mining sector development is among the priorities of the Saudi Vision 2030. There is currently a lot of interest in the role of the mining sector in Saudi Arabia. This research contributes to this debate by empirically assessing the effects of mining on sustainable development in Saudi Arabia during the period 1980-2018. Unlike many previous studies, the three sustainable development dimensions, namely economic, social, and environmental, are jointly considered. The cointegration analysis, based on the ARDL, Gregory-Hansen, and combined cointegration tests, confirms the existence of long-run relationships between mining and all sustainable development dimensions. Furthermore, the findings lend substantial …


Group-Identity And Long-Run Cooperation: An Experiment, Gabriele Camera, Lukas Hohl Jun 2021

Group-Identity And Long-Run Cooperation: An Experiment, Gabriele Camera, Lukas Hohl

ESI Working Papers

We stress-test the limits of the power of group identity in the context of cooperation by constructing laboratory economies where participants confront an indefinitely repeated social dilemma as strangers. Group identity is artificially induced by random assignment to color-coded groups, and reinforced by an initial cooperation task played in-group and in fixed pairs. Subsequently subjects interact in-group and out-group in large economies, as strangers. Indefinite repetition guarantees full cooperation is an equilibrium. Decision-makers can discriminate based on group affiliation, but cannot observe past behaviors. We find no evidence of group biases. This suggests that group effects are less likely to …


The Extent To Which The Provision Of Water And Sanitation Services Affect The Individual’S Decision To Migrate: The Case Of Egypt, Sara Mohamed Soliman Jun 2021

The Extent To Which The Provision Of Water And Sanitation Services Affect The Individual’S Decision To Migrate: The Case Of Egypt, Sara Mohamed Soliman

Theses and Dissertations

Determinants of migration, although researched copiously shed little light on the importance of access to sustainable, basic water and sanitation utilities on an individual’s decision to migrate. This research reveals that individuals originating from rural Upper Egypt, rural and urban Lower Egypt, and rural and urban Alexandria and Suez Canal regions are more likely to migrate relative to those from the urban Greater Cairo region. Access to water has been deemed as insignificant while access to sanitation is a significant factor in determining migration patterns as do macro- economic differences in origin governorates, gender, educational background before migration, and employment …


Do Conditional Cash Transfers Increase School Enrollment? Evidence From Brazil, Jeanette L. Silvernale Jun 2021

Do Conditional Cash Transfers Increase School Enrollment? Evidence From Brazil, Jeanette L. Silvernale

Master's Theses

Conditional cash transfer programs have been widely deployed across the globe. They seek to bolster human capital by providing benefits contingent upon a variety of actions such as school attendance and regular health checkups. Bolsa Familia is the most extensive conditional cash transfer program, serving 46 million Brazilian citizens. Despite its expansive size, there have been seldom large-scale micro evaluations of the program. Limited data has resulted in small sample sizes drawn from a single point in time. Our study diverges from the rest and utilizes a novel administrative dataset with an overall sample of nearly 60 million and a …


Budget Deficit And Economic Growth In Nigeria, A. D. Umaru, H. M. Aliero, M. Abubakar Jun 2021

Budget Deficit And Economic Growth In Nigeria, A. D. Umaru, H. M. Aliero, M. Abubakar

Economic and Financial Review

This paper examines the relationship between budget deficit and economic growth in Nigeria, from a linear and non-linear perspective, using annual time series data from 1981 to 2019. The linear model, which involves the use of an autoregressive distributed lag (ARDL) approach, was compared with a non-linear analysis, using a threshold autoregressive (TAR) model. The ARDL analysis reveals that the growth of national output is positively driven by the persistent budget deficit in Nigeria. This was substantiated by the TAR model which indicates that though budget deficit drives economic growth in Nigeria, the positive relationship holds only if the deficit …


Essays On Economic Uncertainty And Housing Market In China, Humenghe Zhao Jun 2021

Essays On Economic Uncertainty And Housing Market In China, Humenghe Zhao

Dissertations, Theses, and Capstone Projects

This dissertation consists of three chapters that covers topics in macroeconomics.

Chapter 1. Literature Survey of China’s Housing Market and Macroeconomic Uncertainty is a survey of the literature on the history and development of China’s housing market, its unique characteristics, the driving forces behind rising housing prices, and the empirical interactions among housing market, economic uncertainty and the macroeconomy in China.

