Working Papers Series
Papers below are in pdf.
J. Isaac Miller
WP 08-10
Crude Oil and Stock Markets: Stability, Instability, and Bubbles
J. Isaac Miller & Ronald A. Ratti
We analyze the long-run relationship between the world price of crude oil and international stock markets over 1971:1-2008:3 using a cointegrated vector error correction model with additional regressors. Allowing for endogenously identified breaks in the cointegrating and error correction matrices, we find evidence for breaks after 1980:5, 1988:1, and 1999:9. We find a clear long-run relationship between these series for six OECD countries for 1971:1-1980.5 and 1988:2-1999.9, suggesting that stock market indices respond negatively to increases in the oil price in the long run. During 1980.6-1988.1, we find relationships that are not statistically significantly different from either zero or from the relationships of the previous period. The expected negative long-run relationship appears to disintegrate after 1999.9. This finding supports a conjecture of change in the relationship between real oil price and real stock prices in the last decade compared to earlier years, which may suggest the presence of several stock market bubbles and/or oil price bubbles since the turn of the century.
JEL Codes: C13, C32, Q43
Keywords: crude oil, stock market prices, cointegrated VECM, structural stability, stock market bubble, oil price bubble
Forthcoming in Energy Economics (2009), pp. 559-568
WP 08-03
Testing the Bounds: Empirical Behavior of Target Zone Fundamentals
J. Isaac Miller
Standard target zone exchange rate models are based on nonlinear functions of an unobserved economic fundamental, which is assumed to be bounded, similarly to the target zone exchange rates themselves. A violation of this key assumption is a basic structural reason for model failure. Using a novel estimation and testing strategy, we show it is also a testable assumption. Our empirical results cast serious doubt on its validity in practice, providing a primitive reason for well-documented rejections of the basic model. Model failure from this violation is robust to otherwise ideal circumstances (e.g., perfect credibility).
JEL Codes: F3, C5
Keywords: target zone exchange rates, economic fundamental, unscented Kalman filter, rescaled range statistic
WP 08-01
Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory
J. Isaac Miller and Joon Y. Park
We consider nonlinear transformations of random walks driven by thick-tailed innovations that may have infinite means or variances. These three nonstandard characteristics: nonlinearity, nonstationarity, and thick tails interact to generate a spectrum of asymptotic autocorrelation patterns consistent with long-memory processes. Such autocorrelations may decay very slowly as the number of lags increases or may not decay at all and remain constant at all lags. Depending upon the type of transformation considered and how the model error is speci- fied, the autocorrelation functions are given by random constants, deterministic functions that decay slowly at hyperbolic rates, or mixtures of the two. Such patterns, along with other sample characteristics of the transformed time series, such as jumps in the sample path, excessive volatility, and leptokurtosis, suggest the possibility that these three ingredients are involved in the data generating processes of many actual economic and financial time series data. In addition to time series characteristics, we explore nonlinear regression asymptotics when the regressor is observable and an alternative regression technique when it is unobservable. To illustrate, we examine two empirical applications: wholesale electricity price spikes driven by capacity shortfalls and exchange rates governed by a target zone.
Revised version forthcoming in Journal of Econometrics
JEL Codes: C22, C16
Keywords: persistency in memory, nonlinear transformations, random walks,
thick tails, stable distributions, wholesale electricity prices, target zone exchange rates
WP 07-22
Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error
J. Isaac Miller
We consider a cointegrating regression in which the integrated regressors are messy in the sense that they contain data that may be mismeasured, missing, observed at mixed frequencies, or have other irregularities that cause the econometrician to observe them with mildly nonstationary noise. Least squares estimation of the cointegrating vector is consistent. Existing prototypical variance-based estimation techniques, such as canonical cointegrating regression (CCR), are both consistent and asymptotically mixed normal. This result is robust to weakly dependent but possibly nonstationary disturbances.
JEL Codes: C13, C14, C32
Keywords: cointegration, canonical cointegrating regression, near-epoch dependence, messy data, missing data, mixed-frequency data, measurement error, interpolation
WP 06-09
A Random Coefficients Autoregressive Model with Exogenously-Driven Stochastic Unit Roots
J. Isaac Miller
We develop a random coefficients autoregressive (RCA) model with time-varying coefficients generated by a bounded nonlinear function of an exogenous time series that may be a mixingale or integrated. Moreover, we allow for exogenously-driven heteroskedasticity in the error term. By restricting the range of the function essentially to the unit interval, we show that the two series of autoregressive coefficients and variances of such a model are covariance stationary, even though these series may be nonergodic. Time series driven by such a data generating process are stationary, but may have (stochastic) unit or near-unit roots over periods of time. Under appropriate assumptions, we show that maximum likelihood estimation yields asymptotically normal or mixed normal parameter estimates. A data generating process of this form may engender commonly observed time series characteristics that defy the simple I(0)-I(1) dichotomy, but is more structural in nature than statistical I(d) models. Moreover, this approach provides a nonspurious way to model relationships between a nonstationary and a stationary time series. The utility of the proposed econometric model is demonstrated with an empirical application, in which inflation drives the autoregressive coefficient of interest rate volatility.
JEL Codes: C13, C22, C32
Keywords: random coefficients autoregressive models, stochastic unit roots, nonlinear transformations, mixingales, near-epoch dependent processes, integrated processes, interest rate volatility
WP 06-04
Testing for Purchasing Power Parity Under a Target Zone Exchange Rate Regime
J. Isaac Miller
Using a simple flexible price monetary model combined with a standard target zone exchange rate model, we show theoretically that when the latent economic fundamental is integrated (as is generally assumed) the real exchange rate (RER) between currencies whose nominal exchange rates are governed by a target zone regime generally cannot exhibit short memory (mean reversion). Typical cointegration-based tests for long-run purchasing power parity (PPP) are therefore inherently misspecified. We explain how the fundamental in such models may be estimated using nonlinear filtering techniques, such as the extended Kalman filter (EKF). We then use the EKF to estimate the latent fundamental for Denmark and the Euro area. Finding empirical evidence to support the integratedness of this fundamental, our theoretical results thus imply that long-run PPP between Denmark and the Euro area cannot hold, and empirical tests on this RER support this result.
JEL Codes: C13, C22, C32
Keywords: target zone exchange rates, purchasing power parity, nonlinear functions of integrated time series, nonlinear filtering, extended Kalman filter
WP 05-07
Extracting a Common Stochastic Trend: Theory with Some Applications
Yoosoon Chang, J. Isaac Miller and Joon Y. Park
This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of such models -- those with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of inference is valid for this class of models. The models we explicitly consider comprise a special -- yet useful -- class of models that may be employed to extract the common stochastic trend from multiple integrated time series. Such models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of this class of models extracting a common stochastic trend from three sets of time series involving short- and long-term interest rates, stock return volatility and trading volume, and Dow Jones stock prices.
JEL Codes: C13, C32
Keywords: state space model, Kalman filter, common stochastic trend, maximum likelihood estimation, permanent-transitory decomposition, interest rates, volume and volatility, stock price index
Published in Journal of Econometrics 150 (2009), pp. 231-247