Tae Hwy Lee

Pitfalls in Testing for Long Run Relationships

Abstract This paper analyzes the robustness of the two most commonly used cointegration tests: the single equation based test of Engle and Granger (EG) and the system based test of Johansen. We show analytically and numerically several important situations where the Johansen LR tests tend to find spurious cointegration with probability approaching one asymptotically. The situations investigated are of two types. The first one corresponds to variables that have long-memory properties and a trending behavior, but they are not pure I(1) processes although they are difficult to tell from I(1) with standard unit root tests. The second corresponds to I(1) variables whose VAR representation has a singular or near-singular error covariance matrix. In most of the situations investigated in this paper, EG test is more robust than Johansen LR tests. This paper shows that a proper use of the LR test in applied cointegration analysis requires a deeper data analysis than the standard unit root test. We conclude by recommending to use both tests (EG and Johansen) to test for cointegration in order to avoid or to discover a pitfall.

Cointegration tests with conditional heteroskedasticity

Abstract We examine the performance of Johansens (1988) likelihood ratio tests for cointegration in the presence of GARCH and compare with other cointegration tests. The tests tend to overreject the null hypothesis of no cointegration in favor of finding cointegration, but the problem is generally not very serious.

Spread and volatility in spot and forward exchange rates

Abstract This paper is concerned with modeling the conditional heteroscedasticity of the prediction error of foreign exchange rates. As spot and forward rates are cointegrated we use a system of error correction models for mean prediction. To predict the variance we use a vibariate generalized autoregressive conditional heteroscedasticity (GARCH) model as a function of the spread. Using daily series for seven currencies, we find that unmodeled conditional heteroscedasticity by GARCH can generally be explained by the squared spread. This indicates that as the spread is bigger the exchange rates are more volatile. (JEL F31, C32).

To Combine Forecasts or to Combine Information

When the objective is to forecast a variable of interest but with many explanatory variables available, one could possibly improve the forecast by carefully integrating them. There are generally two directions one could proceed: combination of forecasts (CF) or combination of information (CI). CF combines forecasts generated from simple models each incorporating a part of the whole information set, while CI brings the entire information set into one super model to generate an ultimate forecast. Through linear regression analysis and simulation, we show the relative merits of each, particularly the circumstances where forecast by CF can be superior to forecast by CI, when CI model is correctly specified and when it is misspecified, and shed some light on the success of equally weighted CF. In our empirical application on prediction of monthly, quarterly, and annual equity premium, we compare the CF forecasts (with various weighting schemes) to CI forecasts (with principal component approach mitigating the problem of parameter proliferation). We find that CF with (close to) equal weights is generally the best and dominates all CI schemes, while also performing substantially better than the historical mean.

The effect of aggregation on nonlinearity

This paper investigates the interaction between aggregation and nonlinearity through a monte carlo study. Various tests for neglected nonlinearity are used to compare the power of the tests for different nonlinear models to different levels of aggregation. Three types of aggregation, namely, cross-sectional aggregation, temporal aggregation and systematic sampling are considered. Aggregation is inclined to simplify nonlinearity. The degree to which nonlinearity is reduced depends on the importance of common factor and extent of the aggregation. The effect is larger when the size of common factor is smaller and when the extent of the aggregation is larger.

The international transmission of information in Eurodollar futures markets: a continuously trading market hypothesis

Abstract This paper studies the transmission of information in three Eurodollar futures markets, the IMM, SIMEX and LIFFE. The results show that relevant information is revealed during the trading hours of the IMM and LIFFE, but not the SIMEX. The interest rates of the three markets are cointegrated with a single common stochastic trend. Granger-causality runs from the market that is placed in the last trading order within 24 hours in the vector error correction model and this causal relationship is shorter than one day. An approach of variance decomposition and impulse response functions exploring the common factor in the cointegration system is employed. Analogous to the causality results, the common factor is driven by the last trading market in the 24-hour trading sequence. Specifically, each market, while it is trading, impounds all the information and rides on the common stochastic trend. The overall results suggest that these three markets can be considered one continuously trading market.

International linkages in Nikkei Stock Index futures markets

Abstract This paper analyzes the linkages and information transmission of similar Nikkei stock index futures contracts traded on three international exchanges, the OSE, SIMEX, and CME. Comparisons between the trading and nontrading time variances within individual markets and across markets indicate that relevant information is revealed during the trading hours of the OSE and SIMEX, but not the CME. An approach of variance decomposition and impulse response functions exploring the common stochastic trend in the cointegration system is employed. The common factor is found to be simply driven by the last trading market in the 24-hour trading sequence. Specifically, each market, while it is trading, impounds all the information that will affect other markets, and rides on the common stochastic trend. Granger-causality also runs from the market(s) that is placed in the last trading order within 24 hours in the vector error correction model but this causal relationship is shorter than one day. On balance, the three markets are informationally efficient on a daily basis.

Nonparametric Bootstrap Tests for Neglected Nonlinearity in Time Series Regression Models

Various nonparametric kernel regression estimators are presented, based on which we consider two nonparametric tests for neglected nonlinearity in time series regression models. One of them is the goodness-of-fit test of Cai, Fan and Yao (2000) and another is the nonparametric conditional moment test by Li and Wang (1998) and Zheng (1996). Bootstrap procedures are used for these tests and their performance is examined via monte carlo experiments, especially with conditionally heteroskedastic errors.

On the robustness of cointegration tests when series are fractionally intergrated

This paper shows that when series are fractionally integrated, but unit root tests wrongly indicate that they are I(1), Johansen likelihood ratio (LR) tests tend to find too much spurious cointegration, while the Engle-Granger test presents a more robust performance. This result holds asymptotically as well as infinite samples. The different performance of these two methods is due to the fact that they are based on different principles. The Johansen procedure is based on maximizing correlations (canonical correlation) while Engle-Granger minimizes variances (in the spirit of principal components).

Money-Income Granger-Causality in Quantiles

The causal relationship between money and income (output) has been an important topic and has been extensively studied. However, those empirical studies are almost entirely on Granger-causality in the conditional mean. Compared to conditional mean, conditional quantiles give a broader picture of an economy in various scenarios. In this paper, we explore whether forecasting conditional quantiles of output growth can be improved using money growth information. We compare the check loss values of quantile forecasts of output growth with and without using past information on money growth, and assess the statistical significance of the loss-differentials. Using U.S. monthly series of real personal income or industrial production for income and output, and M1 or M2 for money, we find that out-of-sample quantile forecasting for output growth is significantly improved by accounting for past money growth information, particularly in tails of the output growth conditional distribution. On the other hand, money-income Granger-causality in the conditional mean is quite weak and unstable. These empirical findings in this paper have not been observed in the money-income literature. The new results of this paper have an important implication on monetary policy, because they imply that the effectiveness of monetary policy has been under-estimated by merely testing Granger-causality in conditional mean. Money does Granger-cause income more strongly than it has been known and therefore information on money growth can (and should) be more utilized in implementing monetary policy.