Predicting Federal Funds Rate Using Extreme Value Theory

2020 ◽  
Vol 35 (1) ◽  
pp. 1-15
Author(s):  
Ashim Kumar Dey ◽  
Kumer Pial Das
Keyword(s):  
Extreme Events ◽  
Extreme Value Theory ◽  
Simulated Data ◽  
Value Theory ◽  
Extreme Value ◽  
Economic Sectors ◽  
Federal Funds ◽  
Federal Funds Rate ◽  
Estimated Parameters ◽  
The Us

AbstractThe extreme value theory (EVT) is used to assess the risk of extreme events caused by natural calamities or untoward circumstances in the social and economic sectors. The theory can be used to study the frequency of rare events and to build up a predictive model so that one can attempt to forecast the frequency of such future extreme events such as a financial collapse and the amount of damage from such a collapse. Even though many statistical techniques have been used to analyze the manner in which the Federal Reserve determines the level of the Federal Fund Rates, no known study has used EVT to analyze and predict the extreme fund rates. In this study, the US Federal Funds Rate, one of the most publicized and important economic indicators in the financial world, from 1954–2019 has been analyzed. The contributions of this study are: (1) to provide an appropriate model for the normalized Federal Funds Rate data; (2) to compare several estimation techniques in estimating parameters for two possible models; (3) to predict the maximum economic return rate from a Federal Funds Rate in the future by using the concept of the return period; and (4) to investigate the bias of estimated parameters applying a simulation study. Simulated data and real financial data are used for the study, and the outcome satisfies the efficiency of its application.

scholarly journals Using Statistical Approaches to Model Natural Disasters

2016 ◽  
Vol 13 (2) ◽  
Author(s):  
Audrene Edwards ◽  
Kumer Das
Keyword(s):  
Extreme Events ◽  
Extreme Value Theory ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Threshold Values ◽  
Data Set ◽  
Generalized Pareto ◽  
Estimated Parameters

The study of extremes has attracted the attention of scientists, engineers, actuaries, policy makers, and statisticians for many years. Extreme value theory (EVT) deals with the extreme deviations from the median of probability distributions and is used to study rare but extreme events. EVT’s main results characterize the distribution of the sample maximum or the distribution of values above a given threshold. In this study, EVT has been used to construct a model on the extreme and rare earthquakes that have happened in the United States from 1700 to 2011.The primary goal of fitting such a model is to estimate the amount of losses due to those extreme events and the probabilities of such events. Several diagnostic methods (for example, QQ plot and Mean Excess Plot) have been used to justify that the data set follows generalized Pareto distribution (GPD). Three estimation techniques have been employed to estimate parameters. The consistency and reliability of estimated parameters have been observed for different threshold values. The purpose of this study is manifold: first, we investigate whether the data set follows GPD, by using graphical interpretation and hypothesis testing. Second, we estimate GPD parameters using three different estimation techniques. Third, we compare consistency and reliability of estimated parameters for different threshold values. Last, we investigate the bias of estimated parameters using a simulation study. The result is particularly useful because it can be used in many applications (for example, disaster management, engineering design, insurance industry, hydrology, ocean engineering, and traffic management) with a minimal set of assumptions about the true underlying distribution of a data set. KEYWORDS: Extreme Value Theory; QQ Plot; Mean Excess Plot; Mean Residual Plot; Peak Over Threshold; Generalized Pareto Distribution; Maximum Likelihood Method; Method of Moments; Probability-Weighted Moments; Shapiro-Wilk test; Anderson- Darling Test

scholarly journals Extreme events in total ozone over Arosa – Part 1: Application of extreme value theory

2010 ◽  
Vol 10 (20) ◽  
pp. 10021-10031 ◽  
Author(s):  
H. E. Rieder ◽  
J. Staehelin ◽  
J. A. Maeder ◽  
T. Peter ◽  
M. Ribatet ◽  
...  
Keyword(s):  
Time Series ◽  
Frequency Distribution ◽  
Extreme Events ◽  
Extreme Value Theory ◽  
Total Ozone ◽  
Volcanic Eruptions ◽  
Value Theory ◽  
Extreme Value ◽  
Data Set ◽  
Ozone Data

