Testing purchasing power parity: some evidence of the effects of transaction costs

Empirical tests of purchasing power parity often recognize the problems created by simultaneous equations, but seldom recognize the effects of measurement error or transaction costs. Presumably because most researchers believe that they are unimportant. We present evidence that shows that measurement error and transaction costs and create serious econometric problems for testing purchasing power parity. One effect of these problems is that conventional tests of purchasing power parity can accept PPP when predictive errors are relatively large and reject it when predictive errors are relatively small. Another effect is to bias test of cointegration toward accepting the null of no cointegration between exchange rates and relative price indexes. We also construct a simple model of the determination of exchange rates that shows how transaction costs lead to regression switiching.     

Bayesian model selection and parameter estimation for possibly asymmetric and non-stationary time series using a reversible jump Markov chain Monte Carlo approach

A Markov chain Monte Carlo (MCMC) approach, called a reversible jump MCMC, is employed in model selection and parameter estimation for possibly non-stationary and non-linear time series data. The non-linear structure is modelled by the asymmetric momentum threshold autoregressive process (MTAR) of Enders & Granger (1998) or by the asymmetric self-exciting threshold autoregressive process (SETAR) of Tong (1990). The non-stationary and non-linear feature is represented by the MTAR (or SETAR) model in which one ( 𝜌 1 ) of the AR coefficients is greater than one, and the other ( 𝜌 2 ) is smaller than one. The other non-stationary and linear, stationary and nonlinear, and stationary and linear features, represented respectively by ( 𝜌 1 = 𝜌 2 = 1 ), ( 𝜌 1 p 𝜌 2 < 1 ) and ( 𝜌 1 = 𝜌 2 < 1 ), are also considered as possible models. The reversible jump MCMC provides estimates of posterior probabilities for these four different models as well as estimates of the AR coefficients 𝜌 1 and 𝜌 2 . The proposed method is illustrated by analysing six series of US interest rates in terms of model selection, parameter estimation, and forecasting.     

Tests for Unit-Root versus Threshold Specification With an Application to the Purchasing Power Parity Relationship

We consider modeling the real exchange rate by a stationary three-regime self-exciting threshold autoregressive (SETAR) model with possibly a unit root in the middle regime. This representation is consistent with purchasing power parity in the presence of trading costs. Our main contribution is to provide statistical tools for testing unit root versus a SETAR. First, we show that a SETAR with a unit root in the middle regime is stationary and mixing under reasonable assumptions. Second, we derive analytically the asymptotic distribution of our unit-root test under the null. Using monthly real exchange rate data, our test rejects the null of unit-root against a threshold process for five European series.     

An empirical study on the threshold cointegration of Chinese A and H cross-listed shares

We investigate the dynamic relationship between the prices of Chinese A and H market cross-listed shares using the Enders–Siklos threshold cointegration approach. Our data are the daily closing prices of the Hang Seng China AH (A) index and the Hang Seng China AH (H) index from 4 January 2006 to 1 November 2013. We find a threshold cointegration between these two indices, instead of the linear cointegration well established in the literature. The short-term adjustment to the equilibrium shows an asymmetric effect according to the price deviation from the equilibrium. Moreover, using a Granger causality test, we find a bi-directional causality between these two markets, indicating a close relationship between them. A pairs trading rule, based on the estimated threshold cointegration model, demonstrates the usefulness of our results as it generates a significantly higher return than a naive buy-and-hold trading rule.     

非线性财政政策效应下财政赤字 可持续性研究

 财政赤字可持续性检验往往采用线性协整技术来验证跨期预算约束是否成立，但这一检验方法是基于财政政策效应是线性效应理论之上的。在现实中，财政政策既具有凯恩斯效应也具有非凯恩斯效应，财政政策效应是非线性的，财政收支的调整过程也是非线性非对称的。用传统的线性协整技术难以描述财政赤字可持续性过程，本文分析探讨一种用于揭示非平稳时间序列非线性调整过程的模型——两机制门限协整模型，深入研究了该模型的参数估计、检验统计量，并通过自助法(bootstrap)模拟计算其检验统计量临界值及P值。最后利用该模型，揭示了我国财政收支调整是非线性调整过程，并证实了我国财政赤字具有可持续性，但财政赤字规模不应进一步扩大。     

Pitfalls in Estimating Cointegrating Vector when Cointegration Relationship has Nonlinear Adjustment

This article investigates the properties of the estimators of the cointegrating vector when the cointegration error has a nonlinear adjustment. We investigate the properties of three estimators, namely, ordinary least squares (OLS), dynamic OLS (DOLS), and autoregressive distributed lag (ADL) models. Monte Carlo simulation results demonstrate that although all the estimators have consistency under cointegration with a nonlinear adjustment, they suffer from severe size distortions for the t-statistics of the cointegrating vector when the cointegration error has a highly persistent nonlinear adjustment and endogeneity. The results imply that the use of DOLS and ADL for cointegration with nonlinear adjustment cannot sufficiently improve the estimates and size performances.     

