Random walk and breaking trend in financial series: An econometric critique of unit root tests

The present note sheds light on several pitfalls associated with unit root tests that are overlooked by a growing volume of literature in financial economics. Specifically, several studies have confused unit root tests with the Random Walk hypothesis. Unit root tests are not designed for such a task since they aim at investigating whether a time series is difference-stationary or trend-stationary and are not, therefore, predictability tests. Secondly, we emphasize some serious shortcomings associated with the widely used unit root test developed by Zivot and Andrews [Zivot, E. & Andrews, D.W.K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business and Economic Statistics, 10, 251–270.]. In particular, we stress that results from the Zivot–Andrews test are sensitive to the methods employed to calculate the critical values and to select the maxim lag k. Furthermore, Zivot–Andrews test imposes a one time structural break in a time series; however recent studies showed that not counting for other true structural breaks may bias the results and may cause a spurious rejection of the unit root null hypothesis. Finally, we support our arguments by an empirical example based on the findings of Narayan and Smyth [Narayan, K.P. & Smyth, R. (2004). Is South Korea’s stock market efficient? Applied Economics Letters, 11, 707–710.] with regards to the efficiency of South Korean stock market. We show that contrary to what the authors claim, the KSE (KOSPI) price index is predictable, and hence the South Korean stock market is not informationally efficient.     

Asymmetric adjustments in the spread of lending and deposit rates: Evidence from extended threshold unit root tests

In this paper, we test for asymmetric adjustments in the spread of the U.S. prime lending rate and 3-month certificate of deposit rate. In doing so, we extend the pioneering threshold unit root tests of Enders and Granger (1998) to more flexible models where the deterministic terms and short-run dynamics, in addition to the persistent parameters, can differ in two regimes. While some previous works have tested for asymmetric adjustments in the spread of lending and deposit rates using threshold unit root tests, the deterministic terms and short-run dynamics were assumed to be symmetric, which can lead to bias and less accurate conclusions if these conditions do not hold. Overall, we find that the spread in lending and deposit rates is stationary but adjustment to the equilibrium is asymmetric. In particular, we find more rapid adjustment when the spread is narrowing below a threshold level than when widening above this level. Several theoretical implications are suggested.     

基于GARCH模型的黄金指数与美元指数波动性研究

近几年的黄金市场与美元指数市场波动都比较大,但波动的方向不一致。通过对两者的波动进行研究,主要有单位根检验、ARCH效应的检验、GARCH模型分析以及因果关系检验,结果表明,黄金指数GARCH(1,1)最适合描述其市场波动,美元指数GARCH(2,1)最适合描述其市场波动,美元指数的预测对黄金指数的预测会有帮助。     

Market development and market efficiency: evidence based on nonlinear panel unit root tests

This study tests the weak form market efficiency of 32 European stock markets. Utilizing monthly data from June 2006 to June 2017, six different, newly developed nonlinear panel root tests were applied in three different groups of European markets: Frontier, Emerging and Developed. The results show that there is a meaningful relationship between different levels of economic development and the weak form market efficiency. Considering the nonlinear structure of the stock market indices, use of linear models might lead to wrong conclusions regarding market efficiency. Using several nonlinear panel root tests, the results of this study shed more light on the true data generating process of the stock market indices and more appropriately model market efficiency.     

Random walk and efficiency tests in the Asia-Pacific foreign exchange markets: Evidence from the post-Asian currency crisis data

This paper empirically tests the random walk and efficiency hypothesis for 12 Asia-Pacific foreign exchange markets. The hypothesis is tested using individual as well as panel unit root tests and two variance-ratio tests. The study covers the high (daily) and medium (weekly) frequency post-Asian crisis spot exchange rate data from January 1998 to July 2007. The inferential outcomes do not differ substantially between the unit root tests and the variance-ratio tests when using daily data but differ significantly when using weekly data. With the daily data, both types of unit root tests identify unit root components for all the series and two variance-ratio tests provide the evidence of martingale behavior for majority of the exchange rates tested. With the weekly data, panel unit root tests identify unit root component for the exchange rates and, the unit root tests on a single series basis identify unit root component for 10 foreign exchange markets. However, the variance-ratio tests reject the martingale null for the majority of the exchange rates when using weekly data.     

Testing for explosive bubbles in the presence of autocorrelated innovations

We analyze an empirically important issue with recursive right-tailed unit root tests for bubbles in asset prices. First, we show that serially correlated innovations, which is a feature that is present in most financial series used to test for bubbles, can lead to severe size distortions when using either fixed or automatic (based on information criteria) lag-length selection in the auxiliary regressions underlying the test. Second, we propose a sieve-bootstrap version of these tests and show that this results in tests which control size well across a number of simulation designs both with and without highly autocorrelated innovations. We also find that these improvements in size come at a relatively low cost for the power of the tests. Finally, we apply the bootstrap tests on the housing market of OECD countries, and generally find much weaker evidence of housing bubbles compared to existing evidence.     