Chapter 2. The Spatial Correlation of Regional Housing Prices and Economic Uncertainty in China

Rapid real estate development and house price growth in China have garnered significant attention in academia and policy circles. Investigation into highly differentiated but interrelated …


Three Essays On Spatial Econometrics: The Matrix Exponential Spatial Specification, Ye Yang Jun 2021

Three Essays On Spatial Econometrics: The Matrix Exponential Spatial Specification, Ye Yang

Dissertations, Theses, and Capstone Projects

This thesis consists of three essays on the matrix exponential spatial specification. In the first essay, we study the generalized method of moments (GMM) estimation of matrix exponential spatial specification(p,q) (MESS(p,q)). We extend the model to a general higher order case and derive its GMM estimator. The large sample properties are also studied. Under homoskedasticity a best GMM estimator (BGMME) is derived and shown to be consistent and asymptotically normal. Under heteroskedasticity an optimal GMM estimator (OGMME) is derived and shown to be consistent and asymptotically normal as well. Monte Carlo experiments that discuss the large sample properties of quasi-maximum …


Classical Theory Of Competitive Market Price Formation, Sabiou M. Inoua, Vernon L. Smith Jun 2021

Classical Theory Of Competitive Market Price Formation, Sabiou M. Inoua, Vernon L. Smith

ESI Working Papers

We offer an information theory of market price formation, formalizing and elaborating on an old, implicit, classical tradition of supply and demand based on buyers’ and sellers’ mone-tary valuations of commodities (formally their reservation prices) and competition as a multilat-eral higgling and bargaining process. The early laboratory market experiments, as it turns out with hindsight, established the remarkable stability, efficiency, and robustness of the old view of competitive price discovery, and not the neoclassical price theory (based on individual utility and profit maximization for given prices). Herein, we present a partial-equilibrium version of the the-ory in which wealth is implicitly …


The Health Costs Of Political Identity: Evidence From Public Safety Responses In The Us And A Natural Experiment In California, Sahiba Chopra May 2021

The Health Costs Of Political Identity: Evidence From Public Safety Responses In The Us And A Natural Experiment In California, Sahiba Chopra

Master's Theses

The Covid-19 pandemic has brought political polarization in the US to the forefront of the battle against coronavirus. We find that for every one percentage point increase in votes for Trump there are 881 more Covid-19 cases and 17 more Covid-19 deaths. We find that these results are motivated by political identity as it is mediated through public safety behaviors like maskwearing and social distancing. In addition, a natural experiment in California during the first half of the pandemic in the US finds that 36% of the Covid-19 cases at the census tract level in California can be associated with …


Temperature Effects On Prevalence Of Sexually Transmitted Infections Among At-Risk Female Sex Workers In India, Rajshri Suresh May 2021

Temperature Effects On Prevalence Of Sexually Transmitted Infections Among At-Risk Female Sex Workers In India, Rajshri Suresh

Master's Theses

Vulnerability to climate change varies depending on the baseline climate, sensitivity to given exposure, and the presence of social, political, cultural, and institutional inequalities that influence access to essential resources of livelihood, particularly among informal labor market participants. Within the risky informal labor market, the transient nature of sex work implies that sex workers suffer disproportional losses in health, income, protection, and other aspects of general well-being as a result of the effects of climate anomalies. In this paper, I investigate the effect of temperature on the prevalence of sexually transmitted infections in a high-risk population of female sex workers …


Transitioning Into Retirement: Effect Of Pension Expansion On Elderly Labor Force Participation In India, Devaprasad Sahadevan May 2021

Transitioning Into Retirement: Effect Of Pension Expansion On Elderly Labor Force Participation In India, Devaprasad Sahadevan

Master's Theses

The welfare effects of public social security programs have been extensively studied in the context of developing economies where the reliance on state is much larger for the provision of basic goods and services. Pension schemes and reforms, however, are met with much less fiscal investment considering the demographic composition and the requisite demands of the larger proportion of youth- and working age- population. Given the rapid pace of demographic transition, there will inevitably be an ever-growing pressure and economic problems associated with aging are bound to become more apparent. As transitioning into retirement is an under-studied area in countries …


An Inferentially Robust Look At Two Competing Explanations For The Surge In Unauthorized Migration From Central America, Nick Santos May 2021

An Inferentially Robust Look At Two Competing Explanations For The Surge In Unauthorized Migration From Central America, Nick Santos

Dissertations

The last 8 years have seen a dramatic increase in the flow of Central American apprehensions by the U.S. Border Patrol. Explanations for this surge in apprehensions have been split between two leading hypotheses. Most academic scholars, immigrant advocates, progressive media outlets, and human rights organizations identify poverty and violence (the Poverty and Violence Hypothesis) in Central America as the primary triggers responsible. In contrast, while most government officials, conservative think tanks, and the agencies that work in the immigration and border enforcement realm admit poverty and violence may underlie some decisions to migrate, they instead blame lax U.S. immigration …


Latent Local-To-Unity Models, Jun Yu May 2021

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 …