CMB Power Spectrum Estimation via Hierarchical Decomposition

We have developed a fast, accurate and generally applicable method for inferring the power spectrum and its uncertainties from maps of the cosmic microwave background (CMB) in the presence of inhomogeneous and correlated noise. For maps with 10 to 100 thousand pixels, we apply an exact power spectrum estimation algorithm to submaps of the data at various resolutions, and then combine the results in an optimal manner. To analyze larger maps efficiently one must resort to sub-optimal combinations in which cross-map power spectrum error correlations are only calculated approximately. We expect such approximations to work well in general, and in particular for the megapixel maps to come from the next generation of satellite missions.Comment: 10 pages, 5 figures, to be submitted to Phys. Rev.

THE PROCESS FOLLOWED BY PPP DATA. ON THE PROPERTIES OF LINEARITY TESTS

Recent research has reported the lack of correct size in stationarity test for PPP deviations within a linear framework. However, theoretically well motivated nonlinear models, such as the ESTAR, appear to parsimoniously fit the PPP data and provide an explanation for the PPP ¿puzzle¿. Employing Monte Carlo experiments we analyze the size and power of the nonlinear tests against a variety of nonstationary hypotheses. We also fit the ESTAR model to data from high inflation economies. Our results provide further support for ESTAR specification.ESTAR, Real Exchange Rate, Size, Linearity Test.

NONLINEAR PPP UNDER THE GOLD STANDARD

Hegwood and Papell (2002) conclude on the basis of analysis in a linear framework that long-run purchasing power parity (PPP)\ does not hold for sixteen real exchange rate series, analyzed in Diebold, Husted, and Rush (1991) for the period 1792-1913, under the Gold Standard. Rather, purchasing power parity deviations are mean-reverting to a changing equilibrium -a quasi PPP (QPPP) theory. We analyze the real exchange rate adjustment mechanism for their data set assuming a nonlinear adjustment process allowing for both a constant and a mean shifting equilibrium. Our results confirm that real exchange rates at that time were stationary, symmetric, nonlinear processes that revert to a non-constant equilibrium rate. Speeds of adjustment were much quicker when breaks were allowed.Purchasing Power Parity, ESTAR, Bootstrapping.

TEMPORAL AGGREGATION OF AN ESTAR PROCESS: SOME IMPLICATIONS FOR PURCHASING POWER PARITY ADJUSTMENT

Nonlinear models of deviations from PPP have recently provided an important, theoretically well motivated, contribution to the PPP puzzle. Most of these studies use temporally aggregated data to empirically estimate the nonlinear models. As noted by Taylor (2001), if the true DGP is nonlinear, the temporally aggregated data could exhibit misleading properties regarding the adjustment speeds. We examine the effects of different levels of temporal aggregation on\ estimates of ESTAR models of real exchange rates. Our Monte Carlo results show that temporal aggregation does not imply the disappearance of nonlinearity and that adjustment speeds are significantly slower in temporally aggregated data than in the true DGP. Furthermore, the autoregressive structure of some monthly ESTAR estimates found in the literature is suggestive that adjustment speeds are even faster than implied by the monthly estimates.ESTAR, Real Exchange Rate, Purchasing Power Parity, Aggregation.

A NEW ANALYSIS OF THE DETERMINANTS OF THE REAL DOLLAR-STERLING EXCHANGE RATE: 1871-1994

Nonlinear models of deviations from PPP have recently provided an important, theoretically well motivated, contribution to the PPP puzzle. In recent work the equilibrium level has been modeled either as constant or as time varying with very similar statistical fits and very different economic implications. The high persistence of both PPP deviations and the proxy variables for the equilibrium real rate might create a problem of spurious coefficient significance. This paper investigates the possibility of spurious regression within nonlinear models of PPP. Monte Carlo experiments show that standard critical values are not appropriate in such a context. To illustrate we consider the real Dollar-Sterling exchange rate over the period 1871-1994. Due to many exchange rate regime changes over the sample period we employ a Bootstrap methodology that preserves the original structure of the estimated residuals and obtain new critical values of the coefficient estimates. A nonlinear (ESTAR) process with a time varying equilibrium proxied by relative wealth and relative income per capita seems to parsimoniously fit the data. Our results provide further evidence for the nonlinear model with a shifting equilibrium and the implied speed of adjustment is found to be substantially faster than previously reported in the literature.ESTAR, Purchasing Power Parity, Bootstrapping

ASYMMETRY IN THE LINK BETWEEN THE YIELD SPREAD AND INDUSTRIAL PRODUCTION. THRESHOLD EFFECTS AND FORECASTING

We analyze the nonlinear behavior of the information content in the spread for future real economic activity. The spread linearly predicts one year ahead real growth in nine industrial production sectors of the US and four of the UK over the last forty years. However, recent investigations on the spread-real activity relation have questioned both its linear nature and its time-invariant framework. Our, in-sample, empirical evidence suggests that the spread real activity relationship exhibits asymmetries that allow for different predictive power of the spread when past spread values were above or below some threshold value. We then measure the out-of-sample forecast performance of the nonlinear model using predictive accuracy tests. The results show that significant improvement in forecasting accuracy, at least for one-step ahead forecasts, can be obtained over the linear model.industrial production; yield spread; threshold model; forecasting; predictive accuracy

Bubbles in House Prices and their Impact on Consumption: Evidence for the US

This paper provides evidence that some aggregate and regional U.S. real house price indices exhibited a bubble in the last few years according to the Phillips et al. (2007) unit root test. We subsequently investigate whether house price acceleration (deceleration) had a signi.cant impact on consumption in an error correction mechanism implied by a wide class of optimizing models. Our results support the argument that real house prices have their major effect on consumption only during the bubble period