scholarly journals Detecting Lineage-Specific Shifts in Diversification: A Proper Likelihood Approach

2020 ◽  
Author(s):  
Giovanni Laudanno ◽  
Bart Haegeman ◽  
Daniel L Rabosky ◽  
Rampal S Etienne
Keyword(s):  
Model Selection ◽  
Phylogenetic Tree ◽  
Time Dependent ◽  
Parameter Estimates ◽  
Time Varying ◽  
Diversification Rates ◽  
Branching Patterns ◽  
Recent Debate ◽  
Likelihood Approach ◽  
New Framework

Abstract The branching patterns of molecular phylogenies are generally assumed to contain information on rates of the underlying speciation and extinction processes. Simple birth–death models with constant, time-varying, or diversity-dependent rates have been invoked to explain these patterns. They have one assumption in common: all lineages have the same set of diversification rates at a given point in time. It seems likely, however, that there is variability in diversification rates across subclades in a phylogenetic tree. This has inspired the construction of models that allow multiple rate regimes across the phylogeny, with instantaneous shifts between these regimes. Several methods exist for calculating the likelihood of a phylogeny under a specified mapping of diversification regimes and for performing inference on the most likely diversification history that gave rise to a particular phylogenetic tree. Here, we show that the likelihood computation of these methods is not correct. We provide a new framework to compute the likelihood correctly and show, with simulations of a single shift, that the correct likelihood indeed leads to parameter estimates that are on average in much better agreement with the generating parameters than the incorrect likelihood. Moreover, we show that our corrected likelihood can be extended to multiple rate shifts in time-dependent and diversity-dependent models. We argue that identifying shifts in diversification rates is a nontrivial model selection exercise where one has to choose whether shifts in now-extinct lineages are taken into account or not. Hence, our framework also resolves the recent debate on such unobserved shifts. [Diversification; macroevolution; phylogeny; speciation]

Flexible tree-structured signal expansions using time-varying wavelet packets

1997 ◽  
Vol 45 (2) ◽  
pp. 333-345 ◽  
Author(s):  
Zixiang Xiong ◽  
K. Ramchandran ◽  
C. Herley ◽  
M.T. Orchard
Keyword(s):  
Wavelet Packets ◽  
Time Varying

scholarly journals Orthogonal time-varying filter banks and wavelet packets

1994 ◽  
Vol 42 (10) ◽  
pp. 2650-2663 ◽  
Author(s):  
C. Herley ◽  
M. Vetterli
Keyword(s):  
Filter Banks ◽  
Wavelet Packets ◽  
Time Varying

scholarly journals Not so Harmless After All: The Fixed-Effects Model

2018 ◽  
Vol 27 (1) ◽  
pp. 21-45 ◽  
Author(s):  
Thomas Plümper ◽  
Vera E. Troeger
Keyword(s):  
Model Selection ◽  
Fixed Effects ◽  
Time Varying ◽  
Multiple Model ◽  
Fixed Effects Model ◽  
Omitted Variables ◽  
Hausman Test ◽  
Fixed Effects Estimator ◽  
Time Invariant

The fixed-effects estimator is biased in the presence of dynamic misspecification and omitted within variation correlated with one of the regressors. We argue and demonstrate that fixed-effects estimates can amplify the bias from dynamic misspecification and that with omitted time-invariant variables and dynamic misspecifications, the fixed-effects estimator can be more biased than the ‘naïve’ OLS model. We also demonstrate that the Hausman test does not reliably identify the least biased estimator when time-invariant and time-varying omitted variables or dynamic misspecifications exist. Accordingly, empirical researchers are ill-advised to rely on the Hausman test for model selection or use the fixed-effects model as default unless they can convincingly justify the assumption of correctly specified dynamics. Our findings caution applied researchers to not overlook the potential drawbacks of relying on the fixed-effects estimator as a default. The results presented here also call upon methodologists to study the properties of estimators in the presence of multiple model misspecifications. Our results suggest that scholars ought to devote much more attention to modeling dynamics appropriately instead of relying on a default solution before they control for potentially omitted variables with constant effects using a fixed-effects specification.

Time-varying lapped transforms and wavelet packets

1993 ◽  
Vol 41 (12) ◽  
pp. 3293-3305 ◽  
Author(s):  
R.L. de Queiroz ◽  
K.R. Rao
Keyword(s):  
Wavelet Packets ◽  
Time Varying

scholarly journals Model Uncertainty and Exchange Rate Forecasting

2017 ◽  
Vol 52 (1) ◽  
pp. 341-363 ◽  
Author(s):  
Roy Kouwenberg ◽  
Agnieszka Markiewicz ◽  
Ralph Verhoeks ◽  
Remco C. J. Zwinkels
Keyword(s):  
Exchange Rate ◽  
Model Selection ◽  
Model Uncertainty ◽  
Selection Rule ◽  
Time Varying ◽  
Exchange Rate Forecasting ◽  
Out Of Sample ◽  
Small Set ◽  
Strong Performance ◽  
Exchange Rate Models

Exchange rate models with uncertain and incomplete information predict that investors focus on a small set of fundamentals that changes frequently over time. We design a model selection rule that captures the current set of fundamentals that best predicts the exchange rate. Out-of-sample tests show that the forecasts made by this rule significantly beat a random walk for 5 out of 10 currencies. Furthermore, the currency forecasts generate meaningful investment profits. We demonstrate that the strong performance of the model selection rule is driven by time-varying weights attached to a small set of fundamentals, in line with theory.

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