To safeguard economic and financial stability policymakers regularly take actions designed to increase resilience to systemic risks and curb speculative market behavior. To assess the effectiveness of such mitigation policies, we introduce a counterfactual approach tailored to accommodate the mildly explosive dynamics that occur during speculative bubbles. We derive asymptotics of the estimated treatment effect under a common factor structure that allows for explosive, I(1), and stationary factors, thereby having applicability to a wide range of prevailing economic conditions. An inferential procedure is proposed for the policy treatment effect that has asymptotic validity and demonstrates satisfactory finite sample performance. An empirical analysis examines the monetary policy of interest rate hikes implemented by the Reserve Bank of New Zealand, beginning in October 2021. This policy is shown to have exerted a delayed and regionally heterogeneous cooling effect on New Zealand housing markets. While short run impacts are limited, a longer post-treatment window reveals evidence of monetary policy transmission, with house prices clearly declining relative to their counterfactual paths in some regions.

Cointegrating rank selection is studied in a function space reduced rank regression where the data are time series of cross-section curves. Consistent cointegrating rank estimation is developed using information criteria extended to curve time series environments. The asymptotic theory involves two-parameter Gaussian processes that generalise the standard limit processes involved in cointegrating regressions. Simulations provide evidence of the effectiveness of consistent rank selection by the BIC criterion and the tendency of AIC to overestimate order as in standard lag order selection in autoregression, as well as in reduced rank regression with multiple time series.

Time series models are often fitted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and financial data, particularly over long periods. Ignoring such shifts may result in fitting models with spurious dynamics that lead to unsupported and controversial conclusions about time dependence, causality, and the effects of unanticipated shocks. In spite of what may seem as obvious differences between a time series of independent variates with changing variance and a stationary conditionally heteroskedastic (GARCH) process, such processes may be hard to distinguish in applied work using basic time series diagnostic tools. We develop and study some practical and easily implemented statistical procedures to test the mean and variance stability of uncorrelated and serially dependent time series. Application of the new methods to analyze the volatility properties of stock market returns leads to some unexpected surprising findings concerning the advantages of modeling time varying changes in unconditional variance.

A general asymptotic theory is established for sample cross moments of nonstationary time series, allowing for long-range dependence and local unit roots. The theory provides a substantial extension of earlier results on nonparametric regression that include near-cointegrated nonparametric regression as well as spurious nonparametric regression. Many new models are covered by the limit theory, among which are functional coefficient regressions in which both regressors and the functional covariate are nonstationary. Simulations show finite sample performance matching well with the asymptotic theory and having broad relevance to applications, while revealing how dual nonstationarity in regressors and covariates raises sensitivity to bandwidth choice and the impact of dimensionality in nonparametric regression. An empirical example is provided involving climate data regression to assess Earth's climate sensitivity to CO $_2$ , where nonstationarity is a prominent feature of both the regressors and covariates in the model. To our knowledge, this application is the first nonparametric empirical analysis to assess potential nonlinear impacts of CO $_2$ on Earth's climate while allowing for nonstationarity in both the regressors and covariates.

Asset prices are commonly represented as a drift-diffusion process, wherein the drift component denotes the anticipated return of the asset within some time frame, while the diffusion component accommodates random shocks. The drift component has substantial practical significance but accurate estimation is typically challenging and has met with limited success in the existing literature except over large time spans. This paper explores a comprehensive range of drift-diffusion models that include constant, linear, trending, and bursting drift. Conditions are identified under which realized squared drift RSD is a reliable tool for gauging integrated squared drift when the time span Tn is large enough. The recently introduced drift-robust quarticity estimator RiceQ is found to retain consistency under twin asymptotics with Tn- infinity and infill Delta n - 0, subject to some constraints on the divergence rate of Tn across different drift specifications. An inferential method of detecting nonzero drift using RSD and RiceQ is proposed and the drift tests are shown to be consistent under different data generating processes with various conditions on Tn. Simulation studies reveal excellent performance of the realized squared drift measure and the drift test in finite samples. The drift test is demonstrated empirically in real-time surveillance of market abnormalities in the Nasdaq Composite Index over two notable sample periods: the dotcom bubble (1996-2003) and the artificial intelligence boom (2016-2024), using intraday data.

Earth's transient climate response (TCR) quantifies the global mean surface air temperature change due to a doubling of atmospheric CO2 concentration after 70 years of a compounding 1% per year increase. TCR is highly correlated with near-term climate projections, and thus of relevance for climate policy, but remains poorly constrained in part due to uncertainties in the representation of key physical processes in Earth System Models (ESMs). Within state-of-the-art ESMs participating in the Coupled Model Intercomparison Project (CMIP6), the TCR range (1.1 degrees C-2.9 degrees C) is too wide to offer useful guidance to policymakers. Similarly, the sixth report of the Intergovernmental Panel on Climate Change, while not solely reliant on ESMs for its TCR assessment, produced a very likely range of 1.2 degrees C-2.4 degrees C. To complement earlier, ESM-based, estimates, we here present a new TCR estimate of 2.17 (1.72-2.77) degrees C (95% confidence interval), derived based on a statistical relationship between surface air temperature and observational proxies for its main drivers, i.e. changes in atmospheric greenhouse gases and aerosols. We show that, within uncertainty, this method correctly diagnoses TCR from 20 CMIP6 ESMs if the same input variables are taken from the ESMs that are available from observations. This increases confidence in the new observation-based central estimate and range, which is respectively higher and narrower than the mean and spread of the estimates from the entire ensemble of CMIP6. Many ESM-based estimates tend to produce TCRs lower than the observational range reported here. Our findings suggest that a misrepresentation of the aerosol cooling effect could be the cause of this discrepancy. Further, the revised TCR estimate suggests a downward revision of the remaining carbon budgets aligned with the overarching goal of the Paris agreement.