ASSESSING AND TESTING FOR THRESHOLD NONLINEARITY IN STOCK RETURNS

This paper proposes a test for threshold nonlinearity in a time series with generalized autore‐gressive conditional heteroscedasticity (GARCH) volatility dynamics. This test is used to examine whether financial returns on market indices exhibit asymmetric mean and volatility around a threshold value, using a double‐threshold GARCH model. The test adopts the reversible‐jump Markov chain Monte Carlo idea of Green, proposed in 1995, to calculate the posterior probabilities for a conventional GARCH model and a double‐threshold GARCH model. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity with asymmetric behaviour of the mean and volatility. Simulation experiments demonstrate that the test works very well in distinguishing between the conventional GARCH and the double‐threshold GARCH models. In an application to eight international financial market indices, including the G‐7 countries, clear evidence supporting the hypothesis of threshold nonlinearity is discovered, simultaneously indicating an uneven mean‐reverting pattern and volatility asymmetry around a threshold return value.     

Improved model selection criteria for SETAR time series models

The purpose of this paper is threefold. First, we obtain the asymptotic properties of the modified model selection criteria proposed by Hurvich et al. (1990. Improved estimators of Kullback-Leibler information for autoregressive model selection in small samples. Biometrika 77, 709–719) for autoregressive models. Second, we provide some highlights on the better performance of this modified criteria. Third, we extend the modification introduced by these authors to model selection criteria commonly used in the class of self-exciting threshold autoregressive (SETAR) time series models. We show the improvements of the modified criteria in their finite sample performance. In particular, for small and medium sample size the frequency of selecting the true model improves for the consistent criteria and the root mean square error (RMSE) of prediction improves for the efficient criteria. These results are illustrated via simulation with SETAR models in which we assume that the threshold and the parameters are unknown.     

购买力平价及其在亚洲新兴市场中的实证分析

 作为最重要的汇率决定理论之一,购买力平价被广泛应用于实证研究,但是重点针对亚洲新兴市场的研究依然有限。本文对七个亚洲新兴市场进行了购买力平价理论长期均衡关系的实证检验分析。针对购买力平价理论,作者运用单位根检验和协整检验进行数据分析。数据采用1957年至2011年的汇率（以美元作为基础汇率）及季度价格水平（本文采用CPI作为价格水平指数）。实证检验结果表明购买力平价理论的长期均衡在亚洲新兴市场中均不成立。文章最后提出了一些或许会导致其不理想结论的因素,并针对文章的实证研究得出新的改进方法。     

Predictor distribution and forecast accuracy of threshold models

In the present paper the predictor distribution of a SETAR (Self Exciting Threshold Autoregressive) model (Tong and Lim, 1980) has been investigated when the lead time is greater than the threshold delay.After a brief presentation of the model under study, some relevant aspects of the density forecasts are shown highlighting how they can be used to generate more accurate predictions and to estimate an approximation of the probability density function of the SETAR predictors. The performances of competing predictors have been evaluated through a simulation study and an application to financial market data of the daily Nikkey 300 stock market returns.     

非对称单位根检验和非参数方差比

基于三种退势方法较详细研究了方差比检验在非对称单位根检验中的适用性,并通过MC模拟揭示了其检验势性质。结果表明：在不含趋势项的TAR下,两机制TAR数据落在第一机制的比率是影响方差比检验势的重要因素,且比率越高检验势也越高;三机制TAR中落在中间机制的数据比率会影响检验势,随着比率增加检验势呈下降趋势,但程度不大。在含趋势的TAR下,由于趋势项在数据生成过程中具有支配作用,各种检验势会随着趋势设定的不同而不同。数据在不同机制之间的转换概率越高,则ROLS和RDM退势较OLS退势具有明显优势。     

春节模型的设计与应用

 季节调整是经济数据预处理中非常重要的一个步骤。现有的主流季节调整方法X-12-ARIMA 和TRAMO/SEATS中都包含节假日因素的调整。由于不同的国家节假日一般不同,因此各国在进行经济数据的季节调整时,都需要结合本国的假日对季节调整方法进行修正。春节是中国最为重要而且持续时间最长的节日,具体日期可以出现在一月也可以在二月。本文基于X-12-ARIMA方法,同时考虑春节对经济指标的正负性影响效应、春节影响的变化速率以及春节效应的时长三个因素,设计了十二个不同类型的春节模型。本文应用Eviews软件和Demetra软件,采集不同的经济指标,对所设计的春节模型进行了应用研究,并根据异常值改善标准,对最佳的春节模型进行了选择与比较分析。     

The Zellner Thesis Award in Business and Economic Statistics

We analyze the modifications that occur in indirect inference when a nuisance parameter is not identified under the null hypothesis. We develop a testing procedure adapted to this simulation-based estimation method, and detail its use for detecting the threshold effect in threshold moving average models with contemporaneous and lagged asymmetries. In contrast to existing threshold models, these models allow taking into account the presence of asymmetric effects of current and lagged random shocks. We use them to measure the persistence of shocks to U.S. output.     

