金融代写|金融计量经济学代写Financial Econometrics代考|Random Walk Hypothesis

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  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
金融代写|金融计量经济学代写Financial Econometrics代考|Random Walk Hypothesis

金融代写|金融计量经济学Financial Econometrics代考|Background

The basic idea is that movement of the stock prices are unpredictable and random. Jules Augustin Frédéric Regnault, a French stock broker’s subordinate primarily explained the rationale behind the stock prices stochastic movements using a random walk model. Jules in his book titled ” Calcul des chances et philosophie de la bourse” states that “l’écart des cours est en raison directe de la racine carrée des temps”. 1 Which means “the price difference is a direct result of the square root of the times” and it clearly indicates that the stock prices movement follows a stochastic process. Later it becomes the foundation of Louis Bachelier PhD thesis titled “Th’corie de la Sp’eculation”. Louis often credited as the first person to introduce advanced mathematics into the field of finance. He established a mathematical model of the stochastic process (known as Brownian motion) for valuing the stock options. For a longer period of time Louis’ contribution was overlooked or ignored as his study applied mathematics into the field of finance. Possible reason could be during the nineteenth century the field of interdisciplinary research was not developed or quite accustomed. Then in 1964, Paul H. Cootner, a professor of MIT Sloan School of Management in his book titled “The Random Character of Stock Market Prices” educes the ideas on the stochastic process of stock prices movements. Later on the same ideas are well established by the several known scholars namely Eugene Fama, Burton Malkiel, and others.

金融代写|金融计量经济学Financial Econometrics代考|What Is Random Walk Hypothesis and Its Implications

Random walk hypothesis assumes that price movements of individual securities in the stock markets follow a random walk and successive price movements are independent to each other. Therefore, the random walk hypothesis posits that it is impossible to forecast the stock prices movements. Random walk hypothesis also suggests that it is impossible to beat the market by the market participants in the long run. Outperformance of the market by an investor is only possible by taking an extra amount of risk. The Random Walk hypothesis is heavily criticized on several grounds such as market participants differ in terms of the amount of time they spend in the financial market. Then several numbers of the known and unknown factors are responsible for driving the stock prices (Maiti, 2020). It is often not likely to detect the associated trends or patterns that might exist in the stock prices movements due to the presence of several such distinct factors. To test the random walk hypothesis in practice, Wall Street Journal (WSJ) initiated the “Dart Throwing Investment Contest” in the year 1988. Two groups were formed: one group belongs to the professional investors whereas other belongs to the dummy. Professional investors group consists of the professionals working with NYSE whereas WSJ staff groups as the dummy. In other words professional investors represent “skill” whereas dummy represents “luck”. Professional investors selected stocks based on their skills whereas dummy made their selection of stocks based on the outcome of the dart throwing (luck). After 100 contests the outcomes come as following: professional investors won 61 times or skill wins 61 times versus luck. However, professional investors (skill) are able to beat the market (DJIA) 51 times out of 100 . Dart Throwing Investment Contest does not provide any ultimate consensus on “luck versus skills”. The current consensus is that the random walk hypothesis is linked to the efficient market hypothesis (EMH). Mathematically a simple random walk model with a drift is represented by following Eq. (2.1):
\text { Price }{t}=\text { Price }{t-1}+\alpha_{t}
$/ / \operatorname{Mean}(\mu)$ is zero and standard deviation $(\sigma)$ is constant where
Price $_{t}$ represents current stock price at time ( $\left.t\right)$
Price $_{t-1}-$ represents stock price at time $(t-1)$
$\alpha_{t}$ represents the drift term

