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Author:Hjalmarsson, Erik 

Working Paper
A residual-based cointegration test for near unit root variables
Methods of inference based on a unit root assumption in the data are typically not robust to even small deviations from this assumption. In this paper, we propose robust procedures for a residual-based test of cointegration when the data are generated by a near unit root process. A Bonferroni method is used to address the uncertainty regarding the exact degree of persistence in the process. We thus provide a method for valid inference in multivariate near unit root processes where standard cointegration tests may be subject to substantial size distortions and standard OLS inference may lead to spurious results. Empirical illustrations are given by: (i) a re-examination of the Fisher hypothesis, and (ii) a test of the validity of the cointegrating relationship between aggregate consumption, asset holdings, and labor income, which has attracted a great deal of attention in the recent finance literature.
AUTHORS: Hjalmarsson, Erik; Osterholm, Par
DATE: 2007

Working Paper
Frequency of observation and the estimation of integrated volatility in deep and liquid financial markets
Using two newly available ultrahigh-frequency datasets, we investigate empirically how frequently one can sample certain foreign exchange and U.S. Treasury security returns without contaminating estimates of their integrated volatility with market microstructure noise. Using volatility signature plots and a recently-proposed formal decision rule to select the sampling frequency, we find that one can sample FX returns as frequently as once every 15 to 20 seconds without contaminating volatility estimates; bond returns may be sampled as frequently as once every 2 to 3 minutes on days without U.S. macroeconomic announcements, and as frequently as once every 40 seconds on announcement days. With a simple realized kernel estimator, the sampling frequencies can be increased to once every 2 to 5 seconds for FX returns and to about once every 30 to 40 seconds for bond returns. These sampling frequencies, especially in the case of FX returns, are much higher than those often recommended in the empirical literature on realized volatility in equity markets. We suggest that the generally superior depth and liquidity of trading in FX and government bond markets contributes importantly to this difference.
AUTHORS: Hjalmarsson, Erik; Chiquoine, Benjamin; Loretan, Mico; Chaboud, Alain P.
DATE: 2007

Working Paper
Testing for cointegration using the Johansen methodology when variables are near-integrated
We investigate the properties of Johansen's (1988, 1991) maximum eigenvalue and trace tests for cointegration under the empirically relevant situation of near-integrated variables. Using Monte Carlo techniques, we show that in a system with near-integrated variables, the probability of reaching an erroneous conclusion regarding the cointegrating rank of the system is generally substantially higher than the nominal size. The risk of concluding that completely unrelated series are cointegrated is therefore non-negligible. The spurious rejection rate can be reduced by performing additional tests of restrictions on the cointegrating vector(s), although it is still substantially larger than the nominal size.
AUTHORS: Hjalmarsson, Erik; Osterholm, Par
DATE: 2007

Working Paper
The Stambaugh bias in panel predictive regressions
This paper analyzes predictive regressions in a panel data setting. The standard fixed effects estimator suffers from a small sample bias, which is the analogue of the Stambaugh bias in time-series predictive regressions. Monte Carlo evidence shows that the bias and resulting size distortions can be severe. A new bias-corrected estimator is proposed, which is shown to work well in finite samples and to lead to approximately normally distributed t-statistics. Overall, the results show that the econometric issues associated with predictive regressions when using time-series data to a large extent also carry over to the panel case. The results are illustrated with an application to predictability in international stock indices.
AUTHORS: Hjalmarsson, Erik
DATE: 2007

Working Paper
Interpreting long-horizon estimates in predictive regressions
This paper analyzes the asymptotic properties of long-horizon estimators under both the null hypothesis and an alternative of predictability. Asymptotically, under the null of no predictability, the long-run estimator is an increasing deterministic function of the short-run estimate and the forecasting horizon. Under the alternative of predictability, the conditional distribution of the long-run estimator, given the short-run estimate, is no longer degenerate and the expected pattern of coefficient estimates across horizons differs from that under the null. Importantly, however, under the alternative, highly endogenous regressors, such as the dividend-price ratio, tend to deviate much less than exogenous regressors, such as the short interest rate, from the pattern expected under the null, making it more difficult to distinguish between the null and the alternative.
AUTHORS: Hjalmarsson, Erik
DATE: 2008

