How hard is the euro are core? An evaluation of growth cycles using wavelet analysis

Using recent advances in time-varying spectral methods, this research analyses the growth cycles of the core of the euro area in terms of frequency content and phasing of cycles. The methodology uses the con-tinuous wavelet transform (CWT) and also Hilbert wavelet pairs in the setting of a non-decimated discrete wavelet transform in order to analyse bivariate time series in terms of conventional frequency domain measures from spectral analysis. The findings are that coherence and phasing between the three core members of the euro area (France, Germany and Italy) have increased since the launch of the euro.time-varying spectral analysis; coherence; phase; business cycles; EMU; growth cycles; Hilbert trans-form; wavelet analysis

How hard is the euro area core? A wavelet analysis of growth cycles in Germany, France and Italy

Using recent advances in time-varying spectral methods, this research analyses the growth cycles of the core of the euro area in terms of frequency content and phasing of cycles. The methodology uses the continuous wavelet transform (CWT) and also Hilbert wavelet pairs in the setting of a non-decimated discrete wavelet transform in order to analyse bivariate time series in terms of conventional frequency domain measures from spectral analysis. The findings are that coherence and phasing between the three core members of the euro area (France, Germany and Italy) have increased since the launch of the euro

Cross wavelet analysis: significance testing and pitfalls

In this paper, we present a detailed evaluation of cross wavelet analysis of bivariate time series. We develop a statistical test for zero wavelet coherency based on Monte Carlo simulations. If at least one of the two processes considered is Gaussian white noise, an approximative formula for the critical value can be utilized. In a second part, typical pitfalls of wavelet cross spectra and wavelet coherency are discussed. The wavelet cross spectrum appears to be not suitable for significance testing the interrelation between two processes. Instead, one should rather apply wavelet coherency. Furthermore we investigate problems due to multiple testing. Based on these results, we show that coherency between ENSO and NAO is an artefact for most of the time from 1900 to 1995. However, during a distinct period from around 1920 to 1940, significant coherency between the two phenomena occurs

The representation of location by a regional climate model in complex terrain

To assess potential impacts of climate change for a specific location, one typically employs climate model simulations at the grid box corresponding to the same geographical location. But based on regional climate model simulations, we show that simulated climate might be systematically displaced compared to observations. In particular in the rain shadow of moutain ranges, a local grid box is therefore often not representative of observed climate: the simulated windward weather does not flow far enough across the mountains; local grid boxes experience the wrong airmasses and atmospheric circulation. In some cases, also the local climate change signal is deteriorated. Classical bias correction methods fail to correct these location errors. Often, however, a distant simulated time series is representative of the considered observed precipitation, such that a non-local bias correction is possible. These findings also clarify limitations of bias correcting global model errors, and of bias correction against station data

A conceptual ENSO model under realistic noise forcing

We investigated the influence of atmospheric noise on the generation of interannual El Niño variability. Therefore, we perturbed a conceptual ENSO delay model with surrogate windstress data generated from tropical windspeed measurements. The effect of the additional stochastic forcing was studied for various parameter sets including periodic and chaotic regimes. The evaluation was based on a spectrum and amplitude-period relation comparison between model and measured sea surface temperature data. The additional forcing turned out to increase the variability of the model output in general. The noise-free model was unable to reproduce the observed spectral bandwidth for any choice of parameters. On the contrary, the stochastically forced model is capable of producing a realistic spectrum. The weakly nonlinear regimes of the model exhibit a proportional relation between amplitude and period matching the relation derived from measurement data. The chaotic regime, however, shows an inversely proportional relation. A stability analysis of the different regimes revealed that the spectra of the weakly nonlinear regimes are robust against slight parameter changes representing disregarded physical mechanisms, whereas the chaotic regime exhibits a very unstable realistic spectrum. We conclude that the model including stochastic forcing in a parameter range of moderate nonlinearity best matches the real conditions. This suggests that atmospheric noise plays an important role in the coupled tropical pacific ocean-atmosphere system

Reply to “Comment on ‘Bias Correction, Quantile Mapping, and Downscaling: Revisiting the Inflation Issue’”

In his comment, G. Bürger criticizes the conclusion that inflation of trends by quantile mapping is an adverse effect.He assumes that the argument would be ‘‘based on the belief that long-term trends and along with them future climate signals are to be large scale.’’ His line of argument reverts to the so-called inflated regression. Here it is shown, by referring to previous critiques of inflation and standard literature in statistical modeling as well as weather forecasting, that inflation is built upon a wrong understanding of explained versus unexplained variability and prediction versus simulation. It is argued that a sound regressionbased downscaling can in principle introduce systematic local variability in long-term trends, but inflation systematically deteriorates the representation of trends. Furthermore, it is demonstrated that inflation by construction deteriorates weather forecasts and is not able to correctly simulate small-scale spatiotemporal structure

Tempting long-memory - on the interpretation of DFA results

We study the inference of long-range correlations by means of Detrended Fluctuation Analysis (DFA) and argue that power-law scaling of the fluctuation function and thus long-memory may not be assumed a priori but have to be established. This requires the investigation of the local slopes. We account for the variability characteristic for stochastic processes by calculating empirical confidence regions. Comparing a long-memory with a short-memory model shows that the inference of long-range correlations from a finite amount of data by means of DFA is not specific. We remark that scaling cannot be concluded from a straight line fit to the fluctuation function in a log-log representation. Furthermore, we show that a local slope larger than α=0.5 for large scales does not necessarily imply long-memory. We also demonstrate, that it is not valid to conclude from a finite scaling region of the fluctuation function to an equivalent scaling region of the autocorrelation function. Finally, we review DFA results for the Prague temperature data set and show that long-range correlations cannot not be concluded unambiguously

How well do regional climate models simulate the spatial dependence of precipitation? An application of pair-copula constructions

We investigate how well a suite of regional climate models (RCMs) from the ENSEMBLES project represents the residual spatial dependence of daily precipitation. The study area we consider is a 200 km×200 km region in south central Norway, with RCMs driven by ERA-40 boundary conditions at a horizontal resolution of approximately 25 km×25 km. We model the residual spatial dependence with pair-copula constructions, which allows us to assess both the overall and tail dependence in precipitation, including uncertainty estimates. The selected RCMs reproduce the overall dependence rather well, though the discrepancies compared to observations are substantial. All models overestimate the overall dependence in the west-east direction. They also overestimate the upper tail dependence in the north-south direction during winter, and in the west-east direction during summer, whereas they tend to underestimate this dependence in the north-south direction in summer. Moreover, many of the climate models do not simulate the small-scale dependence patterns caused by the pronounced orography well. However, the misrepresented residual spatial dependence does not seem to affect estimates of high quantiles of extreme precipitation aggregated over a few grid boxes. The underestimation of the area-aggregated extreme precipitation is due mainly to the well-known underestimation of the univariate margins for individual grid boxes, suggesting that the correction of RCM biases in precipitation might be feasibl