Testing for structural change in the dynamic adjustment model with autoregressive errors

The dynamic CUSUM test for structural change proposed by Kr?mer, Ploberger and Alt (1988) is investigated when the errors are serially correlated in a linear dynamic model. We show that the dynamic CUSUM test can be modified to allow for serial correlation in the disturbance using the same procedure as in Kao and Ross (1995), and that the modified dynamic CUSUM test retains its asymptotic significance levels. Monte Carlo results suggest that the empirical size of the dynamic CUSUM test is highly distorted while the empirical size of the modified dynamic CUSUM test is fairly robust to the change on the degree of autocorrelation. We also find that the power of the modified test essentially depends on the angle between the mean regressors and the structural shift. First version received: April 1997/Final version received: January 1998     

Testing linear relationships between non-constant variances of economic variables

We aim to assess linear relationships between the non-constant variances of economic variables. A two-step methodology is proposed to solve this problem. First, the conditional mean is filtered by mean of a vector autoregressive (VAR) model. Then, a bootstrap cumulative sum (CUSUM) test is applied to the residuals. Simulations suggest a good behavior of the test, for sample sizes commonly encountered in practice. The tool we provide is intended to highlight relations, or draw common patterns between economic variables, through their non-constant variances. The outputs of this paper are illustrated considering U.S. regional data.     

The FMLS-based CUSUM statistic for testing the null of smooth time-varying cointegration in the presence of a structural break

In this paper we extend the FMLS-based CUSUM cointegration test (Xiao and Phillips, 2002) for testing the smooth time-varying cointegration null hypothesis. For this purpose we use Chebyshev time polynomials to specify time-varying coefficients under the null. We derive the limiting distribution of the statistic, which is pivotal with the order of the Chebyshev time polynomials, and we provide the critical values to conduct the proposed test.     

Power properties of the CUSUM and CUSUMSQ tests for parameter instability

This article investigates the power of CUSUM and CUSUMSQ tests for parameter stability and demonstrates that this depends on the nature of the structural change taking place. If the break is in the intercept of the regression equation then the CUSUM test has higher power. However, if the structural change involves a slope coefficient or the variance of the error term, then the CUSUMSQ test has higher power. This may help to explain why the two tests often produce contradictory findings.     

Long memory and changing persistence

We study the empirical behaviour of semi-parametric estimation for long-memory models when the true data generating process exhibits a change in persistence. Evidence for long memory is likely to be found. Procedures for discrimination between different models are proposed.     

A new test for structural change

In this paper we are interested in detecting structural change at an unknown point. We argue that the CUSUM test may not ideal for this, and propose an alternative test. Critical values for this test are determined based on the multiple studentt test procedure. A Monte Carlo study suggests that the new test is quite powerful when the structural change occurs in the latter part of the sample. The new test also provides information about the location of structural change.     

What explains long memory in futures price volatility?

Long memory in futures price volatility is a well-documented stylized fact with implications for market efficiency, risk management, forecasting and option pricing bias. The implications of long-memory differ, however, based on whether it is of a ‘fractional’ or of a ‘stochastic’ type. The aims of this article are to determine, in the case of agricultural commodity futures data, which type better describes price volatility and also to evaluate several competing explanations for findings of long memory. The evidence presented here finds little support for three out of four potential explanations, namely, excessive noise in the volatility measure, bias in the long-memory estimator and understated SEs of the long-memory parameter. For the data considered, price volatility appears to be most likely generated by a nonfractional long-memory process such as a stochastic break or stochastic unit root.     

The CUSUM of squares test for the stability of regression models with non-stationary regressors

In this paper, we propose a modified CUSUM of squares test in time series regression models with a non-stationary regressor and show that the limiting distribution of this test is the sup of the absolute value of a Brownian bridge.     

On studentizing a test for structural change

We show that the asymptotic null distribution of the CUSUM of squares test is not robust against deviations from normality, and propose a modification which overcomes this deficiency.     

中国股市长期记忆效应的实证研究

股票市场长期记忆效应问题一直是金融经济学家们倍感兴趣的一个研究热点。本文针对中国股票市场中价格指数与个股的日收益序列 ,在已有研究文献主要采用的经典R S分析方法基础上 ,引入修正R S分析与ARFIMA模型进行了实证研究。从研究结果来看 ,2 2个样本序列并不满足传统的正态分布假设 ,序列呈现出尖峰、肥尾、右偏等有偏特征以及独特的自相关与偏自相关结构 ,这些迹象预示着非线性动态系统的存在。而进一步的研究却表明 ,中国股市中代表市场总体的股价指数不存在长期记忆效应 ,而个股收益序列的分布特征存在着较大差异 ,仅少数个股存在长期记忆行为。这一结论明显地有别于以往那些由经典R S分析所得到的研究结果。     

A fractionally integrated exponential STAR model applied to the US real effective exchange rate

The aim of this paper is to study the dynamics of the US real effective exchange rate by capturing non-linearity and long-memory features. In this context, we use the family of fractionally integrated STAR (FISTAR) models proposed by van Dijk et al. (van Dijk, D., Franses, P.H., and Paap, R., 2002. A non-linear longmemory model with an application to US unemployment. Journal of Econometrics 110, 135–165.) in the case when the transition function is an exponential function and we develop an estimation procedure. Indeed, these models can take into account processes characterized by several distinct dynamic regimes and persistence phenomena.     

