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Using computer simulation and a study of the asymptotic distribution, we consider the relative efficiency of M-estimates for the coefficients of the threshold autoregressive equation with respect to the least squares and least absolute deviation estimates. We assume that the updating sequence of the autoregressive equation can have Student’s, logistic, double exponential, normal, or contaminated normal distributions. We prove asymptotic normality of M-estimates with a convex loss function.

This paper establishes the asymptotic uniform linearity of M- and R-scores in a family of nonlinear time series and regression models. It also gives an asymptotic expansion of the standardized sequential residual empirical process in these models. These results are, in turn, used to obtain the asymptotic normality of certain classes of M-, R- and minimum distance estimators of the underlying parameters. The classes of estimators considered include analogs of Hodges-Lehmann, Huber and LAD (least absolute deviation) estimators. Some applications to the change point and testing of the goodness-of-fit problems in threshold and amplitude-dependent exponential autoregression models are also given. The paper thus offers a unified functional approach to some aspects of robust inference for a large class of nonlinear time series models.

Evidence of the asymmetric wealth effect has important implications for investors and continues to merit research attention, not least because much of the evidence based on linear models has been refuted. Indeed, stock and house prices are influenced by economic activity and react non-linearly to positive/negative shocks. This problem justifies our research. The objective of this study is to examine evidence of cointegrations between the US housing and stock markets and between the US and European stock markets, given the international relevance of these exchanges. Using data from 1989:Q1 to 2020:Q2, the Threshold Autoregression model as well as the Momentum Threshold Autoregression model were calculated by combining the US Freddie, DJIA, and SPX indices and the European STOXX and FTSE indices. The results suggest a long-term equilibrium relationship with asymmetric adjustments between the housing market and the US stock markets, as well as between the DJIA, SPX, and FTSE indices. Moreover, the wealth effect is stronger when stock prices outperform house prices above an estimated threshold. This empirical evidence is useful to portfolio managers in their search for non-perfectly related markets that allow investment diversification and control risk exposure across different assets.

This article studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a two-regime structure according to the magnitude of the lagged observations. Generalized from the Poisson autoregression, it allows more flexible, and even negative correlation, in the observations, which cannot be produced by the single-regime model. Classical Markov chain theory and Lyapunov's method are used to derive the conditions under which the process has a unique invariant probability measure and to show a strong law of large numbers of the intensity process. Moreover, the asymptotic theory of the maximum likelihood estimates of the parameters is established. A simulation study and a real-data application are considered, where the model is applied to the number of major earthquakes in the world. Supplementary materials for this article are available online.

We propose a straightforward algorithm to estimate large Bayesian time-varying parameter vector autoregressions with mixture innovation components for each coefficient in the system. The computational burden becomes manageable by approximating the mixture indicators driving the time-variation in the coefficients with a latent threshold process that depends on the absolute size of the shocks. Two applications illustrate the merits of our approach. First, we forecast the US term structure of interest rates and demonstrate forecast gains relative to benchmark models. Second, we apply our approach to US macroeconomic data and find significant evidence for time-varying effects of a monetary policy tightening.

As an important part of urban vitality, street vitality is an external manifestation of street economic prosperity and is affected by the built environment and the surrounding street vitality. However, existing research on the formation mechanism of street vitality focuses only on the built environment itself, ignoring the spatial spillover effect on street vitality. This study uses 5290 street segments in Shenzhen as examples. Utilizing geospatial and other multisource big data, this study creates spatial weight matrices at varying distances based on different living circle ranges. By combining the panel threshold model (PTM) and the spatial panel Durbin model (SPDM), this study constructs a spatial autoregressive threshold model to explore the spatial nonlinear effects of street vitality, considering various spatial weight matrices and thresholds of construction intensity and functional diversity. Our results show the following: (1) Street vitality exhibits significant spatial spillover effects, which gradually weaken as the living circle range expands (Moran indices are 0.178***, 0.160***, and 0.145*** for the 500 m, 1000 m, and 1500 m spatial weight matrices, respectively). (2) Construction intensity has a threshold, which is 0.1466 under spatial matrices of different distances. Functional diversity has two thresholds: 0.6832 and 2.2065 for the 500 m spatial weight matrix, and 0.6832 and 1.4325 for the 1000 m matrices, and 0.6832 and 1.2724 for 1500 m matrices. (3) As an international metropolis, street accessibility in Shenzhen has a significant and strong positive impact on its street vitality. This conclusion provides stakeholders with spatial patterns that influence street vitality, offering a theoretical foundation to further break down barriers to street vitality.

The phenomenon of hysteresis has been observed in many economic time series, especially in unemployment rates. To study the hysteretic patterns at different quantiles, this study considers a conditional quantile estimation for hysteretic autoregressive models, and derives its asymptotic properties. Simulation experiments are conducted to evaluate the finite-sample performance of our method, and its usefulness is further demonstrated by an analysis of the growth rates of unemployment rates.

Intensive longitudinal data provide rich information, which is best captured when specialized models are used in the analysis. One of these models is the multilevel autoregressive model, which psychologists have applied successfully to study affect regulation as well as alcohol use. A limitation of this model is that the autoregressive parameter is treated as a fixed, trait-like property of a person. We argue that the autoregressive parameter may be state-dependent, for example, if the strength of affect regulation depends on the intensity of affect experienced. To allow such intra-individual variation, we propose a multilevel threshold autoregressive model. Using simulations, we show that this model can be used to detect state-dependent regulation with adequate power and Type I error. The potential of the new modeling approach is illustrated with two empirical applications that extend the basic model to address additional substantive research questions.

This paper extends the classical two-regime threshold autoregressive model by introducing hysteresis to its regime-switching structure, which leads to a new model: the hysteretic autoregressive model. The proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism. A sufficient condition is given for geometric ergodicity. Conditional least squares estimation is discussed, and the asymptotic distributions of its estimators and information criteria for model selection are derived. Simulation results and an example support the model.

This work investigates how the state of credit markets affects the impact of fiscal policies. We estimate a threshold vector autoregression (TVAR) model on US quarterly data for the period 1984–2010. We employ the spread between BAA-rated corporate bond yield and 10-year treasury constant maturity rate as a proxy for credit conditions. We find that the response of output to fiscal policy shocks is stronger and more persistent when the economy is in the ‘tight’ credit regime. Fiscal multipliers are significantly different in the two regimes: they are abundantly and persistently higher than one when firms face increasing financing costs, whereas they are feebler and often lower than one in the ‘normal’ credit regime. The results appear to be robust to different model specifications, fiscal foresight, alternative threshold variables, different measure of variables and sample periods.