ABSTRACT. In many applied settings, effective modeling of high-dimensional time series data requires accounting for multiple, overlapping seasonal patterns that unfold at different frequencies. This complexity is particularly evident in domains such as energy demand forecasting, where consumption often varies substantially over the course of a day, differs between weekdays and weekends, and shifts throughout the year. In this work, we introduce a novel framework for simultaneously disentangling and forecasting these intricate seasonal structures within a high-dimensional setting. We develop and illustrate the approach using U.S. electricity demand data, where hourly consumption from multiple providers displays pronounced intra-day, intra-week, and annual seasonalities, as well as strong cross-sectional correlations. We propose a new tensor factor modeling framework designed to handle these multiple layers of seasonality. To exploit the strengths of this framework, we restructure the hourly electricity demand data into a sequence of weekly tensors. Each weekly tensor is a three-mode array whose dimensions correspond to the hours of the day, the days of the week, and the number of providers. This multi-dimensional representation enables a factor decomposition that distinguishes among the various seasonal patterns along each mode: factor loadings over the hour dimension highlight intra-day cycles, factor loadings over the day dimension capture differences across weekdays and weekends, and factor loadings over the provider dimension reveal commonalities and shared dynamics among the different entities. We rigorously compare the predictive performance of our tensor factor model against several benchmarks, including traditional vector factor models and cutting-edge functional time series methods. The results consistently demonstrate that the tensor-based approach delivers superior forecasting accuracy at different horizons and provides interpretable factors that align with domain knowledge. Beyond its empirical advantages, our framework offers a systematic way to gain insight into the underlying processes that shape electricity demand patterns. In doing so, it paves the way for more nuanced, data-driven decision-making and can be adapted to address similar challenges in other high-dimensional time series applications.

ABSTRACT. This paper challenges the standard assumption of no contemporaneous feedback between temperatures and the economy when data are observed at a higher frequency than annual. Using a unique dataset of retrospective temperature records in Europe, we show that the short-range temperature forecast error is the only temperature shock that is not Granger-caused by prices, suggesting that this is the appropriate measure for assessing temperature effects. We argue that this finding underlies the role of temperature in shaping price expectations, particularly in commodity markets. We substantiate this claim by showing odd effects of anticipated temperature changes and temperature surprises, while also highlighting demand-side implications that characterize the response on the European gas market.

ABSTRACT. Geopolitical shocks are not all alike – different classes of geopolitical shocks can have different macroeconomic implications, particularly on inflation. This paper exploits the comovement between the Geopolitical Risk Index (GPR) and oil prices across major geopolitical events to disentangle two types of geopolitical shocks within a structural VAR model for the US economy. The VAR estimates suggest that geopolitical shocks associated with disruptions in energy markets are inflationary and contractionary. In contrast, geopolitical shocks associated with macroeconomic developments that are unrelated to energy markets are deflationary and contractionary. To support this interpretation, the paper exploits the heterogeneity across sectoral output and prices of the US economy to show that a sector’s response to a geopolitical shock depends on its energy intensity. Sectors characterized by higher energy intensity are subject to larger output losses and price increases in response to geopolitical energy shocks, while the same does not hold for geopolitical macro shocks.

ABSTRACT. This paper proposes a model suite for forecasting inflation in the energy component of the Harmonised Index of Consumer Prices (HICP) in the euro area. The suite can be also used to shed light on the transmission of energy price shocks in different international markets to consumer energy prices. It consists of Bayesian Vector Autoregressions (BVARs) for different components of HICP energy. It incorporates a wide range of drivers of consumer energy prices, including crude and refined oil prices, natural gas prices, producer prices of energy and taxes. Model specification allows for state dependent elasticities to commodity price shocks. The models fit data well and produce reasonable forecasts. The disaggregation of energy HICP and further model features enhance forecast accuracy, particularly in the short-term. We also demonstrate sizable variation in the impact of commodity price shocks at different levels of commodity prices.