Nonlinear trends in real exchange rates: A panel unit root test approach

We analyze the possibility of nonlinear trend stationarity as the alternative to unit roots in 23 OECD real exchange rates, 1974–1998, by adding nonlinear time terms to the CIPS panel unit root test of Pesaran (2007). We follow a thorough bootstrapping approach and propose a technique to adjust statistical significance for the use of multiple tests over several time trend orders. The unit root null that all real exchange rates have unit roots is rejected at better than the 0.05 level. Bootstrapped results from a procedure of Chortareas and Kapetanios (2009) suggest that the hypothesis that all are stationary is reasonable. We argue that nonlinear trend stationarity is the most likely alternative hypothesis for at least some of the real exchange rates because: (1) the strongest CIPS rejection occurs when quadratic trends are specified; (2) nonlinear time terms are statistically significant at the 0.10 level; (3) the actual CIPS statistics are more consistent with CIPS sampling distributions from bootstrapped nonlinear trend stationary processes than from linear trend or mean stationary processes.     

Multivariate unit root tests of the PPP hypothesis

So far, most univariate tests of Purchasing Power Parity (PPP) have provided mixed support for PPP. In contrast, this paper focuses on a multivariate framework, which produces much stronger results. Unlike previous panel tests, however, we do not impose a common speed of mean reversion. The contribution of this paper is to show that the increased power of multivariate tests stems from high correlations across series, and not necessarily from imposing a common speed of mean reversion. We find strong evidence in favor of long-run PPP, which we show can be traced to the dollar vs. European currencies.     

Inequality Constraints in the Fractionally Integrated GARCH Model

In this article we derive necessary and sufficient conditionsfor the nonnegativity of the conditional variance in the fractionallyintegrated generalized autoregressive conditional heteroskedastic(p, d, q) (FIGARCH) model of the order p 2 and sufficient conditionsfor the general model. These conditions can be seen as beinganalogous to those derived by Nelson and Cao (1992, Journalof Business & Economic Statistics 10, 229–235) forthe GARCH(p, q) model. However, the inequality constraints whichwe derive for the FIGARCH model illustrate two remarkable propertiesof the FIGARCH model which are in contrast to the GARCH model:(i) even if all parameters are nonnegative, the conditionalvariance can become negative and (ii) even if all parametersare negative (apart from d), the conditional variance can benonnegative almost surely. In particular, the conditions forthe (1, d, 1) model substantially enlarge the sufficient parameterset provided by Bollerslev and Mikkelsen (1996, Journal of Econometrics73, 151–184). The importance of the result is illustratedin an empirical application of the FIGARCH(1, d, 1) model toJapanese yen versus U.S. dollar exchange rate data.     

A comparison of statistical tests for the adequacy of a neural network regression model

An integral part of econometric practice is to test the adequacy of model specifications. If a model is adequately specified, it should not leave interesting features of the data-generating process in the errors. Despite the common tradition, the importance of diagnostic checking as a safeguard against mis-specification has only recently been recognized by neural network (NN) practitioners, possibly because this type of semi-parametric methodology was not originally designed for economic and financial applications. The purpose of this paper is to compare a number of analytical statistical testing procedures suitable to diagnostic checking on a neural network regression model. We present the standard Lagrange multiplier (LM) testing framework designed under the assumption of identically distributed disturbances and also examine two modifications that are robust to heteroskedasticity in errors. One modification also gives the researcher an opportunity to incorporate information concerning the volatility structure of the data-generating process in the testing procedure. By means of a Monte Carlo simulation, we investigate the performance of these tests under GARCH-type heteroskedasticity in errors and various distributional assumptions. The results show that although the primary concern of the researcher may be to design a regression model that accurately captures relations in the mean of the conditional distribution, developing a good approximation of the underlying volatility structure generally increases the efficiency of tests in detecting non-adequacy of a NN model.     

Multivariate GARCH Modeling of Exchange Rate Volatility Transmission in the European Monetary System

We construct a series of 3‐, 4‐ and 5‐variable multivariate GARCH models of exchange rate volatility transmission across the important European Monetary System (EMS) currencies including the French franc, the German mark, the Italian lira, and the European Currency Unit. The models are estimated without imposing the common restriction of constant correlation on both daily and weekly data from April 1979–March 1997. Our results indicate the importance of checking for specification robustness in multivariate Generalized Autoregressive Conditional Heleroskedasticity (GARCH) modeling, we find that increased temporal aggregation reduces observed volatility transmission, and that the mark plays a dominant position in terms of volatility transmission.     

Volatility Forecasting in the Hang Seng Index using the GARCH Approach

The aim of this paper is to add to the literature on volatility forecasting using data from the Hong Kong stock market to determine if forecasts from GARCH based models can outperform simple historical averaging models. Overall, unlike previous studies we find that the GARCH models with non-Normal distributions show a robust volatility forecasting performance in comparison to the historical models. The results indicate that although not all models outperform simple historical averaging, the EGARCH based models, with non-normal conditional volatility, tend to produce more accurate out-of-sample forecasts using both standard measures of forecast accuracy and financial loss functions. In addition we test for asymmetric adjustment in the Hang Seng, finding strong evidence of asymmetries due to the domination of financial and property firms in this market.     

