Data Generating Process with Output Specific Efficiencies

2002 ◽  
pp. 83-87
Author(s):  
Dieter Gstach
Keyword(s):  
Data Generating Process

scholarly journals On the Connection between the GEP Performances and the Time Series Properties

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1853
Author(s):  
Alina Bărbulescu ◽  
Cristian Ștefan Dumitriu
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Functional Form ◽  
Financial Time Series ◽  
Gene Expression Programming ◽  
Parametric Models ◽  
Statistical Characteristics ◽  
Data Series ◽  
Financial Time ◽  
Data Generating Process

Artificial intelligence (AI) methods are interesting alternatives to classical approaches for modeling financial time series since they relax the assumptions imposed on the data generating process by the parametric models and do not impose any constraint on the model’s functional form. Even if many studies employed these techniques for modeling financial time series, the connection of the models’ performances with the statistical characteristics of the data series has not yet been investigated. Therefore, this research aims to study the performances of Gene Expression Programming (GEP) for modeling monthly and weekly financial series that present trend and/or seasonality and after the removal of each component. It is shown that series normality and homoskedasticity do not influence the models’ quality. The trend removal increases the models’ performance, whereas the seasonality elimination results in diminishing the goodness of fit. Comparisons with ARIMA models built are also provided.

scholarly journals Uncertainty quantification of the effects of biotic interactions on community dynamics from nonlinear time-series data

2018 ◽  
Vol 15 (147) ◽  
pp. 20180695 ◽  
Author(s):  
Simone Cenci ◽  
Serguei Saavedra
Keyword(s):  
Time Series ◽  
Community Dynamics ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Model Averaging ◽  
Biotic Interactions ◽  
Series Data ◽  
Time Intervals ◽  
Novel Approach ◽  
Data Generating Process

Biotic interactions are expected to play a major role in shaping the dynamics of ecological systems. Yet, quantifying the effects of biotic interactions has been challenging due to a lack of appropriate methods to extract accurate measurements of interaction parameters from experimental data. One of the main limitations of existing methods is that the parameters inferred from noisy, sparsely sampled, nonlinear data are seldom uniquely identifiable. That is, many different parameters can be compatible with the same dataset and can generalize to independent data equally well. Hence, it is difficult to justify conclusive assertions about the effect of biotic interactions without information about their associated uncertainty. Here, we develop an ensemble method based on model averaging to quantify the uncertainty associated with the effect of biotic interactions on community dynamics from non-equilibrium ecological time-series data. Our method is able to detect the most informative time intervals for each biotic interaction within a multivariate time series and can be easily adapted to different regression schemes. Overall, this novel approach can be used to associate a time-dependent uncertainty with the effect of biotic interactions. Moreover, because we quantify uncertainty with minimal assumptions about the data-generating process, our approach can be applied to any data for which interactions among variables strongly affect the overall dynamics of the system.

Temporal aggregation of random walk processes and implications for economic analysis

2019 ◽  
Vol 24 (2) ◽  
Author(s):  
Yamin S Ahmad ◽  
Ivan Paya
Keyword(s):  
Random Walk ◽  
Autoregressive Process ◽  
Potential Effect ◽  
Temporal Aggregation ◽  
Time Averaging ◽  
Fat Tails ◽  
Data Generating Process ◽  
Variance Ratios ◽  
Interval Sampling ◽  
The Impact

AbstractThis paper examines the impact of time averaging and interval sampling data assuming that the data generating process for a given series follows a random walk with iid errors. We provide exact expressions for the corresponding variances, and covariances, for both levels and higher order differences of the aggregated series, as well as that for the variance ratio, demonstrating exactly how the degree of temporal aggregation impacts these properties. We empirically investigate this issue on exchange rates and find that the values of the variance ratios and autocorrelation coefficients at different frequencies are consistent with our theoretical results. We also conduct a simulation exercise that illustrates the potential effect that conditional heteroskedasticity and fat tails may have on the temporal aggregation of a random walk and of a highly persistent autoregressive process.

scholarly journals A case study of the residual-based cointegration procedure

2003 ◽  
Vol 7 (1) ◽  
pp. 29-48
Author(s):  
Riccardo Biondini ◽  
Yan-Xia Lin ◽  
Michael Mccrae
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Real Life ◽  
Arima Models ◽  
Financial Time ◽  
Long Run ◽  
Data Generating Process ◽  
Finance Theory ◽  
The Relationship

The study of long-run equilibrium processes is a significant component of economic and finance theory. The Johansen technique for identifying the existence of such long-run stationary equilibrium conditions among financial time series allows the identification of all potential linearly independent cointegrating vectors within a given system of eligible financial time series. The practical application of the technique may be restricted, however, by the pre-condition that the underlying data generating process fits a finite-order vector autoregression (VAR) model with white noise. This paper studies an alternative method for determining cointegrating relationships without such a pre-condition. The method is simple to implement through commonly available statistical packages. This ‘residual-based cointegration’ (RBC) technique uses the relationship between cointegration and univariate Box-Jenkins ARIMA models to identify cointegrating vectors through the rank of the covariance matrix of the residual processes which result from the fitting of univariate ARIMA models. The RBC approach for identifying multivariate cointegrating vectors is explained and then demonstrated through simulated examples. The RBC and Johansen techniques are then both implemented using several real-life financial time series.

scholarly journals The Future Strikes Back: Using Future Treatments to Detect and Reduce Hidden Bias