ABSTRACT. The typical predictor variable in predictive regressions for stock returns exhibits high persistence, which leads to nonstandard limiting distributions of the least-squares estimator and the associated t statistic. While there are several methods to deal with the issue of nonstandard distributions, high predictor persistence also opens the door to spurious regression findings induced by the use of imperfect predictors, i.e. when the predictors do not perfectly span the conditional mean of the stock returns. We robustify IVX predictive regression (Kostakis et al., 2015, Review of Financial Studies 28, 1506–1553) to the presence of smoothly varying components of the predictive system. In specific, we resort to a filter which exploits the slow variation to identify the mean component of the stock returns unaccounted for by the imperfect predictors. The limiting distribution of the resulting modified IVX t statistic is derived under sequences of local alternatives, and a wild bootstrap implementation improving the finite-sample behavior is provided. Compared to standard IVX predictive regression, there is a price to pay for such robustness in terms of power; at the same time, the IVX statistic without adjustment consistently rejects the false null of no predictability in the presence of imperfect predictors.

ABSTRACT. Given its relevance for the efficient functioning of financial markets, forecasting illiquidity has become a matter of interest both for market makers and investors. In this paper, we investigate the possibility of forecasting market illiquidity in both a linear and nonlinear framework. Inspired by Amihud (2002), illiquity is measured by the ratio between daily realized volatility and trading volume (see Ranaldo and Santucci de Magistris, 2022 and Lacava et al., 2023). We consider a set of econometric models that are able to account for extremely large realizations of illiquidty, namely illiquidity jumps. We consider the illiquidity conditions of several stock markets, and we show that in all cases the inclusion of jumps drastically increases the forecasting capability of the models at least in a short horizon (1-step ahead). Furthermore, we asses the role of conditional jumps in determining the distributional properties of the realized Amihud, with the goal of introducing the concept of Illiquidity-at-Risk (IlliqaR). Accounting for illiquiity jumps allows for a correct probability coverage of extreme illiquidity events.

ABSTRACT. Based on a continuous-time stochastic volatility model with a linear drift, we develop a test for explosive behavior in financial asset prices at a low frequency when prices are sampled at a higher frequency. The test exploits the volatility information in the high-frequency data. The method consists of devolatizing increments of logarithmic cryptocurrency price with realized volatility measures and performing a supremum-type recursive Dickey-Fuller test on the devolatized sample. The proposed test has a nuisance-parameter-free asymptotic distribution and is easy to implement. We study the size and power properties of the test in Monte Carlo simulations. A real-time date-stamping strategy based on the devolatized sample is proposed for the origination and conclusion dates of the explosive regime. Conditions under which the real-time date-stamping strategy is consistent are established. The test and the date-stamping strategy are used to study explosive behavior in Bitcoin and Ethereum.

ABSTRACT. We compute a common factor summarizing asymmetries in the expected distributions of a large set of survey-based data series for the euro area. This expected skewness factor is distinct from lower-moment factors and can help improve forecasts of risks to economic activity. In addition, within a monthly VAR model we show that revisions to survey-based expected skewness have macroeconomic and financial implications, even when the average assessment and expected volatility reflected in the surveys remains unchanged. The skewness measure we propose could benefit timely quantitative risk assessments at economic policy institutions to monitor the balance of risks.

ABSTRACT. We analyze economic growth vulnerability across the four largest Euro Area (EA) countries, focusing on the lower quantiles of GDP growth under stressed macroeconomic and financial conditions, both within and across countries. Vulnerability is found to be higher in countries either more exposed to EA-wide economic conditions, as Germany, or with large country-specific sectoral dynamics, as Spain. Stress tests highlight that (i) financial factors significantly amplify adverse macroeconomic conditions, and (ii) even severe sectoral shocks, whether common or country-specific, fail to fully explain the observed low vulnerability during systemic stress. Our results underscore the importance of monitoring both local and EA-wide macro-financial conditions to design effective policies for mitigating growth vulnerability.

ABSTRACT. This paper develops the concept of Growth and Inflation at Risk (GIaR), which is the curve representing all pairs of (negative) growth and inflation that are jointly exceeded with a given probability, conditionally on covariates. This is a bivariate generalisation of the concepts of Growth-at-Risk (GaR) and Inflation-at-Risk (IaR). We propose a novel approach to identify and estimate GIaR and provide uniformly valid upper and lower confidence bands. We first apply our procedure to predict the conditional probability of stagflation. Second, we compute worst-case scenarios for a policy maker who is concerned about the joint tail risk of low growth and high inflation. Overall, our empirical findings show that a tightening of financial conditions increases downside risks to both growth and inflation.