Working Paper
What drives volatility persistence in the foreign exchange market?
We analyze the factors driving the widely-noted persistence in asset return volatility using a unique dataset on global euro-dollar exchange rate trading. We propose a new simple empirical specification of volatility, based on the Kyle-model, which links volatility to the information flow, measured as the order flow in the market, and the price sensitivity to that information. Through the use of high-frequency data, we are able to estimate the time-varying market sensitivity to information, and movements in volatility can therefore be directly related to movements in two observable variables, the order flow and the market sensitivity. The empirical results are very strong and show that the model is able to explain almost all of the long-run variation in volatility. Our results also show that the variation over time of the market's sensitivity to information plays at least as important a role in explaining the persistence of volatility as does the rate of information arrival itself. The econometric analysis is conducted using novel estimation techniques which explicitly take into account the persistent nature of the variables and allow us to properly test for long-run relationships in the data.
AUTHORS: Howorka, Edward; Berger, David W.; Chaboud, Alain P.; Hjalmarsson, Erik
DATE: 2006

Working Paper
Estimation of average local-to-unity roots in heterogenous panels
This paper considers the estimation of average autoregressive roots-near-unity in panels where the time-series have heterogenous local-to-unity parameters. The pooled estimator is shown to have a potentially severe bias and a robust median based procedure is proposed instead. This median estimator has a small asymptotic bias that can be eliminated almost completely by a bias correction procedure. The asymptotic normality of the estimator is proved. The methods proposed in the paper provide a useful way of summarizing the persistence in a panel data set, as well as a complement to more traditional panel unit root tests.
AUTHORS: Hjalmarsson, Erik
DATE: 2005

Working Paper
Jackknifing stock return predictions
We show that the general bias reducing technique of jackknifing can be successfully applied to stock return predictability regressions. Compared to standard OLS estimation, the jackknifing procedure delivers virtually unbiased estimates with mean squared errors that generally dominate those of the OLS estimates. The jackknifing method is very general, as well as simple to implement, and can be applied to models with multiple predictors and overlapping observations. Unlike most previous work on inference in predictive regressions, no specific assumptions regarding the data generating process for the predictors are required. A set of Monte Carlo experiments show that the method works well in finite samples and the empirical section finds that out-of-sample forecasts based on the jackknifed estimates tend to outperform those based on the plain OLS estimates. The improved forecast ability also translates into economically relevant welfare gains for an investor who uses the predictive regression, with jackknifed estimates, to time the market.
AUTHORS: Chiquoine, Benjamin; Hjalmarsson, Erik
DATE: 2008

Working Paper
Predicting global stock returns
I test for stock return predictability in the largest and most comprehensive data set analyzed so far, using four common forecasting variables: the dividend- and earnings-price ratios, the short interest rate, and the term spread. The data contain over 20,000 monthly observations from 40 international markets, including 24 developed and 16 emerging economies. In addition, I develop new methods for predictive regressions with panel data. Inference based on the standard fixed effects estimator is shown to suffer from severe size distortions in the typical stock return regression, and an alternative robust estimator is proposed. The empirical results indicate that the short interest rate and the term spread are fairly robust predictors of stock returns in developed markets. In contrast, no strong or consistent evidence of predictability is found when considering the earnings- and dividend-price ratios as predictors.
AUTHORS: Hjalmarsson, Erik
DATE: 2008

Working Paper
Inference in Long-Horizon Regressions
I develop new results for long-horizon predictive regressions with overlapping observations. I show that rather than using auto-correlation robust standard errors, the standard t-statistic can simply be divided by the square root of the forecasting horizon to correct for the effects of the overlap in the data; this is asymptotically an exact correction and not an approximate result. Further, when the regressors are persistent and endogenous, the long-run OLS estimator suffers from the same problems as does the short-run OLS estimator, and it is shown how similar corrections and test procedures as those proposed for the short-run case can also be implemented in the long-run. New results for the power properties of long-horizon tests are also developed. The theoretical results are illustrated with an application to long-run stock-return predictability, where it is shown that once correctly sized tests are used, the evidence of predictability is generally much stronger at short rather than long horizons.
AUTHORS: Hjalmarsson, Erik
DATE: 2006

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