Vector autoregression | EPFL Graph Search

Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of stochastic process model. VAR models generalize the single-variable (univariate) autoregressive model by allowing for multivariate time series. VAR models are often used in economics and the natural sciences. Like the autoregressive model, each variable has an equation modelling its evolution over time. This equation includes the variable's lagged (past) values, the lagged values of the other variables in the model, and an error term. VAR models do not require as much knowledge about the forces influencing a variable as do structural models with simultaneous equations. The only prior knowledge required is a list of variables which can be hypothesized to affect each other over time. Specification Definition A VAR model describes the evolution of a set of k variables, called endogenous variables, over time. Each p

Robust Multivariate and Nonlinear Time Series Models

Time series modeling and analysis is central to most financial and econometric data modeling. With increased globalization in trade, commerce and finance, national variables like gross domestic productivity (GDP) and unemployment rate, market variables like indices and stock prices and global variables like commodity prices are more tightly coupled than ever before. This translates to the use of multivariate or vector time series models and algorithms in analyzing and understanding the relationships that these variables share with each other. Autocorrelation is one of the fundamental aspects of time series modeling. However, traditional linear models, that arise from a strong observed autocorrelation in many financial and econometric time series data, are at times unable to capture the rather nonlinear relationship that characterizes many time series data. This necessitates the study of nonlinear models in analyzing such time series. The class of bilinear models is one of the simplest nonlinear models. These models are able to capture temporary erratic fluctuations that are common in many financial returns series and thus, are of tremendous interest in financial time series analysis. Another aspect of time series analysis is homoscedasticity versus heteroscedasticity. Many time series data, even after differencing, exhibit heteroscedasticity. Thus, it becomes important to incorporate this feature in the associated models. The class of conditional heteroscedastic autoregressive (ARCH) models and its variants form the primary backbone of conditional heteroscedastic time series models. Robustness is a highly underrated feature of most time series applications and models that are presently in use in the industry. With an ever increasing amount of information available for modeling, it is not uncommon for the data to have some aberrations within itself in terms of level shifts and the occasional large fluctuations. Conventional methods like the maximum likelihood and least squares are well known to be highly sensitive to such contaminations. Hence, it becomes important to use robust methods, especially in this age with high amounts of computing power readily available, to take into account such aberrations. While robustness and time series modeling have been vastly researched individually in the past, application of robust methods to estimate time series models is still quite open. The central goal of this thesis is the study of robust parameter estimation of some simple vector and nonlinear time series models. More precisely, we will briefly study some prominent linear and nonlinear models in the time series literature and apply the robust S-estimator in estimating parameters of some simple models like the vector autoregressive (VAR) model, the (0, 0, 1, 1) bilinear model and a simple conditional heteroscedastic bilinear model. In each case, we will look at the important aspect of stationarity of the model and analyze the asymptotic behavior of the S-estimator.

EPFL2010

On the rate of convergence for the autocorrelation operator in functional autoregression

Alessia Caponera, Victor Panaretos

We consider the problem of estimating the autocorrelation operator of an autoregressive Hilbertian process. By means of a Tikhonov approach, we establish a general result that yields the convergence rate of the estimated autocorrelation operator as a function of the rate of convergence of the estimated lag zero and lag one autocovariance operators. The result is general in that it can accommodate any consistent estimators of the lagged autocovariances. Consequently it can be applied to processes under any mode of observation: complete, discrete, sparse, and/or with measurement errors. An appealing feature is that the result does not require delicate spectral decay assumptions on the autocovariances but instead rests on natural source conditions. The result is illustrated by application to important special cases. (C) 2022 The Author(s). Published by Elsevier B.V.

ELSEVIER2022

Essays in Financial Economics

Christopher Trevisan

This thesis is structured in three chapters, each pertaining to a specific problem in financial economics. The first chapter, titled 'High-Frequency Jump Analysis of the Bitcoin Market' and co-authored with Prof. Olivier Scaillet and Adrien Treccani of the University of Geneva, studies the market for bitcoin, a pioneer virtual currency, and its price dynamics. Using data for all the trades that took place on the exchange Mt. Gox during the period June 2011 to November 2013, we analyse the occurrence of jumps in the price process and conclude that they are frequent (one jump per week, on average) and that they tend to cluster in time. They are predicted by the order flow imbalance and the preponderance of aggressive traders. Jumps have a short-term positive impact on market activity and illiquidity and see a persistent change in the price. The second chapter, titled 'Price Formation in the Bitcoin Market', studies the same bitcoin market from the point of view of information and the way it is incorporated in the price. I analyse different measures of liquidity and price impact and find that bitcoin exhibits more adverse selection than comparable stocks. I examine the potential profits of liquidity provision and conclude that they are insufficient, which explains the absence of market makers and consequently the low market depth. I estimate a vector autoregressive model for the returns and a trade indicator and find that the effect of past returns and past trades on contemporaneous trades is significant and singular, indicating that agents infer considerable information which leads them to update their beliefs about the future evolution of the price, consistent with the view that bitcoin is a Keynesian beauty contest. The third chapter, titled 'Cash Holdings and Credit Risk', investigates the a priori surprising empirical phenomenon that firms with larger cash holdings appear to be riskier with regards to the valuation of their debt. It is explained by the endogeneity affecting the relation between a firm's cash holdings and credit spread. Indeed, a firm facing more risk (for instance, because its cash flows are more volatile) will optimally choose larger cash holdings as a hedge. I review the related literature and present a class of continuous-time capital structure models capable of capturing this phenomenon.

EPFL2016

Essays in Financial Economics

Christopher Trevisan

EPFL2016

Robust Multivariate and Nonlinear Time Series Models

EPFL2010