具有GARCH（1，1）-正态误差项的非对称单位根检验研究

摘　　要:理论研究表明许多经济变量呈现出非对称的门限自回归（TAR）或动态门限自回归（M-TAR）数据生成机制,因而非对称单位根检验就成为该领域的主要研究方向之一。本文对非对称单位根检验Enders-Granger方法在GARCH（1,1）-正态误差项下的检验水平与检验势作了系统的仿真研究。研究表明：GARCH（1,1）-正态误差项的TAR或M-TAR模型会对该方法的检验水平和检验势产生重要影响。     

On finite sample properties of the tests of robinson (1994) for fractional integration

This article proposes a bootstrap version of the tests of Robinson (1994) for testing unit and/or fractional roots. The finite-sample behaviour of the tests, based on these bootstrap critical values is compared with those based on asymptotic and on finite-sample results and with a number of leading unit-root tests. The Monte-Carlo simulations indicate that the bootstrap version of the tests of Robinson (1994) outperforms the other tests, including the one using finite-sample critical values. The improvement in the size and the power is particularly important under AR(1) alternatives. A small empirical application is also carried out with inflation for a panel of 16 European countries. The results show that the differences across countries depend on the critical values used: whereas the I (1) property of inflation is unclear with the asymptotic tests in some countries, the bootstrap version of Robinson's (1994) tests cannot reject the presence of a unit-root in inflation.     

Cointegration and Threshold Adjustment

This article proposes an extension to the Engle–Granger testing strategy by permitting asymmetry in the adjustment toward equilibrium in two different ways. We demonstrate that our test has good power and size properties over the Engle–Granger test when there are asymmetric departures from equilibrium. We consider an application—namely, whether there exists cointegration among interest rates for instruments with different maturities. This issue has been widely tested with mixed results. We argue that either cautious policy, or possibly opportunistic behavior on the part of the Federal Reserve implies that an equilibrium relationship between short- and long-term interest rates exists but that adjustments from disequilibrium are asymmetric in nature. Empirical tests using U.S. yields confirm the asymmetric nature of error correction among interest rates of different maturities.     

Asymmetric autoregressive models: statistical aspects and a financial application under COVID-19 pandemic

In the present study, we provide a motivating example with a financial application under COVID-19 pandemic to investigate autoregressive (AR) modeling and its diagnostics based on asymmetric distributions. The objectives of this work are: (i) to formulate asymmetric AR models and their estimation and diagnostics; (ii) to assess the performance of the parameters estimators and of the local influence technique for these models; and (iii) to provide a tool to show how data following an asymmetric distribution under an AR structure should be analyzed. We take the advantages of the stochastic representation of the skew-normal distribution to estimate the parameters of the corresponding AR model efficiently with the expectation-maximization algorithm. Diagnostic analytics are conducted by using the local influence technique with four perturbation schemes. By employing Monte Carlo simulations, we evaluate the statistical behavior of the corresponding estimators and of the local influence technique. An illustration with financial data updated until 2020, analyzed using the methodology introduced in the present work, is presented as an example of effective applications, from where it is possible to explain atypical cases from the COVID-19 pandemic.     

On nonlinear models for time series

The paper is a review of nonlinear processes used in time series analysis and presents some new original results about stationary distribution of a nonlinear autoregres-sive process of the first order. The following models are considered: nonlinear autoregessive processes, threshold AR processes, threshold MA processes, bilinear models, auto-regressive models with random parameters including double stochastic models, exponential AR models, generalized threshold models and smooth transition autoregressive models, Some tests for linearity of processes are also presented.     

A residual-based test of the null of cointegration in panel data

This paper proposes a residual-based Lagrange Multiplier (LM) test for the null of cointegration in panel data. The test is analogous to the locally best unbiased invariant (LBUI) for a moving average (MA) unit root. The asymptotic distribution of the test is derived under the null. Monte Carlo simulations are performed to study the size and power properties of the proposed test.

overall, the empirical sizes of the LM-FM and LM-DOLs are close to the true size even in small samples. The power is quite good for the panels where T ≥ 50, and decent with panels for fewer observation in T. In our fixed sample of N = 50 and T = 50, the presence of a moving average and correlation between the LM-DOLS test seems to be better at correcting these effects, although in some cases the LM-FM test is more powerful.

Although much of the non-stationary time series econometrics has been criticized for having more to do with the specific properties of the data set rather than underlying economic models, the recent development of the cointegration literature has allowed for a concrete bridge between economic long run theory and time series methods. Our test now allows for the testing of the null of cointegration in a panel setting and should be of considerable interest to economists in a wide variety of fields.     

Simulation-based estimation of threshold moving average models with contemporaneous shock asymmetry and an application to Turkish business cycles

Persistence of shocks to economic time series may differ depending on the sign of the shock or on a threshold value. Threshold moving average (TMA) models, by explicitly taking into account threshold behavior, can help discriminate whether there exists persistence asymmetry. This article considers TMA models in which both contemporaneous and lagged asymmetric effects are both present and examines the properties of simulation-based efficient method of moments estimation using Monte Carlo simulation experiments. The model is applied to analyze the persistence properties of shocks to growth rates of gross domestic product and industrial production index in Turkish economy.