Path Forecast Evaluation

A path forecast refers to the sequence of forecasts 1 to H periods into the future. A summary of the range of possible paths the predicted variable may follow for a given confidence level requires construction of simultaneous confidence regions that adjust for any covariance between the elements of the path forecast. This paper shows how to construct such regions with the joint predictive density and Scheffé’s (1953) S-method. In addition, the joint predictive density can be used to construct simple statistics to evaluate the local internal consistency of a forecasting exercise of a system of variables. Monte Carlo simulations demonstrate that these simultaneous confidence regions provide approximately correct coverage in situations where traditional error bands, based on the collection of marginal predictive densities for each horizon, are vastly off mark. The paper showcases these methods with an application to the most recent monetary episode of interest rate hikes in the U.S. macroeconomy.path forecast, simultaneous confidence region, error bands

Estimation and Inference by the Method of Projection Minimum Distance

A covariance-stationary vector of variables has a Wold representation whose coefficients can be semi-parametrically estimated by local projections (Jordà, 2005). Substituting the Wold representations for variables in model expressions generates restrictions that can be used by the method of minimum distance to estimate model parameters. We call this estimator projection minimum distance (PMD) and show that its parameter estimates are consistent and asymptotically normal. In many cases, PMD is asymptotically equivalent to maximum likelihood estimation (MLE) and nests GMM as a special case. In fact, models whose ML estimation would require numerical routines (such as VARMA models) can often be estimated by simple least-squares routines and almost as efficiently by PMD. Because PMD imposes no constraints on the dynamics of the system, it is often consistent in many situations where alternative estimators would be inconsistent.We provide several Monte Carlo experiments and an empirical application in support of the new techniques introduced.Econometric and statistical methods

The announcement effect: evidence from open market desk data

Paper for a conference sponsored by the Federal Reserve Bank of New York entitled Financial Innovation and Monetary TransmissionOpen market operations ; Monetary policy ; Federal Open Market Committee ; Federal funds market (United States)

Carry trade

It does not take much sophistication for a speculator to generate risk-adjusted positive returns with the carry trade. A number of obvious improvements (such as optimally designed portfolios, strategies that permit the speculator to remain in a cash position when expected returns are small or uncertain, and others not considered here) would only improve the speculator's returns further. That this is so poses a challenge to conventional notions of market efficiency and long-standing puzzles in international finance. The carry trade is a risky investment but its positive returns are hard to justify on the basis of the investor's tolerance for exposure or how returns correlate with a wide range of alternative risk factors

Model-Free Impulse Responses

This paper introduces methods for computing impulse response functions that do not require specification and estimation of the unknown dynamic multivariate system itself. The central idea behind these methods is to estimate flexible local projections at each period of interest rather than extrapolating into increasingly distant horizons from a given model, as it is usually done in vector autoregressions (VAR). The advantages of local projections are numerous: (1) they can be estimated by simple regression techniques with standard regression packages; (2) they are more robust to misspecification; (3) standard error calculation is direct; and (4) they easily accommodate experimentation with highly non-linear and flexible specifications that may be impractical in a multivariate context. Therefore, these methods are a natural alternative to estimating impulse responses from VARs. An application to a simple, closed-economy monetary model suggests that the output loss and inflation effects of an interest rate shock depend on the stage of the business cycle

Measuring systematic monetary policy

Monetary policy

A chronology of turning points in economic activity: Spain 1850-2011

This paper codifies in a systematic and transparent way a historical chronology of business cycle turning points for Spain reaching back to 1850 at annual frequency, and 1939 at monthly frequency. Such an exercise would be incomplete without assessing the new chronology itself and against others —this we do with modern statistical tools of signal detection theory. We also use these tools to determine which of several existing economic activity indexes provide a better signal on the underlying state of the economy. We conclude by evaluating candidate leading indicators and hence construct recession probability forecasts up to 12 months in the future.Business cycles ; Spain

Empirical simultaneous confidence regions for path-forecasts

Measuring and displaying uncertainty around path-forecasts, i.e. forecasts made in period T about the expected trajectory of a random variable in periods T+1 to T+H is a key ingredient for decision making under uncertainty. The probabilistic assessment about the set of possible trajectories that the variable may follow over time is summarized by the simultaneous confidence region generated from its forecast generating distribution. However, if the null model is only approximative or altogether unavailable, one cannot derive analytic expressions for this confidence region, and its non-parametric estimation is impractical given commonly available predictive sample sizes. Instead, this paper derives the approximate rectangular confidence regions that control false discovery rate error, which are a function of the predictive sample covariance matrix and the empirical distribution of the Mahalanobis distance of the path-forecast errors. These rectangular regions are simple to construct and appear to work well in a variety of cases explored empirically and by simulation. The proposed techniques are applied to provide confidence bands around the Fed and Bank of England real-time path-forecasts of growth and inflation. --Path forecast,forecast uncertainty,simultaneous confidence region,Scheffé's S-method,Mahalanobis distance,false discovery rate

The Body as a Representation of a Damaged Environment

A study of how the image of a damaged body in Animal's People can be seen as the representation of a corrupted natural environmentUn estudio de como la imagen del cuerpo dañado del protagonista de la novela Animal's People corresponde al medio natural degradad

Empirical Simultaneous Confidence Regions for Path-Forecasts

Measuring and displaying uncertainty around path-forecasts, i.e. forecasts made in period T about the expected trajectory of a random variable in periods T+1 to T+H is a key ingredient for decision making under uncertainty. The probabilistic assessment about the set of possible trajectories that the variable may follow over time is summarized by the simultaneous confidence region generated from its forecast generating distribution. However, if the null model is only approximative or altogether unavailable, one cannot derive analytic expressions for this confidence region, and its non-parametric estimation is impractical given commonly available predictive sample sizes. Instead, this paper derives the approximate rectangular confidence regions that control false discovery rate error, which are a function of the predictive sample covariance matrix and the empirical distribution of the Mahalanobis distance of the path-forecast errors. These rectangular regions are simple to construct and appear to work well in a variety of cases explored empirically and by simulation. The proposed techniques are applied to provide con.dence bands around the Fed and Bank of England real-time path-forecasts of growth and inflation.path forecast, forecast uncertainty, simultaneous confidence region, Scheffé’s S-method,Mahalanobis distance, false discovery rate.