Functional coefficient (FC) cointegrating regressions offer empirical investigators flexibility in modeling economic relationships by introducing covariates that influence the direction and intensity of comovement among nonstationary time series. FC regression models are also useful when formal cointegration is absent, in the sense that the equation errors may themselves be nonstationary, but where the nonstationary series display well-defined FC linkages that can be meaningfully interpreted as correlation measures involving the covariates. The present paper proposes new nonparametric estimators for such FC regression models where the nonstationary series display linkages that enable consistent estimation of the correlation measures between them. Specifically, we develop root n-consistent estimators for the functional coefficient and establish their asymptotic distributions, which involve mixed normal limits that facilitate inference. Two novel features that appear in the limit theory are (i) the need for non-diagonal matrix normalization due to the presence of stationary and nonstationary components in the regression; and (ii) random bias elements that appear in the asymptotic distribution of the kernel estimators, again resulting from the nonstationary regression components. Numerical studies reveal that the proposed estimators achieve significant efficiency improvements compared to the estimators suggested in earlier work by Sun et al. (2011). Easily implementable specification tests with standard chi-square asymptotics are suggested to check for constancy of the functional coefficient. These tests are shown to have faster divergence rate under local alternatives and enjoy superior performance in simulations than tests proposed in Gan et al. (2014). An empirical application based on the quantity theory of money is included, illustrating the practical use of correlated but non-cointegrated regression relations.

This paper explores implications of weak identification in common 'long memory' and recent 'rough' approaches to modeling volatility dynamics of financial assets. We unveil an asymptotic near-observational equivalence between a long memory model with weak autoregressive dynamics and a rough model with a near-unit autoregressive root. Standard methods struggle to distinguish them, and conventional asymptotics are invalid. We propose an identification-robust approach to construct confidence sets that reveal the uncertainty and aid inference. Empirical studies based on realized volatility and trading volume often fail to statistically reject either model, thereby providing evidence of their potential coexistence.

This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor model for the latent curves with common trends. A functional PCA technique is applied to estimate the common stochastic trends and functional factor loadings. Under some regularity conditions we derive the mean square convergence and limit distribution theory for the developed estimates, allowing the dimension and sample size to jointly diverge to infinity. We propose an easy-to-implement criterion to consistently select the number of common stochastic trends and further discuss model estimation when the nonstationary factors are cointegrated. Extensive Monte-Carlo simulations and two empirical applications to large-scale temperature curves in Australia and log-price curves of S P 500 stocks are conducted, showing finite-sample performance and providing practical implementations of the new methodology.

The recent artificial intelligence (AI) boom covers a period of rapid innovation and wide adoption of AI intelligence technologies across diverse industries. These developments have fueled an unprecedented frenzy in the Nasdaq, with AI-focused companies experiencing soaring stock prices that raise concerns about speculative bubbles and real-economy consequences. Against this background, this study investigates the formation of speculative bubbles in the Nasdaq stock market with a specific focus on the so-called Magnificent Seven (Mag-7) individual stocks during the AI boom, spanning the period from January 2017 to January 2025. We apply the real-time PSY bubble detection methodology of Phillips et al. (2015a, 2015b) while controlling for market and industry factors for individual stocks. Confidence intervals to assess the degree of speculative behavior in asset price dynamics are calculated using the near-unit root approach of Phillips (2023). The findings reveal the presence of speculative bubbles in the Nasdaq stock market and across all Mag-7 stocks. Nvidia and Microsoft experience the longest speculative periods over January 2017-December 2021, while Nvidia and Tesla show the fastest rates of explosive behavior. Speculative bubbles persist in the market and in six of the seven stocks (excluding Apple) from December 2022 to January 2025. Near-unit-root inference indicates mildly explosive dynamics for Nvidia and Tesla (2017-2021) and local-to-unity near explosive behavior for all assets in both periods.

In GMM estimation, it is well known that if the moment dimension grows with the sample size, the asymptotics of GMM differ from the standard finite dimensional case. The present work examines the asymptotic properties of infinite dimensional GMM estimation when the weight matrix is formed by inverting Brownian motion or Brownian bridge covariance kernels. These kernels arise in econometric work such as minimum Cram & eacute;r-von Mises distance estimation when testing distributional specification. The properties of GMM estimation are studied under different environments where the moment conditions converge to a smooth Gaussian or non-differentiable Gaussian process. Conditions are also developed for testing the validity of the moment conditions by means of a suitably constructed J-statistic. In case these conditions are invalid we propose another test called the U-test. As an empirical application of these infinite dimensional GMM procedures the evolution of cohort labor income inequality indices is studied using the Continuous Work History Sample database. The findings show that labor income inequality indices are maximized at early career years, implying that economic policies to reduce income inequality should be more effective when designed for workers at an early stage in their career cycles.