ABSTRACT. The main aim of this paper is to review recent advances in the multivariate autoregressive index model [MAI], originally proposed by Reinsel (1983), and their applications to economic and financial time series. MAI has recently gained momentum because it can be seen as a link between two popular but distinct multivariate time series approaches: vector autoregressive modeling [VAR] and the dynamic factor model [DFM]. Indeed, on the one hand, the MAI is a VAR model with a peculiar reduced-rank structure; on the other hand, it allows for identification of common components and common shocks in a similar way as the DFM. The focus is on recent developments of the MAI, which include extending the original model with individual autoregressive structures, stochastic volatility, time-varying parameters, high-dimensionality, and cointegration. In addition, new insights on previous contributions and a novel model are also provided.

ABSTRACT. We provide estimation and inference for the Generalised Dynamic Factor Model (GDFM) under the assumption that the dynamic common component can be expressed in terms of a finite number of lags of contemporaneously pervasive factors. The proposed estimator is simply an OLS regression of the observed variables on factors extracted via static principal components and therefore avoids frequency domain techniques entirely.

ABSTRACT. Many authors have discussed the presence of rate-weak factors in factor models. Tests even have been proposed for the null hypothesis of a strong factor against the alternative of a weak one (linear versus sublinear divergence of the corresponding eigenvalues). We show that this existence of rate-weak factors is incompatible with the natural assumption that the cross-sectional ordering of the panel, which usually is arbitrary, should remain irrelevant.

ABSTRACT. Ensuring a stable supply of critical minerals at reasonable prices is essential for the clean energy transition. The security of supply of critical minerals is particularly susceptible to geopolitical risk. In this paper, we use constant and time-varying parameter local projection (TVP-LP) regression models to examine the effect of geopolitical risk on prices of six critical minerals: aluminium, copper, nickel, platinum, tin and zinc. We propose a conceptual framework in which we make two predictions. The first is that the responsiveness of prices for critical minerals to geopolitical risk will depend on the non-technical risk associated with procuring each critical mineral, which will be reflected in the elasticity of supply. The second is that geopolitical threats will have a bigger effect on critical mineral prices than geopolitical acts. With the exception of platinum prices, which have suffered a downward structural demand side shock associated with the growth of the electric vehicle market, we find empirical support for the first prediction. Our results are also consistent with the second prediction. We find considerable evidence that the effect of geopolitical risk on the prices of critical minerals are time varying with time-varying effects of geopolitical shocks observed during the Gulf War, following the 9/11 terrorist attacks and during the COVID-19 pandemic with the time varying effects generally being stronger for geopolitical threats than geopolitical acts.

ABSTRACT. We study the impact of climate scenarios on sovereign credit risk, measured by Credit Default Swaps (CDS), analysing the interplay of climate risk exposure, fiscal and financial characteristics of European countries. We develop and estimate a panel threshold model using annual data from 2010 to 2022 for 24 European countries. The country’s indebtedness level defines the threshold of the estimated regimes. Then, we project the path of sovereign risk up to 2050 using the climate scenarios of the Network for Greening the Financial System. Results show a temporal and structural dimension of climate sovereign risks. First, in the short term, sovereign risk may worsen due to GDP and fiscal revenue adjustments, and for some countries, particularly in a delayed transition. However, in the long run, an orderly (Net Zero 2050) transition brings co-benefits in terms of lower sovereign risk compared to a delayed transition scenario. Second, countries with a debt-to-GDP ratio equal to or higher than 60% are the most sensitive to increased credit risk conditioned to scenarios of delayed transition and chronic physical risk, due to the economic and financial implications induced by stranded assets. Third, climate sovereign risk is stronger in economies based on traditional sectors, and in countries with higher political instability. Our results show the importance of European governments credibly committing to an orderly and early Net Zero transition to preserve sovereign financial stability.

ABSTRACT. We focus on the impact of flood risk on credit supply to Italian SMEs. We contribute to the existing literature by, first, estimating a province (NUTS3) specific indicator of credit supply for Italian SMEs. A further contribution is to explore the role played by climate concern when interacting with flood risk in shaping credit supply dynamics. The empirical evidence suggests that flood risk is not a confounding factor with GDP per capita in limiting access to credit.

ABSTRACT. The original and corrected Akaike information criteria (AIC) have been routinely used for model selection for ages. The penalty terms in these criteria are tied to the classical normal linear regression, characterized by conditional homoskedasticity and a small number of regressors relative to the sample size. We derive, from the same principles, a general version that takes account of conditional heteroskedasticity and regressor numerosity. The new AICm penalty takes a form of a ratio of certain weighted average error variances, and can be operationalized via unbiased estimation of individual variances. The feasible AICm criterion still minimizes the expected Kullback-Leibler divergence up to an asymptotically negligible term that does not relate to regressor numerosity. In simulations, the feasible AICm does select models that deliver systematically better out-of-sample predictions than the classical criteria.