Abstract. In this study ideas from extreme value theory are for the first time applied in the field of stratospheric ozone research, because statistical analysis showed that previously used concepts assuming a Gaussian distribution (e.g. fixed deviations from mean values) of total ozone data do not adequately address the structure of the extremes. We show that statistical extreme value methods are appropriate to identify ozone extremes and to describe the tails of the Arosa (Switzerland) total ozone time series. In order to accommodate the seasonal cycle in total ozone, a daily moving threshold was determined and used, with tools from extreme value theory, to analyse the frequency of days with extreme low (termed ELOs) and high (termed EHOs) total ozone at Arosa. The analysis shows that the Generalized Pareto Distribution (GPD) provides an appropriate model for the frequency distribution of total ozone above or below a mathematically well-defined threshold, thus providing a statistical description of ELOs and EHOs. The results show an increase in ELOs and a decrease in EHOs during the last decades. The fitted model represents the tails of the total ozone data set with high accuracy over the entire range (including absolute monthly minima and maxima), and enables a precise computation of the frequency distribution of ozone mini-holes (using constant thresholds). Analyzing the tails instead of a small fraction of days below constant thresholds provides deeper insight into the time series properties. Fingerprints of dynamical (e.g. ENSO, NAO) and chemical features (e.g. strong polar vortex ozone loss), and major volcanic eruptions, can be identified in the observed frequency of extreme events throughout the time series. Overall the new approach to analysis of extremes provides more information on time series properties and variability than previous approaches that use only monthly averages and/or mini-holes and mini-highs.

Extreme Value Distribution Theory and its Application in Durability Analysis

2012 ◽  
Author(s):  
Zhigang Wei ◽  
Pingsha Dong ◽  
Litang Gao ◽  
Robert Kurth
Keyword(s):  
Fatigue Life ◽  
Fatigue Damage ◽  
Extreme Events ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Life Assessment ◽  
Assessment Process ◽  
Fatigue Life Assessment ◽  
Axial Fatigue

Risk based treatment of degradation and failure in engineering components is an important topic in recent years with an emphasis on obtaining more detailed information for extreme events. Fatigue damage and life degradation caused by variable amplitude cyclic loading is dominated by such extreme events, and can be properly treated with the extreme value theory, which could help understand the damage nature of the fatigue damage process as well as to provide more efficient and robust approaches for engineering applications. In this paper, advanced extreme value theory is reviewed first. Methods such as peak counting, block maxima, and peaks over thresholds are investigated and compared in this paper with an emphasis on the relationship between the extreme value theory and the existing methods for fatigue life assessment. A few simple examples of uniaxial and multi-axial fatigue life assessment process are provided and the results are discussed. It is found that, if properly used, the extreme value theories can improve the efficiency of fatigue life assessment. Finally, a hybrid time- and frequency-based multi-axial fatigue life assessment procedure is proposed for wide band loadings.

scholarly journals Mixed Method of Extreme Value Theory, with Application to the Calculation of the Portion of Each Claim Payable by the Reinsurer of Excess of Sinister

2016 ◽  
Vol 5 (2) ◽  
pp. 100
Author(s):  
Yingmei Xu ◽  
Kane Ladji ◽  
Diawara Daouda
Keyword(s):  
Bayesian Methods ◽  
Extreme Value Theory ◽  
Mixed Method ◽  
Simulated Data ◽  
Value Theory ◽  
Extreme Value ◽  
Graphical Methods ◽  
Insurance Company

<p>In the literature many determinists approaches (numerical and graphical methods), probability (the probability law, extreme value theory, Bayesian methods) exist for the detection of grave sinister. In this paper, we will give a new characterization of the mixed method of extreme value theory. These results are applied to the simulated data of a Malian insurance company.</p>

scholarly journals Extreme events in total ozone over Arosa – Part 1: Application of extreme value theory

2010 ◽  
Vol 10 (5) ◽  
pp. 12765-12794 ◽  
Author(s):  
H. E. Rieder ◽  
J. Staehelin ◽  
J. A. Maeder ◽  
T. Peter ◽  
M. Ribatet ◽  
...  
Keyword(s):  
Time Series ◽  
Frequency Distribution ◽  
Extreme Events ◽  
Extreme Value Theory ◽  
Total Ozone ◽  
Volcanic Eruptions ◽  
Value Theory ◽  
Extreme Value ◽  
Data Set ◽  
Ozone Data