Power monotonicity in detecting volatility levels change

We show that the CUSUM and LM tests for structural change in the volatility process enjoy monotonic power. The framework is general including many recently proposed non-stationary GARCH-type models. The result is in contrast to the well-known issue of non-monotonic power for the CUSUM-based tests for changing mean. Simulations and an empirical example provide further support.     

A modification of the CUSUM test in the linear regression model with lagged dependent variables

We consider testing for structural change in a dynamic linear regression model, and show that the well known CUSUM test, which has been initially devised only for the standard static model, can easily be modified such as to remain asymptotically valid also in this nonstandard situation.     

Long memory and structural breaks in the returns and volatility of gold: evidence from Turkey

This article examines the long-memory properties and structural breaks in spot and futures gold returns and volatility in Turkey. The data cover the period from 2008 through 2013 in which gold prices hit an all-time high. ARFIMA–FIGARCH model provides evidence of dual long memory in spot series and a lack of long-memory property in futures returns. Anti-persistence in spot returns is indicative of an overreaction of gold prices to new information, thus disconfirming the weak form of market efficiency. The findings further provide evidence of one structural break, which is associated with correction in the gold prices during the post-global financial crisis. The analyses suggest that the long memory is true, not spurious. This implies that long memory is a feature of the data instead of an outcome of structural changes.     

Testing for parameter stability in structural econometric relationships

This letter discusses CUSUM and CUSUM of squares tests for parameter stability in an equation which forms part of a structural simultaneous equations model.     

Fractional integration and structural breaks in U.S. macro dynamics

This article identifies structural breaks in the post-World War II joint dynamics of U.S. inflation, unemployment and the short-term interest rate. We use a structural break-date procedure which allows for long-memory behavior in all three series and perform the analysis for alternative data frequencies. Both long-memory and short-run coefficients are relevant for characterizing the changing patterns of U.S. macroeconomic dynamics. We provide an economic interpretation of those changes by examining the link between macroeconomic events and structural breaks.     

Co-integration and causality analysis between stock market prices and their determinates in Jordan

The current study examines the short- and long-term equilibrium relationship between the stock price index (SPI) and the macroeconomic variables in Jordan. Annual time series data over the 1978–2010 period for industrial production (IP), money supply (M2), exchange rate (EX), and discount rate (DR) were used. The ADF, bound testing approach, CUSUM, and CUSUMQ tests were applied to test the stationary and co-integration among variables. The results suggest the existence of a long-term equilibrium relationship between SPI and the macroeconomic variables (i.e., IP, M2, EX, and DR).     

Multiple cyclical fractional structures in financial time series

This article analyses multiple cyclical structures in financial time series. In particular, we focus on the monthly structure of the Nasdaq, the Dow–Jones and the S&P stock market indices. The three series are modelled as long-memory processes with poles in the spectrum at multiple frequencies, including the long-run or zero frequency.     

Services sector and economic growth in India

This study examines the long-run equilibrium and short-run dynamic relationship between services sector and Gross Domestic Product (GDP) and between services and nonservices sectors in India. The model is estimated using the optimal single-equation and the maximum-likelihood system estimators. All the estimators consistently suggest the cointegrating relationship between services sector and GDP as well as between services and nonservices sectors. The estimates of long-run elasticity parameters are statistically significant and dimensionally consistent across the estimators. The conventional Cumulative Sum (CUSUM) and the new CUSUM and Moving Sum (MOSUM) tests suggest the stability of the equilibrium residuals and reinforce the cointegrating relationship between the model series. The error correction model provides some support for unidirectional Granger-causality from services sector to GDP. The impulse response and variance decomposition analyses instead suggest the bidirectional causality between services sector and GDP and between services and nonservices sectors. The stable growth of services sector is essentially crucial to absorb the adverse effects of exogenous weather shocks in agriculture and industry and provide resilience to the economy.     

Model evaluation based on residual analysis of two similar models

Models that may appear to have different properties may in fact produce residuals that differ only in subtle ways. By analysing the relationships between model residuals the problems in distinguishing between models can perhaps be discovered, as illustrated by the econometric examples considered. Regressing residuals gives the long-memory residual, which is the difference between two models, but this difference is very subtle and deeply hidden, which explains why the traditional standard technique does not find this difference.