基于GARCH类模型的人民币汇率非线性依赖关系研究

利用三类不同结构的基本 GARCH 类模型对四个不同时间跨度上人民币汇率序列进行拟合和效度检验;并进一步结合窗口检验程序,借助相关性 C 统计量和双相关 H 统计量对实证对象的 GARCH 类非线性结构的稳定性及 GARCH 类模型中有关非线性相关的基本假设进行检验。结果表明,人民币汇率系统是一个典型的非线性动态复杂系统,人民币汇率序列中的 GARCH 类非线性结构表现出了非持续和瞬时性的特点。     

Multiperiod hedging in the presence of stochastic volatility

In this paper, we characterize the multiperiod minimum-risk hedge strategy within the stochastic volatility (SV) framework and compare it to other hedge strategies on the basis of hedging performance. Using crude oil markets as an example, we demonstrate that the SV model is appropriate in depicting price behaviour. However, ex ante and ex post comparisons indicate that the SV strategy is inferior to conventional hedging strategies. There is also evidence that the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) strategy may be better than the SV strategy, at least in terms of variance reduction.     

Forecasting the weekly time-varying beta of UK firms: GARCH models vs. Kalman filter method

This paper investigates the forecasting ability of three different Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models and the Kalman filter method. The three GARCH models applied are: bivariate GARCH, BEKK GARCH, and GARCH-GJR. Forecast errors based on 20 UK company's weekly stock return (based on time-varying beta) forecasts are employed to evaluate the out-of-sample forecasting ability of both the GARCH models and the Kalman method. Measures of forecast errors overwhelmingly support the Kalman filter approach. Among the GARCH models, GJR appears to provide somewhat more accurate forecasts than the two other GARCH models.     

Equity market integration in the NAFTA region: Evidence from unit root and cointegration tests

This study examines integration of the three participating equity markets before and after the 1993 passage of NAFTA based on daily, weekly, and monthly data. As expected, unit root tests for the overall period 1988-2001 and the two subperiods, 1988-1993 (pre-NAFTA) and 1994-2001 (post-NAFTA), indicate that stock prices are non-stationary but stock returns are generally stationary for all three markets for all three periods. However, daily, weekly, and monthly equity prices in the three NAFTA countries are cointegrated only for the post-NAFTA period. Similarly, US stock prices are more integrated with both Canadian and Mexican stock prices after the passage of NAFTA. This evidence of increased financial integration and co-movement in NAFTA equity markets after the passage of NAFTA has important implications for policymakers and managers.     

The timing ability and global performance of Tunisian mutual fund managers: A multivariate GARCH approach

It is well-established in the financial literature that the global performance of mutual fund managers is the result of two skills: selectivity and market timing. This paper examines whether the multivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) approach improves our perception of the global performance of fund managers compared with the unconditional approach and the conditional approach based on instruments. We find strong evidence that the multivariate GARCH method makes mutual fund performance looks better relative to the existent approaches, but this improvement in the global performance does not mean necessarily that mutual funds outperform traditional benchmarks. Indeed, mixed mutual funds yield neutral performance relative to benchmarks, whereas bond mutual funds generate significant positive global coefficients. The strong performance of bond fund managers comes from their ability to pick profitable bonds, not from their ability to time the market. Also, the empirical tests highlight that the best (worst) bond funds in the past remain at the top (bottom) of the ranking in the following years. These findings suggest that the Tunisian bond market presents strong opportunities for sophisticated investors.     

Detecting volatility persistence in GARCH models in the presence of the leverage effect

Most asset prices are subject to significant volatility. The arrival of new information is viewed as the main source of volatility. As new information is continually released, financial asset prices exhibit volatility persistence, which affects financial risk analysis and risk management strategies. This paper proposes a nonlinear regime-switching threshold generalized autoregressive conditional heteroskedasticity model which can be used to analyse financial data. The empirical results based on quasi-maximum likelihood estimation presented in this paper suggest that the proposed model is capable of extracting information about the sources of volatility persistence in the presence of the leverage effect.     

International linkage of the Russian market and the Russian financial crisis: A multivariate GARCH analysis

This study considers the linkage of the Russian equity market to the world market, examining the international transmission of the Russia's 1998 financial crisis utilizing the GARCH–BEKK model proposed by Engle and Kroner [Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Economet. Theor. 11, 122–150]. We find evidence of direct linkage between the Russian equity market with regards to returns and volatility, while the weakness of the linkage suggests that the Russian equity market was only partially integrated into the world market. At the time of the crisis, evidence of contagion is clear.     

Forecasting value‐at‐risk in oil prices in the presence of volatility shifts

Recent evidence suggests shifts (structural breaks) in the volatility of returns causes non‐normality by significantly increasing kurtosis. In this paper, we endogenously detect significant shifts in the volatility of oil prices and incorporate this information to estimate Value‐at‐Risk (VaR) to accurately forecast large declines in oil prices. Our out‐of‐sample performance results indicate that the model, which incorporates both time varying volatility (without making any distributional assumptions) and shifts in volatility, produces more accurate VaR forecasts than several benchmark methods. We make a timely contribution as the recent more frequent occurrences of unexpected large oil price declines has gained significant attention because of its substantial impact on the financial markets and the global economy.