Abstract. In this study ideas from extreme value theory are for the first time applied in the field of stratospheric ozone research, because statistical analysis showed that previously used concepts assuming a Gaussian distribution (e.g. fixed deviations from mean values) of total ozone data do not adequately address the structure of the extremes. We show that statistical extreme value methods are appropriate to identify ozone extremes and to describe the tails of the Arosa (Switzerland) total ozone time series. In order to accommodate the seasonal cycle in total ozone, a daily moving threshold was determined and used, with tools from extreme value theory, to analyse the frequency of days with extreme low (termed ELOs) and high (termed EHOs) total ozone at Arosa. The analysis shows that the Generalized Pareto Distribution (GPD) provides an appropriate model for the frequency distribution of total ozone above or below a mathematically well-defined threshold, thus providing a statistical description of ELOs and EHOs. The results show an increase in ELOs and a decrease in EHOs during the last decades. The fitted model represents the tails of the total ozone data set with high accuracy over the entire range (including absolute monthly minima and maxima), and enables a precise computation of the frequency distribution of ozone mini-holes (using constant thresholds). Analyzing the tails instead of a small fraction of days below constant thresholds provides deeper insight into the time series properties. Fingerprints of dynamical (e.g. ENSO, NAO) and chemical features (e.g. strong polar vortex ozone loss), and major volcanic eruptions, can be identified in the observed frequency of extreme events throughout the time series. Overall the new approach to analysis of extremes provides more information on time series properties and variability than previous approaches that use only monthly averages and/or mini-holes and mini-highs.

scholarly journals Extreme value theory in analysis of differential expression in microarrays where either only up- or down-regulated genes are relevant or expected

2008 ◽  
Vol 90 (4) ◽  
pp. 347-361 ◽  
Author(s):  
RENATA IVANEK ◽  
YRJÖ T. GRÖHN ◽  
MARTIN T. WELLS ◽  
SARITA RAENGPRADUB ◽  
MARK J. KAZMIERCZAK ◽  
...  
Keyword(s):  
Differential Expression ◽  
Extreme Value Theory ◽  
Empirical Bayes ◽  
Simulated Data ◽  
Real Data ◽  
Value Theory ◽  
Extreme Value ◽  
Type Versus ◽  
Wild Type ◽  
Gene Markers

SummaryWe propose an empirical Bayes method based on the extreme value theory (EVT) (BE) for the analysis of data from spotted microarrays where the interest of the investigator (e.g. to identify up-regulated gene markers of a disease) or the design of the experiment (e.g. in certain ‘wild-type versus mutant’ experiments) limits identification of differentially expressed genes to those regulated in a single direction (either up or down). In such experiments, unlike in genome-wide microarrays, analysis is restricted to the tail of the distribution (extremes) of all the genes in the genome. The EVT provides a platform to account for this extreme behaviour, and is therefore a natural candidate for inference about differential expression. We compared the performance of the developed BE method with two other empirical Bayes methods on two real ‘wild-type versus mutant’ datasets where a single direction of regulation was expected due to experimental design, and in a simulation study. The BE method appears to have a better fit to the real data. In the analysis of simulated data, the BE method showed better accuracy and precision while being robust to different characteristics of microarray experiments. The BE method, therefore, seems promising and useful for inference about differential expression in microarrays where either only up- or down-regulated genes are relevant or expected.

scholarly journals Extreme Value Theory

2019 ◽  
pp. 39-60
Author(s):  
Maria Jacob ◽  
Cláudia Neves ◽  
Danica Vukadinović Greetham
Keyword(s):  
Probability Theory ◽  
Natural Disasters ◽  
Extreme Events ◽  
Extreme Value Theory ◽  
General Public ◽  
Value Theory ◽  
Extreme Value ◽  
Public Realm ◽  
Reliability Engineering ◽  
The Public

Abstract From travel disruptions to natural disasters, extreme events have long captured the public’s imagination and attention. Due to their rarity and often associated calamity, they make waves in the news (Fig. 3.1) and stir discussion in the public realm: is it a freak event? Events of this sort may be shrouded in mystery for the general public, but a particular branch of probability theory, notably Extreme Value Theory (EVT), offers insight to their inherent scarcity and stark magnitude. EVT is a wonderfully rich and versatile theory which has already been adopted by a wide variety of disciplines in a plentiful way. From its humble beginnings in reliability engineering and hydrology, it has now expanded much further; it can be used to model the occurrences of records (say for example in athletic events) or quantify the probability of floods with magnitude greater than what has been observed in the past, i.e it allows us extrapolate beyond the range of available data!

Sign in / Sign up

Export Citation Format

Share Document