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11
Generalized Autoregressive Conditional Heteroskedasticity
 JOURNAL OF ECONOMETRICS
, 1986
"... A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametri ..."
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Cited by 1023 (18 self)
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A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.
A Nonlocal Perspective on the Power Properties of the CUSUM and CUSUM of Squares Tests for Structural Change
, 2007
"... We consider the power properties of the CUSUM and CUSUM of squares tests in the presence of a onetime change in the parameters of a linear regression model. A result due to Ploberger and Krämer (1990) is that the CUSUM of squares test has only trivial asymptotic local power in this case, while the ..."
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Cited by 3 (1 self)
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We consider the power properties of the CUSUM and CUSUM of squares tests in the presence of a onetime change in the parameters of a linear regression model. A result due to Ploberger and Krämer (1990) is that the CUSUM of squares test has only trivial asymptotic local power in this case, while the CUSUM test has nontrivial local asymptotic power unless the change is orthogonal to the mean regressor. The main theme of the paper is that such conclusions obtained from a local asymptotic framework are not reliable guides to what happens in finitesamples. Theapproachwetakeisto derive expansions of the test statistics that retain terms related to the magnitude of the change under the alternative hypothesis. This enables us to analyze what happens for nonlocal to zero breaks. Our theoretical results are able to explain how the power function of the tests can be drastically different depending on whether one deals with a static regression with uncorrelated errors, a static regression with correlated errors, a dynamic regression with lagged dependent variables, or whether a correction for nonNormality is applied in the case of the CUSUM of squares. We discuss in which cases the tests are subject to a nonmonotonic power function that goes to zero as the magnitude of the change increases, and uncover some curious properties. All theoretical results are verified to yield good guides to the finite sample power through simulation experiments. We finally highlight the practical importance of our results.
Does an Intertemporal Tradeoff between Risk and Return Explain Mean Reversion in Stock Prices?
, 2000
"... : When volatility feedback is taken into account, there is strong evidence of a positive tradeoff between stock market volatility and expected returns on a market portfolio. In this paper, we ask whether this intertemporal tradeoff between risk and return is responsible for the reported evidence ..."
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Cited by 3 (0 self)
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: When volatility feedback is taken into account, there is strong evidence of a positive tradeoff between stock market volatility and expected returns on a market portfolio. In this paper, we ask whether this intertemporal tradeoff between risk and return is responsible for the reported evidence of mean reversion in stock prices. There are two relevant findings. First, price movements not related to the effects of Markovswitching market volatility are largely unpredictable over long horizons. Second, timevarying parameter estimates of the longhorizon predictability of stock returns reject any inherent mean reversion in favour of behaviour implicit in the historical tradeoff between risk and return. JEL classification: G12; G14 Keywords: Volatility Feedback; Mean Reversion; Markov Switching; TimeVarying Parameter 1 1. Introduction More than a decade has passed since Fama and French (1988) and Poterba and Summers (1988) reported that price movements for market portfolios...
TimeVariation and Structural Change in the Forward Discount: Implications for the Forward Rate Unbiasedness Hypothesis
, 2005
"... It is a well accepted empirical result that forward exchange rate unbiasedness is rejected in tests using the “differences regression ” of the change in the logarithm of the spot exchange rate on the forward discount. The result is referred to in the International Finance literature as the forward d ..."
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Cited by 2 (0 self)
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It is a well accepted empirical result that forward exchange rate unbiasedness is rejected in tests using the “differences regression ” of the change in the logarithm of the spot exchange rate on the forward discount. The result is referred to in the International Finance literature as the forward discount puzzle. Competing explanations of the negative bias of the forward discount coefficient include the possibilities of a timevarying risk premium or the existence of “peso problems. ” We offer an alternative explanation for this anomaly. One of the stylized facts about the forward discount is that it is highly persistent. We model the forward discount as an AR(1) process and argue that its persistence is exaggerated due to the presence of structural breaks. We document the temporal variation in persistence, using a timevarying parameter specification for the AR(1) model, with Markovswitching disturbances. We also show, using a stochastic multiple break model, suggested recently by Bai and Perron (1998), that for the G7 countries, with the exception of Japan, the forward discount persistence is substantially less, if one allows for multiple structural breaks in the mean of the process. These breaks could be identified as monetary shocks to the central bank’s reaction function, as discussed in Eichenbaum and Evans (1995). Using Monte Carlo simulations we show that if we do not account for structural breaks which are present in the forward discount process, the forward discount coefficient in the “differences regression ” is severely biased downward, away from its true value of 1. The authors would like to thank Charles Engel and the participants of the macroeconomics seminar at the New York Federal Reserve Bank for helpful comments and suggestions and Jushan Bai for generously providing the GAUSS code to estimate the multiple break models. The usual disclaimer applies
Human Brain Mapping 6:403–408(1998) � Dynamic Changes in Effective Connectivity Characterized by Variable Parameter Regression and Kalman Filtering
"... Abstract: Attention to visual motion can increase the responsiveness of the motionselective cortical area V5 and the posterior parietal cortex. We addressed attentional modulation of effective connectivity using variable parameter regression and functional magnetic resonance imaging. We present dat ..."
