J. Isaac Miller

Testing for Cointegration with Temporally Aggregated and Mixed‐Frequency Time Series

We examine the effects of mixed sampling frequencies and temporal aggregation on standard tests for cointegration. We find that the effects of aggregation on the size of the tests may be severe. Matching sampling schemes of all series generally reduces size, and the nominal size is obtained when all series are skip sampled in the same way. When matching all schemes is not feasible, but when some high-frequency data are available, we show how to use mixed-frequency models to improve the size distortion of the tests. We test stock prices and dividends for cointegration as an empirical demonstration.

Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory☆

In this paper, we consider nonlinear transformations of random walks driven by thick-tailed innovations with infinite means or variances. In particular, we show how nonlinearity, nonstationarity, and thick tails interact to generate persistency in memory, and we clearly demonstrate that this triad may generate a broad spectrum of persistency patterns. Time series generated by nonlinear transformations of random walks with thick-tailed innovations have asymptotic autocorrelations that decay very slowly as the number of lags increases or do not even decay at all and remain constant at all lags. Depending upon the type of transformation considered and how the model error is specified, they are given by random constants, deterministic functions which decay slowly at polynomial rates, or mixtures of the two. These autocorrelation patterns, along with other sample characteristics of the transformed time series, suggest the possibility that these three ingredients are involved in the data generating processes for many actual economic and financial time series data. We also discuss nonlinear regression asymptotics when the regressor is observable and an alternative regression technique when it is unobservable. We use our model to analyze two empirical applications: exchange rates governed by a target zone and electricity price spikes driven by capacity shortfalls.

Conditionally Efficient Estimation of Long-Run Relationships Using Mixed-Frequency Time Series

I analyze efficient estimation of a cointegrating vector when the regressand and regressor are observed at different frequencies. 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 low-frequency series and differs from the unconditional bound defined by the full-information high-frequency data-generating process, which is infeasible due to aggregation of at least one series. I modify a conventional estimator, canonical cointegrating regression (CCR), to accommodate cases in which the aggregation weights are known. The correlation structure may be utilized to offset the potential information loss from aggregation, resulting in a conditionally efficient estimator. In the case of unknown weights, the correlation structure of the error term generally confounds identification of conditionally efficient weights. Efficiency is illustrated using a simulation study and an application to estimating a gasoline demand equation.

LONG-TERM OIL PRICE FORECASTS: A NEW PERSPECTIVE ON OIL AND THE MACROECONOMY

We examine how future real GDP growth relates to changes in the forecasted long-term average of discounted real oil prices and to changes in unanticipated fluctuations of real oil prices around the forecasts. Forecasts are conducted using a state-space oil market model, in which global real economic activity and real oil prices share a common stochastic trend. Changes in unanticipated fluctuations and changes in the forecasted long-term average of discounted real oil prices sum to real oil price changes. We find that these two components have distinctly different relationships with future real GDP growth. Positive and negative changes in the unanticipated fluctuations of real oil prices correlate with asymmetric responses of future real GDP growth. In comparison, changes in the forecasted long-term average are smaller in magnitude but are more influential on real GDP. Persistent upward revisions of forecasts in the 2000s had a substantial negative impact on real GDP growth, according to our estimates.

Cointegrating regressions with messy regressors and an application to mixed‐frequency series

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, are both consistent and asymptotically mixed normal. This result is robust to weakly dependent but possibly nonstationary disturbances.

On the Size Distortion from Linearly Interpolating Low-frequency Series for Cointegration Tests

We analyze the sizes of standard cointegration tests applied to data subject to linear interpolation, discovering evidence of substantial size distortions induced by the interpolation. We propose modifications to these tests to effectively eliminate size distortion from such tests conducted on data interpolated from end-of-period sampled low-frequency series. Our results generally do not support linear interpolation when alternatives such as aggregation or mixed-frequency-modified tests are possible.

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

A 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 (IVs) 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.

Implementing Residual‐Based KPSS Tests for Cointegration with Data Subject to Temporal Aggregation and Mixed Sampling Frequencies

We show how different data types (stocks and flows) and temporal aggregation affect the size and power of the dynamic ordinary least squares residual‐based Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test of the null of cointegration. Size may be more effectively controlled by setting the minimum number of leads equal to one – as opposed to zero – when selecting the lag/lead order of the dynamic ordinary least squares regression using aggregated data, but at a cost to power. If high‐frequency data for one or more series are available – that is, the model has mixed sampling frequencies – we show how to effectively utilize the high‐frequency data to increase power while controlling size.

Modeling and Extrapolating Wheat Producer Support Using Income and Other Factors

Using wheat market support data from 55 countries for 1961–2011 from the World Bank Agricultural Distortion database, we develop a fixed effect model that shows a more complicated, nonlinear relationship between income and wheat support and its components than previously realised. We find that income generally has a greater effect on border market price support than on domestic price support. Moreover, the difference between these types of support is greater for net importers than for net exporters and has increased with the URAA or WTO accession. Holding other variables constant, the wheat support level of China, driven mainly by border market price support, is projected to rise with future income growth. Meanwhile, Japan is projected to maintain its high level of support, while the US and EU are projected to maintain their lower levels of support. These results are relevant in the context of multilateral trade negotiations, arguing against a narrow focus on past or current policy profiles and for long†run analyses that might mistakenly rest on the inconsistent assumptions of constant agricultural policies against the backdrop of rising incomes.