Cointegrating MiDaS Regressions and a MiDaS Test

This paper introduces cointegrating mixed data sampling (CoMiDaS) regressions, generalizing nonlinear MiDaS regressions in the extant literature. Under a linear mixed-frequency data-generating process, MiDaS regressions provide a parsimoniously parameterized nonlinear alternative when the linear forecasting model is over-parameterized and may be infeasible. In spite of potential correlation of the error term both serially and with the regressors, I find that nonlinear least squares consistently estimates the minimum mean-squared forecast error parameter vector. The exact asymptotic distribution of the difference may be non-standard. I propose a novel testing strategy for nonlinear MiDaS and CoMiDaS regressions against a general but possibly infeasible linear alternative. An empirical application to nowcasting global real economic activity using monthly covariates illustrates the utility of the approach.cointegration, mixed-frequency series, mixed data sampling

Testing the Bounds: Empirical Behavior of Target Zone Fundamentals

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).target zone exchange rates, economic fundamental, unscented Kalman filter, rescaled range statistic

Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error

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 variancebased 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.cointegration, canonical cointegrating regression, near-epoch dependence, messy data, missing data, mixed-frequency data, measurement error, interpolation

Conditionally Efficient Estimation of Long-run Relationships Using Mixed-frequency Time Series

I analyze efficient estimation of a cointegrating vector when the regressand is observed at a lower frequency than the regressors. Previous authors have examined the effects of specific temporal aggregation or sampling schemes, finding conventionally efficient techniques to be efficient only when both the regressand and the regressors are average sampled. Using an alternative method for analyzing aggregation under more general weighting schemes, I derive an efficiency bound that is conditional on the type of aggregation used on the regressand and differs from the unconditional bound defined by the infeasible full-information high-frequency data-generating process. I modify a conventional estimator, canonical cointegrating regression (CCR), to accommodate cases in which the aggregation weights are either unknown or known. In the unknown case, the correlation structure of the error term generally confounds identification of the conditionally efficient weights. In the known case, the correlation structure may be utilized to offset the potential information loss from aggregation, resulting in a conditionally efficient estimator. Efficiency is illustrated using a simulation study and an application to estimating a gasoline demand equation.cointegration, canonical cointegrating regression, temporal aggregation, mixed-frequency series, mixed data sampling, price elasticity of gasoline demand

Crude Oil and Stock Markets: Stability, Instability, and Bubbles

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.crude oil, stock market prices, cointegrated VECM, structural stability, stock market bubble, oil price bubble

Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory

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.persistency in memory, nonlinear transformations, random walks, thick tails, stable distributions, wholesale electricity prices, target zone exchange rates

Testing the Bounds: Empirical Behavior of Target Zone Fundamentals

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)

Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory

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

Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error

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

A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels

Reproduced with permission from the Journal of Time Series Econometrics. doi: 10.2202/1941-1928.1057A test for the rank of a vector error correction model (VECM) or panel VECM based on the well-known trace test is proposed. The proposed test employs instrumental variables (IV's)generated by a class of nonlinear functions of the estimated stochastic trends of the VECM under the null. The test improves on the standard trace test by replacing the non-standard critical values with chi-squared critical values. Extending the result to the panel VECM case, the test is robust to cross-sectional correlation of the disturbances. The nonlinear IV rank test also extends earlier research on nonlinear IV unit root tests. However, the optimal instrument in the univariate case is not admissible in the more general multivariate case. The chi-squared result suggests that IV tests may be used to replace limits of other standard tests with integrated time series that are given by nonstandard stochastic integrals, even without a panel with which to pool test statistics