2019 ◽  
pp. 004912411987595
Author(s):  
Felix Elwert ◽  
Fabian T. Pfeffer
Keyword(s):  
State Dependence ◽  
Nonparametric Test ◽  
Treatment Variable ◽  
Unmeasured Confounder ◽  
Omitted Variable Bias ◽  
The Future ◽  
Data Generating Process ◽  
Future Value ◽  
Future Treatments ◽  
Variable Bias

Conventional advice discourages controlling for postoutcome variables in regression analysis. By contrast, we show that controlling for commonly available postoutcome (i.e., future) values of the treatment variable can help detect, reduce, and even remove omitted variable bias (unobserved confounding). The premise is that the same unobserved confounder that affects treatment also affects the future value of the treatment. Future treatments thus proxy for the unmeasured confounder, and researchers can exploit these proxy measures productively. We establish several new results: Regarding a commonly assumed data-generating process involving future treatments, we (1) introduce a simple new approach and show that it strictly reduces bias, (2) elaborate on existing approaches and show that they can increase bias, (3) assess the relative merits of alternative approaches, and (4) analyze true state dependence and selection as key challenges. (5) Importantly, we also introduce a new nonparametric test that uses future treatments to detect hidden bias even when future-treatment estimation fails to reduce bias. We illustrate these results empirically with an analysis of the effect of parental income on children’s educational attainment.

Assessing Fit Quality and Testing for Misspecification in Binary-Dependent Variable Models

2012 ◽  
Vol 20 (4) ◽  
pp. 480-500 ◽  
Author(s):  
Justin Esarey ◽  
Andrew Pierce
Keyword(s):  
Political Science ◽  
Test Statistic ◽  
Critical Test ◽  
Variable Model ◽  
Data Set ◽  
Fit Statistics ◽  
Interaction Terms ◽  
Data Generating Process ◽  
Binary Dependent Variable

In this article, we present a technique and critical test statistic for assessing the fit of a binary-dependent variable model (e.g., a logit or probit). We examine how closely a model's predicted probabilities match the observed frequency of events in the data set, and whether these deviations are systematic or merely noise. Our technique allows researchers to detect problems with a model's specification that obscure substantive understanding of the underlying data-generating process, such as missing interaction terms or unmodeled nonlinearities. We also show that these problems go undetected by the fit statistics most commonly used in political science.

The Skewness of the Stock Market over Long Horizons

2020 ◽  
Author(s):  
Anthony Neuberger ◽  
Richard Payne
Keyword(s):  
Asset Pricing ◽  
Stock Market ◽  
Stock Index ◽  
Leverage Effect ◽  
Higher Moments ◽  
Data Generating Process ◽  
Short Horizon ◽  
Stock Index Returns ◽  
Standard Techniques ◽  
Daily Returns

Abstract Higher moments of long-horizon returns are important for asset pricing but are hard to measure accurately using standard techniques. We provide theory showing that short-horizon (e.g., daily) returns can be used to construct precise estimates of long-horizon (e.g., annual) moments without making strong assumptions about the data-generating process. Skewness comprises two components: skewness of short-horizon returns and a leverage effect, that is, covariance between variance and lagged returns. We provide similar results for kurtosis. An application to U.S. stock index returns shows that skew is large and negative and attenuates only slowly as one moves from monthly to multiyear horizons.

scholarly journals Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance

2019 ◽  
Vol 12 (1) ◽  
pp. 28
Author(s):  
Thi Nguyen ◽  
Anne Ruiz-Gazen ◽  
Christine Thomas-Agnan ◽  
Thibault Laurent
Keyword(s):  
Maximum Likelihood ◽  
Covariance Matrix ◽  
Mean Squared Error ◽  
Financial Assets ◽  
Multivariate Normal ◽  
Graphical Tool ◽  
Data Generating Process ◽  
Competing Models ◽  
Heavy Tailed ◽  
Gaussian Regression

To model multivariate, possibly heavy-tailed data, we compare the multivariate normal model (N) with two versions of the multivariate Student model: the independent multivariate Student (IT) and the uncorrelated multivariate Student (UT). After recalling some facts about these distributions and models, known but scattered in the literature, we prove that the maximum likelihood estimator of the covariance matrix in the UT model is asymptotically biased and propose an unbiased version. We provide implementation details for an iterative reweighted algorithm to compute the maximum likelihood estimators of the parameters of the IT model. We present a simulation study to compare the bias and root mean squared error of the ensuing estimators of the regression coefficients and covariance matrix under several scenarios of the potential data-generating process, misspecified or not. We propose a graphical tool and a test based on the Mahalanobis distance to guide the choice between the competing models. We also present an application to model vectors of financial assets returns.

scholarly journals On marginal and conditional parameters in logistic regression models

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 732-739
Author(s):  
Elena Stanghellini ◽  
Marco Doretti
Keyword(s):  
Logistic Regression ◽  
Regression Models ◽  
Conditional Logistic Regression ◽  
Exact Formula ◽  
Logistic Regression Models ◽  
Conditional Models ◽  
Data Generating Process ◽  
Binary Random Variables ◽  
Intermediate Variables ◽  
Relevant Covariates

Summary We derive the exact formula linking the parameters of marginal and conditional logistic regression models with binary mediators when no conditional independence assumptions can be made. The formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditional models vanish, thereby recovering well-known results as particular cases. It also permits the disentangling of direct and indirect effects as well as quantifying the distortion induced by the omission of relevant covariates, opening the way to sensitivity analysis. As the parameters of the conditional models are multiplied by terms that are always bounded, the derivations may also be used to construct reasonable bounds on the parameters of interest when relevant intermediate variables are unobserved. We assume that, conditionally on a set of covariates, the data-generating process can be represented by a directed acyclic graph. We also show how the results presented here lead to the extension of path analysis to a system of binary random variables.

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