ABSTRACT. In this paper, we derive explicit formulas of Kendall's tau and Spearman's rho rank correlations for two general classes of skew-elliptical copulas: normal location-scale mixture copulas and skew-normal scale mixture copulas. These formulas establish mappings from copula parameters to rank correlation coefficients, facilitating robust rank-based estimation of skew-elliptical copula models. Additionally, we investigate the impact of asymmetry parameters on the properties of both rank correlations within these two classes of skew-elliptical models, which employ different methods for introducing asymmetry into elliptical symmetry. Notably, we find that the differences in rank correlation properties between the two classes of models are more pronounced than their similarities. Specifically, some desirable properties of rank correlations for elliptical copulas are preserved when asymmetry is introduced in skew-normal scale mixture copulas, but not when it is introduced in normal location-scale mixture copulas.

ABSTRACT. Violations of the assumptions underlying classical asymptotic theory frequently lead to unreliable statistical inference. This paper proposes a novel bootstrap-based diagnostic procedure to detect such violations. The suggested approach (i) focuses on the distance between the conditional distribution of a bootstrap statistic and the (limiting) Gaussian distribution, and (ii) proposes a method to assess whether this distance is large enough to indicate the invalidity of the asymptotic approximation. The method, which is computationally straightforward, involves applying standard normality tests to a set of bootstrap repetitions of a reference estimator or test statistic, in order to assess significant deviations from the Gaussian distribution. It is studied under what conditions the randomness in the data mixes with the randomness in the bootstrap repetitions in a way such that the diagnostics asymptotically (a) induce no pre-testing bias under the null, (b) can be performed using the same critical values in a broad range of applications, and (c) consistently detect deviations from asymptotic Gaussianity. To demonstrate the practical relevance and broad applicability of our diagnostic procedure, we discuss five scenarios where the asymptotic Gaussian approximation fails: (i) detecting infinite variance innovations in a location model for i.i.d. data; (ii) identifying non-stationary behavior in autoregressive time series; (iii) parameters near or at the boundary of the parameter space; (iv) invalidity of the delta method due to (near-)rank deficiency in the implied Jacobian matrix; and (v) weak instruments in instrumental variable regression. An illustration drawn from the empirical macroeconomic literature concludes.

ABSTRACT. We examine the uniqueness of the posterior distribution within an Empirical Bayes framework using a discretized prior. To achieve this, we impose Rational Expectations conditions on the prior, focusing on coherence and stability properties. We derive the conditions necessary for posterior uniqueness when observations are drawn from either discrete or continuous distributions. Additionally, we discuss the properties of our discretized prior as an approximation of the true underlying prior.

ABSTRACT. This paper revisits the conclusions of a recent influential study, which identifies a single shock as the main driver of business cycle fluctuations. We argue that the VAR used in that study is informationally deficient, that is, it is unable to recover the main shock driving cyclical fluctuations. Using a large-dimensional Structural Dynamic Factor model, we present an alternative view of U.S. business cycles, more in line with classical AD-AS theory. This underscores the multivariate nature of cycles and challenges the existence of a Main Business-Cycle shock.

ABSTRACT. We investigate the presence of non-linearities in the transmission of geopolitical risk (GPR) shocks. We incorporate a non-linear function of the shock into a VARX model and examine its impulse response functions and historical decomposition. We observe significant non-linearities that amplify the effects of GPR shocks as the size increases. These non-linearities are triggered by heightened uncertainty, which prompts precautionary saving behaviors, exerting a strong impact on consumption and reducing activity. The response of inflation is overall more subdued due to the opposite effects on prices caused by reduced demand and the increase in uncertainty. However, we find that geopolitical shocks related to threats of future events exhibit marked non-linearities and exert a stronger impact on prices through an increase in oil prices and inflation expectations.

