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23 industrial countries account for cross-sectional allowing for cross-sectional alternative AR(p asymptotic critical values autocovariances best fitting common benchmark currency covariance matrix cross-sectional dependence arising current float deviations from PPP Discussion Paper distribution Econometrics empirical equilibrium real exchange error covariance matrix exchange rate regimes finite sample heteroscedasticity International Money Jean Tirole Journal of International Koedijk Levin Lothian LR cov MacDonald Money and Finance NH test non-parametric NULL OF STATIONARY null of unit Nyblom and Harvey Panel Data panel of real panel studies panel unit root panel version parametric correction Parametric estimation PPP serves PPP studies purchasing power parity pwr2 pwr2 p-val real exchange rates real rate regime changes Rogoff run covariance matrix sample critical values sample statistic serial correlation simulations small sample critical stationarity stationary real exchange support for PPP Table test for stationarity testing of PPP treatment of serial unit root tests