Very large data sets in economics are already available and will soon become commonplace. The econometric techniques currently in use may not be relevant and new techniques will have to be devised. It can be argued that most tests of significance, linear models, assumptions of normality, and procedures to reduce bias, for example, will be replaced. The usefulness of asymptotic theory is discussed. It is suggested that methods for extracting conditional distributions will be becomes especially useful and a few particular possible techniques are suggested.

This is the speech that Professor Granger gave at Nobel Prize Awards 2004

In this paper we compare the relative efficiency of different methods of forecasting the aggregate of spatially correlated variables. Small sample simulations confirm the asymptotic result that improved forecasting performance can be obtained by imposing a priori constraints on the amount of spatial correlation in the system. One way to do so is to aggregate forecasts from a Space-Time Autoregressive model (Cliff et al., 1975), which offers a solution to the 'curse of dimensionality' that arises when forecasting with VARs. We also show that ignoring spatial correlation, even when it is weak, leads to highly inaccurate forecasts. Finally, if the system satisfies a 'poolability' condition, there is a benefit in forecasting the aggregate variable directly.

This paper introduces a new type of nonlinear model, the min-max model, and analyzes the properties for a pair of series. Stability conditions of this system are given for the nonlinearly integrated bivariate series. Under these stability conditions, the difference of the two series has a threshold-type nonlinearity. One can construct a threshold error correction model from min-max processes. Neglected nonlinearity tests are applied, to the univariate series and to the system, to detect nonlinearity, and it turns out that the tests using the system have better power. We apply the min-max model to U.S. Treasury bill and commercial paper interest rates. The spread of these interest rates shows a threshold-type nonlinearity, and this model outperforms a linear model in terms of its predictability out-of-sample

This paper shows that a linear process with breaks can mimic autocorrelations and other properties of I(d) processes, where d can be a fraction. Simulation results show that S&P 500 absolute stock returns are more likely to show the "long memory" property because of the presence of breaks in the series rather than an I(d) process.

Possibly hitherto unnoticed cointegrating relationships among integrated components of data series are identified. If the components are cointegrated, the data are said to ahve hidden cointegration. The implication of hidden cointegration on modeling data series themselves is discussed throughwhat we call crouching error correction models. We show that hidden cointegration is a simple example of nonlinear cointegration. Economic examples are provided with U.S. short-term and long-term interest rates and output and unemployment, for which no evidence of standard cointegration is found.

This paper shows that the properties of nonlinear transformations of a fractionally integrated process depend strongly on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d > 0 leads to a long-memory process with the same or a smaller long-memory parameter depending on the Hermite rank of the transformation. Any nonlinear transformation of an antipersistent Gaussian I(d) process is I(0). For non-stationary I(d) processes, every integer power transformation is non-stationary and exhibits a deterministic trend in mean and in variance. In particular, the square of a non-stationary Gaussian I(d) process still has long memory with parameter d, whereas the square of a stationary Gaussian I(d) process shows less dependence than the initial process. Simulation results for other transformations are also discussed.

A variable is defined to be self-generating if it can be forecast efficiently from its own past only. Conditions are derived for certain linear combinations to be self-generating in error correction models. Interestingly, there are only two candidates for self-generation in an error correction model. They are cointegrating relationships and common stochastic trends defined by Gonzalo and Granger (1995). The usefulness of self-generation as a multivariate-modelling tool is investigated. A simple testing procedure is also presented. Some interesting economic hypothesis can be easily tested in the self-generation framework. For example, for forward exchange rate to have forecasting power for the future movements in spot rate, the latter should not be self-generating. Given that they are cointegrated, the spot exchange rate should not be a common stochastic trend, which can be easily tested. We also provide additional examples.

Many standard structural models in economics have the property that they induce persistent, partially predictable heteroskedasticity ("volatility clustering") in their key dependent variables, even when their underlying stochastic shock variables are all serially independent and homoskedastic, and their structural parameters are all time-invariant. This paper presents examples of this phenomenon, and examines the nature of such induced volatility clustering.

A spurious regression occurs when a pair of independent series, but with strong temporal properties, are found apparently to be related according to standard inference in an OLS regression. Although this is well known to occur with pairs of independent unit root processes, this paper finds evidence that similar results are found with positively autocorrelated autoregressive series on long moving averages. This occurs regardless of the sample size and for various distributions of the error terms.