ABSTRACT. This paper studies the effect of aggregate shocks on micro-level outcomes. We develop and estimate a cross-sectional units vector autoregression (csuVAR) that combines aggregate variables with unit-level outcomes, earnings in our application. The csuVAR also allows us to reconstruct the cross-sectional distribution from the unit-level outcomes. We contrast the csuVAR with a functional VAR model (fVAR) that is designed to directly track the evolution of macroeconomic aggregates and a cross-sectional distribution, but not individual units. In an empirical application we examine the effect of productivity shocks on the unit-level labor earnings dynamics in Germany, using a panel data set constructed from the Sample of Integrated Labour Market Biographies (SIAB) published by Institute for Employment Research (IAB) of the German Federal Employment Agency.

ABSTRACT. Which shocks explain the volatility in US real GDP? We study this question using a vector autoregressive model with t-distributed shocks. We first show that a simple reparameterization allows for the development of the first Gibbs sampler for this model. This improves upon existing methods that require a computationally more demanding Metropolis-Hastings step, allowing us to use larger VAR models than in the previous literature. Our application to US data suggests that there is no such thing as a single, main business cycle shock. No shock explains more than 20% of the variability of real GDP, with the largest role played by a weakly inflationary demand shock.

ABSTRACT. The substantial fluctuations in oil prices in the wake of the COVID-19 pandemic and the Russian invasion of Ukraine have highlighted the importance of tail events in the global oil market which call for careful risk assessment. In this paper we focus on forecasting tail risks for the real price of oil using three model classes that are popular for studying tail behavior. We show that a nonparametric approach, based on Bayesian additive regression trees, where shocks are driven by a stochastic volatility (SV) model, improves in terms of tail forecasts upon three competing models: quantile regressions, a Bayesian VAR with SV, and the random walk with SV. We quantify the role of various economic determinants for upside and downside oil price risks, and we provide evidence that monetary policy actions can be explained by higher moments of the predictive distribution of oil prices. We also illustrate the practical relevance of our new approach by tracking the evolution of predictive densities during three recent economic and geopolitical crisis episodes, by developing consumer and producer distress indices, and by conducting stress tests based on risk scenarios for 2024.

ABSTRACT. We propose a reverse unrestricted mixed-frequency Bayesian panel (RU-PMIDAS) where employing a hierarchical structure, random effects introduce interdependence across countries and high-frequency time periods. We consider a novel hourly dataset and use the model to study the impact of hourly forecasted demand, renewable energy sources (RES), and daily fossil fuel prices on hourly electricity prices in a multi-country panel that includes several European countries. We are able to measure the degree of integration in the European electricity markets through the model's random effects.

ABSTRACT. This paper provides a comprehensive analysis of the forecastability of the real price of natural gas in the United States at the monthly frequency considering a universe of models that differ in their complexity and economic content. Our key finding is that considerable reductions in mean-squared prediction error relative to a random walk benchmark can be achieved in real time for forecast horizons of up to two years. A particularly promising model is a six-variable Bayesian vector autoregressive model that includes the fundamental determinants of the supply and demand for natural gas. To capture real-time data constraints of these and other predictor variables, we assemble a rich database of historical vintages from multiple sources. We also compare our model-based forecasts to readily available model-free forecasts provided by experts and futures markets. Given that no single forecasting method dominates all others, we explore the usefulness of pooling forecasts and find that combining forecasts from individual models selected in real time based on their most recent performance delivers the most accurate forecasts.

ABSTRACT. It has long been argued that the yield curve is a powerful descriptor of the economy and the expectation of the markets. Although not universal, a very common approach to give a statistical description on the yield curve relies on the idea that a small number of factors can describe adequately the whole curve. Under this assumption, it may be thought that if one could observe the factors, then these can be used to forecast real activity. In this paper, we argue that optimal extraction of the factor is key for squeezing out information from the yields when considering an approximate factor model. In fact, with a rotation of the factor model including cointegration, as proposed in Casoli and Lucchetti (2022), we reduce the cross-sectional correlation of the idiosyncratic components. We show that this advantage produces better forecasts of relevant macroeconomic variables in periods of economic instability and financial turmoil.

ABSTRACT. We show that, for a certain class of scaling matrices including the commonly used inverse square-root of the conditional Fisher Information, score-driven factor models are identifiable up to a multiplicative scalar constant under very mild restrictions. This result has no analogue in parameter-driven models, as it exploits the different structure of the score-driven factor dynamics. Consequently, score-driven models offer a clear advantage in terms of economic interpretability compared to parameter-driven factor models, which are identifiable only up to orthogonal transformations. Our restrictions are order-invariant and can be generalized to score-driven factor models with dynamic loadings and nonlinear factor models. We test extensively the identification strategy using simulated and real data. The empirical analysis on financial and macroeconomic data reveals a substantial increase of log-likelihood ratios and significantly improved out-of-sample forecast performance when switching from the classical restrictions adopted in the literature to our more flexible specifications.

