Moving average

Summary

In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating a series of averages of different selections of the full data set. It is also called a moving mean (MM) or rolling mean and is a type of finite impulse response filter. Variations include: simple, cumulative, or weighted forms (described below). A moving average filter is sometimes called a boxcar filter, especially when followed by decimation. Given a series of numbers and a fixed subset size, the first element of the moving average is obtained by taking the average of the initial fixed subset of the number series. Then the subset is modified by "shifting forward"; that is, excluding the first number of the series and including the next value in the subset. A moving average is commonly used with time series data to smooth out short-term fluctuations and highlight longer-term trends or cycles. The threshold between short-term and long-term depends on the applic

Official source

https://en.wikipedia.org/wiki/Moving_average

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Robust Parameter Estimation for the Ornstein-Uhlenbeck Process

Sonja Rieder

In this thesis, we treat robust estimation for the parameters of the Ornstein–Uhlenbeck process, which are the mean, the variance, and the friction. We start by considering classical maximum likelihood estimation. For the simulation study, where we also investigate the choice of the time lag, we use the method of moment (MoM) estimator as initial estimator for the friction parameter of the maximum likelihood estimator (MLE). However, in several aspects the MLE is not robust. For robustification, we first derive elementary M-estimates by extending the method of M-estimation from Huber (1981). We use an intuitively robustified MoM estimate as initial estimate and compare by means of simulation the M-estimate with the MLE. This approach is, however, only ad-hoc since Huber’s minimum Fisher information and minimax asymptotic variance theory remains incomplete for simultaneous location and scale, and does not cover more general models (as for example the Ornstein–Uhlenbeck process). A more general robustness concept due to Kohl et al. (2010), Rieder (1994), and Staab (1984) is based on local asymptotic normality (LAN), asymptotically linear (AL) estimates, and shrinking neighborhoods. We then apply this concept to the Ornstein–Uhlenbeck process. As a measure of robustness, we consider the maximum asymptotic mean square error (maxasyMSE), which is determined by the influence curve (IC) of AL estimates. The IC represents the standardized influence of an individual observation on the estimator given the past. For two kind of neighborhoods (average and average square neighborhoods) we obtain optimally robust ICs. In case of average neighborhoods, their graph exhibits surprising, redescending behavior. For average square neighborhoods the graph is between the one of the elementary M-estimates and the MLE. Finally, we discuss the estimator construction, that is, the problem of constructing an estimator from the family of optimal ICs. We carry out in our context the One-Step construction dating back to LeCam and use both an intuitively robustified MoM estimate and the elementary M-estimate as initial estimate. This results in optimally AL estimates (for average and average square neighborhoods). By means of simulation we then compare the different estimators: MLE, elementary M-estimates, and optimally AL estimates. In addition, we give an application to electricity prices.

EPFL2012

This thesis consists of three chapters that study separate subjects in the area of corporate governance and financial intermediation. In the first chapter, I study a protectionist anti-takeover law introduced in 2014 in France that covers a subset of all firms in the economy. The law decreased affected firms' likelihood of becoming the target of a merger or acquisition and had a negative impact on shareholder value. There is no evidence that management of those firms subsequently altered firm policies in its interest. Investment, employment, wages, profitability, and capital structure remain unchanged. The share of annual CEO compensation consisting of equity instruments increased by 8.4 percentage points, suggesting that boards reacted to the loss in monitoring by the takeover market by increasing the pay-for-performance sensitivity. In the second chapter, which is co-authored work with Rüdiger Fahlenbrach, we conduct a detailed analysis of investors in successful initial coin offerings (ICOs). The average ICO has 4,700 contributors. The median participant contributes small amounts and many investors sell their tokens before the underlying product is developed. Large presale investors obtain tokens at a discount and flip part of their allocation shortly after the ICO. ICO contributors lack the protections traditionally afforded to investors in early stage financing. Nevertheless, returns nine months after the ICO are positive on average, driven mostly by an increase in the value of the Ethereum cryptocurrency. In the third chapter, which is joint work with Christoph Herpfer, we investigate how bankers use information from lending relationships to help borrowers combine resources in strategic alliances. Firms that have borrowed from the same banker or share an indirect connection through a network of bankers are significantly more likely to enter an alliance. Consistent with bankers overcoming informational frictions, their ability to facilitate alliances decreases with network distance, and is stronger for opaque borrowers. Firms connected to more potential partners via banker networks enter more alliances. These alliances are associated with positive announcement returns and brokering banks are more likely to receive future underwriting mandates.

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POD-Kriging reduced method’s application in Tandem Cylinders’ flow

Jan Sickmann Hesthaven, Han Xiao

The configuration of Tandem Cylinders is a typical one in researching noise and interactions between different components, where the Distance-diameter ratio is a very significant parameter with which the flow form varies a lot. To clearly research the ratio’s effect on Tandem Cylinders flow as well as the unsteady flow physics, a reduced-order model is built where Proper orthogonal Decomposition(POD) is used to extract reduced basis modes, and Kriging model is used to train sample data and interpolate projection coefficents for each reduced basis. To ensure the snapshots’ accuracy, the scale-adaptive simulation (SAS) model based on k-SST turbulence model is used to predict time-dependent flow field. By comparing with solutions provided by the numerical solver as well as experimental data, the reduced model presents a good accuracy and efficiency. And then based on the reduced basis, the change regulation of the time-average flow is summarized.

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EPFL2020

Robust Parameter Estimation for the Ornstein-Uhlenbeck Process

Sonja Rieder

EPFL2012