Limit theory for functional coefficient cointegrating regression was recently found to be considerably more complex than earlier understood. The issues were explained and correct limit theory derived for the kernel weighted local level estimator in Phillips and Wang (2023b). The present paper provides complete limit theory for the general kernel weighted local pth order polynomial estimators of the functional coefficient and the coefficient derivatives. Both stationary and nonstationary regressors are allowed. Implications for bandwidth selection are discussed. An adaptive procedure to select the fit order p is proposed and found to work well. A robust t-ratio is constructed following the new limit theory, which corrects and improves the usual t-ratio in the literature. The robust t-ratio is valid and works well regardless of the properties of the regressors, thereby providing a unified procedure to compute the t-ratio and facilitating practical inference. Testing constancy of the functional coefficient is also considered. Finite sample studies are provided that corroborate the new asymptotic theory.

This paper shows that the mixed normal asymptotic limit of the trend IV estimator with a fixed number of deterministic instruments (fTIV) holds in both singular (multicointegrated) and nonsingular cointegration systems, thereby relaxing the exogeneity condition in (Phillips and Kheifets, 2024, Theorem 1(ii)). The mixed normality of the limiting distribution of fTIV allows for asymptotically pivotal F and t tests about the cointegration parameters and for simple efficiency comparisons of the estimators for different numbers K of instruments, as well as comparisons with the trend IV estimator when K -> infinity with the sample size.

This paper discusses pitfalls in two way fixed effects (TWFE) regressions when the outcome variables contain nonlinear and possibly stochastic trend components. If a policy change shifts trend paths of outcome variables, TWFE estimation can distort results and invalidate inference, especially in a context of evolving policy decisions. A robust solution is proposed by allowing for dynamic club membership empirically using a relative convergence test procedure. The determinants of respective club memberships are assessed by panel ordered logit regressions. The approach allows for policy evolution and shifts in outcomes according to a convergence cluster framework with transitions over time and the possibility of eventual convergence to a single cluster as policy impacts mature. The long run impact of a policy can thus be examined via its impact on convergence club membership. An application to new weekly US Covid-19 vaccination policy data reveals that federal level vaccine mandates produced a merger of state vaccination rates into a single convergence cluster by mid-September 2021.

A semiparametric triangular systems approach shows how multicointegrating linkages occur naturally in an I(1) cointegrated regression model when the long run error variance matrix in the system is singular. Under such singularity, cointegrated I(1) systems embody a multicointegrated structure that makes them useful in many empirical settings. Earlier work shows that such systems may be analyzed and estimated without appealing to the associated I(2) system but with suboptimal convergence rates and potential asymptotic bias. The present paper develops a robust approach to estimation and inference of such systems using high dimensional IV methods that have appealing asymptotic properties like those known to apply in the optimal estimation of cointegrated systems (Phillips, 1991). The approach uses an extended version of high-dimensional trend IV (Phillips, 2006, 2014) estimation with deterministic orthonormal instruments. The methods and derivations involve new results on high-dimensional IV techniques and matrix normalization in the limit theory that are of independent interest. Wald tests of general linear restrictions are constructed using a fixed-b long run variance estimator that leads to robust pivotal HAR inference in both cointegrated and multicointegrated cases. Simulations show good properties of the estimation and inferential procedures in finite samples. An empirical illustration to housing stocks, starts and completions is provided.

This paper studies a linear panel data model with interactive fixed effects wherein regressors, factors and idiosyncratic error terms are all stationary but with potential long memory. The setup involves a new formulation of panel data models, where weakly dependent regressors, factors and idiosyncratic errors are embedded as a special case. Standard methods based on principal component decomposition and least squares estimation, as in Bai (2009), are found to be biased and distorted in inference. To cope with this failure and to provide a simple implementable estimation procedure, a frequency domain least squares estimation is proposed. The limit distribution of the frequency domain estimator is established and a self-normalized approach to inference without the need for plug-in estimation of memory parameters is developed. Simulations show that the frequency domain estimator performs robustly under short memory and outperforms the time domain estimator when long range dependence is present. An empirical illustration is provided, examining the long-run relationship between stock returns and realized volatility.

This paper examines methods of inference concerning quantile treatment effects (QTEs) in randomized experiments with matched-pairs designs (MPDs). Standard multiplier bootstrap inference fails to capture the negative dependence of observations within each pair and is therefore conservative. Analytical inference involves estimating multiple functional quantities that require several tuning parameters. Instead, this paper proposes two bootstrap methods that can consistently approximate the limit distribution of the original QTE estimator and lessen the burden of tuning parameter choice. Most especially, the inverse propensity score weighted multiplier bootstrap can be implemented without knowledge of pair identities.