ABSTRACT. We develop an estimation methodology for a factor model for a high-dimensional matrix-valued time series, where both common stochastic trends and common stationary factors can be present. We study, in particular, the estimation of (row and column) loading spaces, of the common stochastic trends and of the common stationary factors, and the row and column ranks thereof. In a set of (negative) preliminary results, we show that a projection-based technique fails to improve the rates of convergence compared to a ``flattened'' estimation technique which does not take into account the matrix nature of the data. Hence, we develop a three-step algorithm where: (i) we first project the data onto the orthogonal complement to the (row and column) loadings of the common stochastic trends; (ii) we subsequently use such ``trend free''\ data to estimate the stationary common component; (iii) we remove the estimated common stationary component from the data, and re-estimate, using a projection-based estimator, the row and column common stochastic trends and their loadings. We show that this estimator succeeds in refining the rates of convergence of the initial, ``flattened''\ estimator. As a by-product, we develop eigenvalue-ratio based estimators for the number of stationary and nonstationary common factors, and a test for the null hypothesis that the matrix-valued data have a unit root.

ABSTRACT. We estimate the short-run effects of weather-related disasters on local economic activity and cross-border spillovers that operate through economic linkages between U.S. states. To this end, we use emergency declarations triggered by natural disasters and estimate their effects using a monthly Global Vector Autoregressive (GVAR) model for U.S. states. Impulse responses highlight the nationwide effects of weather-related disasters that hit individual regions. Taking into account economic linkages between states allows capturing much stronger spillovers than those associated with mere spatial adjacency. Moreover, geographic heterogeneity is crucial for assessing the nationwide impact of weather-related disasters, and network effects amplify the local effects of such shocks.

ABSTRACT. To what extent emission reductions are driven by aggregate shocks? This study explores the drivers of aggregate greenhouse gas emissions intensity reductions in the UK from 1990 to 2020, utilizing a novel time series dataset of greenhouse gas emissions for 108 industries. This is the first time that an industry-level emissions dataset covers such a long time span, giving us an opportunity to not only study trends, but also co-movement, allowing us to identify the relative importance of industry-level vs. aggregate shocks. We fit a block-level dynamic factor model, which provides a decomposition of the variation of emissions intensity into contributions from a common factor, industry group factors, and industry-specific idiosyncratic shocks. We find that the economy-wide (common) factor, while having a non negligible effect, has had limited contribution to declining emissions intensity. This suggests that industry-level policies and technological innovations have been the dominant forces, thus far.

ABSTRACT. This paper examines the impact of climate-driven disasters on commodity prices. Using extensive archival sources including census data and declassified CIA intelligence reports, I develop a global geospatial dataset to identify the locations of key commodity-producing sites at subnational level since the 1970s. By linking these regions to climate disaster events, I find that, over time, production has become increasingly concentrated in high-risk areas. Leveraging this dataset, I analyze how commodity futures respond to climate-driven shocks and uncover significant cross-sectional differences. Specifically, a long-only portfolio of vulnerable commodities yields a significant monthly alpha of 0.90%, whereas that of resilient commodities, albeit still significant, is negative at -0.43%, reflecting a premium paid for protection against climate shocks. Furthermore, I find that vulnerable commodities experience slower recoveries from past shocks.

ABSTRACT. In this study we examine the return performance of a Green minus Brown portfolio aiming to hedge climate risk. While existing studies focus on the empirical analysis within the time domain, we analyze the contribution of climate risk to return performance to be varying across frequency bands. For this purpose, we use the Maximal Overlapping Discrete Wavelet filter to retrieve the wavelet coefficients of the risk market adjusted return on a Green and Brown portfolio and an index climate concern. Then, through factor decomposition (via ML) of the scale covariance matrix (which varies across frequency bands) we find that green stock outperformance during period of increase climate concern is concentrated over the short run (less than one year). Moreover, focusing on the long run, we find evidence of a climate risk premium underlying the expected return of brown stocks higher than the one associated with green stocks. Finally we propose a Likelihood ratio statistics based on non-parametric multiresolution analysis is to test the homogeneity restrictions of the coefficients across frequency bands as implied by traditional factor models