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Abstract: Attention to visual motion can increase the responsiveness of the motionselective cortical area V5 and the posterior parietal cortex. We addressed attentional modulation of effective connectivity using variable parameter regression and functional magnetic resonance imaging. We present data from a single subject scanned under identical stimulus conditions (visual motion) while varying only the attentional component of the task. Variable parameter regression of the influence of V5 on PP revealed increased effective connectivity during attention to visual motion. With this dynamic measure of effective connectivity we were able to make inferences about the source of modulation by looking for regions that predicted the observed changes in connectivity. Using an ordinary regression analysis, we showed that activity in the prefrontal cortex could explain these changes and was sufficient to account for these modulatory influences on connections in the dorsal visual pathway. Hum. Brain Mapping 6:403–408, 1998. � 1998 WileyLiss, Inc. Key words: effective connectivity; fMRI; attention; Kalman filter; variable parameter regression
The Search for a Stable Money Demand Equation
"... Quarterly Review vol. 4, no. 3 This publication primarily presents economic research aimed at improving policymaking by the Federal Reserve System and other governmental authorities. ..."
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Quarterly Review vol. 4, no. 3 This publication primarily presents economic research aimed at improving policymaking by the Federal Reserve System and other governmental authorities.
Journal qf‘hternational Monell and Finance (1993). 12, 182l 94 Exchange rate risk premiums
"... A state space model which allows for the covariation of risk premiums and unexpected rates of depreciation is used to study exchange rate risk premiums. We find that exchange rate risk premiums have a high degree of persistence and the covariance of risk premiums and unexpected rates of depreciation ..."
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A state space model which allows for the covariation of risk premiums and unexpected rates of depreciation is used to study exchange rate risk premiums. We find that exchange rate risk premiums have a high degree of persistence and the covariance of risk premiums and unexpected rates of depreciation is negative. Regressions of the estimated risk premium on its determinants implied by the equilibrium model of Lucas (1982) show limited support for the model. (JEL F31). The presence of risk premiums in foreign exchange markets has significant implications for models of exchange rate determination, effectiveness of sterilized intervention, and individuals ’ investment decisions. Various approaches have been advanced to model and investigate foreign exchange rate risk premiums. Earlier efforts on the search for risk premiums in foreign exchange markets show little support for the risk premium hypothesis and are reviewed in, for example,
Break Tests
, 2009
"... The occurrence of abnormal returns before unscheduled announcements is usually identified with informed price movements. Therefore, the detection of these observations beyond the range of returns due to the normal daytoday activity of financial markets is a concern for regulators monitoring the ri ..."
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The occurrence of abnormal returns before unscheduled announcements is usually identified with informed price movements. Therefore, the detection of these observations beyond the range of returns due to the normal daytoday activity of financial markets is a concern for regulators monitoring the right functioning of financial markets and for investors concerned about their investment portfolios. In this article we introduce a novel method to detect informed price movements via structural break tests for the intercept of an extended CAPM model describing the risk premium of financial returns. These tests are based on the use of a Ustatistic type process that is sensitive to detecting changes in the intercept that occur very early in the evaluation period and that can be used to construct a consistent estimator of the timing of the change. As a byproduct, we show that estimators of the timing of change constructed from standard CUSUM statistics are inconsistent and therefore fail to provide useful information about the presence of informed price movements.
Limited Efficient Tests for General Persistent Time Variation in Regression Coefficients
 REVIEW OF ECONOMIC STUDIES
, 2006
"... There are a large number of tests for instability or breaks in coefficients in regression models designed for different possible departures from the stable model. We make two contributions to this literature. First, we consider a large class of persistent breaking processes that lead to asymptotical ..."
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There are a large number of tests for instability or breaks in coefficients in regression models designed for different possible departures from the stable model. We make two contributions to this literature. First, we consider a large class of persistent breaking processes that lead to asymptotically equivalent efficient tests. Our class allows for many or relatively few breaks, clustered breaks, regularly occurring breaks, or smooth transitions to changes in the regression coefficients. Thus, asymptotically nothing is gained by knowing the exact breaking process of the class. Second, we provide a test statistic that is simple to compute, avoids any need for searching over high dimensions when there are many breaks, is valid for a wide range of datagenerating processes and has good power and size properties even in heteroscedastic models.