Testing Dependence Among Serially Correlated Multi-category Variables

The contingency table literature on tests for dependence among discrete multi-category variables assume that draws are independent, and there are no tests that account for serial dependencies − a problem that is particularly important in economics and finance. This paper proposes a new test of independence based on the maximum canonical correlation between pairs of discrete variables. We also propose a trace canonical correlation test using dynamically augmented reduced rank regressions or an iterated weighting method in order to account for serial dependence. Such tests are useful, for example, when testing for predictability of one sequence of discrete random variables by means of another sequence of discrete random variables as in tests of market timing skills or business cycle analysis. The proposed tests allow for an arbitrary number of categories, are robust in the presence of serial dependencies and are simple to implement using multivariate regression methods

How Costly is it to Ignore Breaks when Forecasting the Direction of a Time Series?

Empirical evidence suggests that many macroeconomic and financial time-series are subject to occasional structural breaks. In this paper we present analytical results quantifying the effects of such breaks on the correlation between the forecast and the realisation, and on the ability to forecast the sign or direction of a time-series that is subject to breaks. Our results suggest that it can be very costly to ignore breaks. Forecasting approaches that condition on the most recent break are likely to perform better over unconditional approaches that use expanding or rolling estimation windows, provided that the break is reasonably large

Small Sample Properties of Forecasts from Autoregressive Models under Structural Breaks

Autoregressive models are used routinely in forecasting and often lead to better performance than more complicated models. However, empirical evidence is also suggesting that the autoregressive representations of many macroeconomic and financial time series are likely to be subject to structural breaks. This paper develops a theoretical framework for the analysis of small-sample properties of forecasts from general autoregressive models under a structural break. Our approach is quite general and allows for unit roots both pre- and post-break. We derive finite-sample results for the mean squared forecast error of one-step-ahead forecasts, both conditionally and unconditionally and present numerical results for different types of break specifications. Implications of breaks for the determination of the optimal window size are also discussed.small sample properties of forecasts, RMSFE, structural breaks, autoregression

How Costly is it to Ignore Breaks when Forecasting the Direction of a Time Series?

Empirical evidence suggests that many macroeconomic and financial time series are subject to occasional structural breaks. In this paper we present analytical results quantifying the effects of such breaks on the correlation between the forecast and the realization and on the ability to forecast the sign or direction of a time-series that is subject to breaks. Our results suggest that it can be very costly to ignore breaks. Forecasting approaches that condition on the most recent break are likely to perform better over unconditional approaches that use expanding or rolling estimation windows provided that the break is reasonably large.sign prediction, estimation window, structural breaks

Real Time Econometrics

This paper considers the problems facing decision-makers using econometric models in real time. It identifies the key stages involved and highlights the role of automated systems in reducing the effect of data snooping. It sets out many choices that researchers face in construction of automated systems and discusses some of the possible ways advanced in the literature for dealing with them. The role of feedbacks from the decision-maker’s actions to the data generating process is also discussed and highlighted through an example.specification search, data snooping, recursive/sequential modelling, automated model selection

Coherent Resonat millenial-scale climate transitions triggered by massive meltwater pulses

The role of mean and stochastic freshwater forcing on the generation of millennial-scale climate variability in the North Atlantic is studied using a low-order coupled atmosphere–ocean–sea ice model. It is shown that millennial-scale oscillations can be excited stochastically, when the North Atlantic Ocean is fresh enough. This finding is used in order to interpret the aftermath of massive iceberg surges (Heinrich events) in the glacial North Atlantic, which are characterized by an excitation of Dansgaard–Oeschger events. Based on model results, it is hypothesized that Heinrich events trigger Dansgaard–Oeschger cycles and that furthermore the occurrence of Heinrich events is dependent on the accumulated climatic effect of a series of Dansgaard–Oeschger events. This scenario leads to a coupled ocean–ice sheet oscillation that shares many similarities with the Bond cycle. Further sensitivity experiments reveal that the timescale of the oscillations can be decomposed into stochastic, linear, and nonlinear deterministic components. A schematic bifurcation diagram is used to compare theoretical results with paleoclimatic data

Testing Dependence among Serially Correlated Multi-category Variables

The contingency table literature on tests for dependence among discrete multi-category variables is extensive. Existing tests assume, however, that draws are independent, and there are no tests that account for serial dependencies−a problem that is particularly important in economics and finance. This paper proposes a new test of independence based on the maximum canonical correlation between pairs of discrete variables. We also propose a trace canonical correlation test using dynamically augmented reduced rank regressions or an iterated weighting method in order to account for serial dependence. Such tests are useful, for example, when testing for predictability of one sequence of discrete random variables by means of another sequence of discrete random variables as in tests of market timing skills or business cycle analysis. The proposed tests allow for an arbitrary number of categories, are robust in the presence of serial dependencies and are simple to implement using multivariate regression methods. Monte Carlo experiments show that the proposed tests have good finite sample properties. An empirical application to survey data on forecasts of GDP growth demonstrates the importance of correcting for serial dependencies in predictability tests.contingency tables, canonical correlations, serial dependence, tests of predictability

Learning, Structural Instability and Present Value Calculations

Present value calculations require predictions of cash flows both at near and distant future points in time. Such predictions are generally surrounded by considerable uncertainty and may critically depend on assumptions about parameter values as well as the form and stability of the data generating process underlying the cash flows. This paper presents new theoretical results for the existence of the infinite sum of discounted expected future values under uncertainty about the parameters characterizing the growth rate of the cash flow process. Furthermore, we explore the consequences for present values of relaxing the stability assumption in a way that allows for past and future breaks to the underlying cash flow process. We find that such breaks can lead to considerable changes in present values

Learning, Structural Instability and Present Value Calculations

Present value calculations require predictions of cash flows both at near and distant future points in time. Such predictions are generally surrounded by considerable uncertainty and may critically depend on assumptions about parameter values as well as the form and stability of the data generating process underlying the cash flows. This paper presents new theoretical results for the existence of the infinite sum of discounted expected future values under uncertainty about the parameters characterizing the growth rate of the cash flow process. Furthermore, we explore the consequences for present values of relaxing the stability assumption in a way that allows for past and future breaks to the underlying cash flow process. We find that such breaks can lead to considerable changes in present values.present value, stock prices, structural breaks, Bayesian learning