金融代写|金融计量经济学Financial Econometrics代考|Efficient Market Hypothesis

Efficient market hypothesis assumes that the security prices reflect all available information and follow a random walk. However, the strength of these assumptions depends on the form of EMH as explained by Fama (1970). Thus, the direct implication of EMH is that it is impossible to beat the market steadily merely by ensuing a specific risk adjusted strategy. Fama (1970) labels efficient market hypothesis into three types based on the level of the relevant information as weak, semi-strong and strong forms of EMH, respectively. Weak forms of EMH assume that all historical stock prices information is impounded in the current price of the stock. Then a semi-strong form of EMH assumes that all publicly available information in addition to those historical stock prices information are well impounded in the current price of the stock. Finally, strong forms of EMH assume that all available information both private (insider information) and public is fully impounded in the current price of the stock. The joint hypothesis problem makes it difficult to test the EMH. The argument put forward as the EMH could only be tested with the help of a market equilibrium model (Asset pricing model). The EMH basically tests whether the properties of expected returns suggested by the assumed market equilibrium model (asset pricing model) are noticed in actual returns. If the tests reject, then it is difficult to interpret whether the rejection is made due to the inefficiency of the market or a bad market equilibrium model (asset pricing model). Fama (1970) stressed that the EMH is always tested jointly along with the market equilibrium model and vice versa. Thereafter significant number of studies are done on EMH and asset pricing. All of these studies unanimously emphasized that the $\mathrm{EMH}$ is very simple in principle but testing it proved to be difficult. Both the random walk hypothesis and efficient market hypothesis have significant importance in applied financial econometrics study as both of them could provide some relevant information on relative market efficiency. Still distinct views exist on whether markets are really efficient? There are several studies that evidence support for EMH such as on an average mutual funds do not able to outperformed the market. Then “Dart Throwing Investment Contest” results show that the performance of skills versus luck are quite similar in beating the market. On the other hand, there are group of studies that evidence against EMH is as follows: presence of stock market anomalies, presence of excessive volatility in the stock market, behavioural finance theories, and others.

金融代写|金融计量经济学代写Financial Econometrics代考|Random Walk Hypothesis


金融代写|金融计量经济学Financial Econometrics代考|Background

基本思想是股票价格的变动是不可预测的和随机的。法国股票经纪人的下属 Jules Augustin Frédéric Regnault 主要使用随机游走模型解释了股票价格随机变动背后的基本原理。Jules 在他的书“Calcul des chance et philosophie de la bourse”中指出“l’écart des cours est en raison directe de la racine carrée des temps”。1 这意味着“价格差异是时间平方根的直接结果”,它清楚地表明股票价格走势遵循随机过程。后来它成为 Louis Bachelier 博士论文“Th’corie de la Sp’eculation”的基础。路易斯经常被誉为将高等数学引入金融领域的第一人。他建立了用于评估股票期权的随机过程(称为布朗运动)的数学模型。在很长一段时间内,路易斯的贡献被忽视或忽视,因为他的研究将数学应用于金融领域。可能的原因可能是在 19 世纪,跨学科研究领域没有发展或相当习惯。然后在 1964 年,麻省理工学院斯隆管理学院教授 Paul H. Cootner 在他的《股票市场价格的随机特征》一书中提出了关于股票价格变动随机过程的观点。后来,几位著名的学者,即尤金·法玛、伯顿·马尔基尔和其他人,也确立了同样的观点。在很长一段时间内,路易斯的贡献被忽视或忽视,因为他的研究将数学应用于金融领域。可能的原因可能是在 19 世纪,跨学科研究领域没有发展或相当习惯。然后在 1964 年,麻省理工学院斯隆管理学院教授 Paul H. Cootner 在他的《股票市场价格的随机特征》一书中提出了关于股票价格变动随机过程的观点。后来,几位著名的学者,即尤金·法玛、伯顿·马尔基尔和其他人,也确立了同样的观点。在很长一段时间内,路易斯的贡献被忽视或忽视,因为他的研究将数学应用于金融领域。可能的原因可能是在 19 世纪,跨学科研究领域没有发展或相当习惯。然后在 1964 年,麻省理工学院斯隆管理学院教授 Paul H. Cootner 在他的《股票市场价格的随机特征》一书中提出了关于股票价格变动随机过程的观点。后来,几位著名的学者,即尤金·法玛、伯顿·马尔基尔和其他人,也确立了同样的观点。麻省理工学院斯隆管理学院教授在他的《股票市场价格的随机特征》一书中提出了关于股票价格变动随机过程的观点。后来,几位著名的学者,即尤金·法玛、伯顿·马尔基尔和其他人,也确立了同样的观点。麻省理工学院斯隆管理学院教授在他的《股票市场价格的随机特征》一书中提出了关于股票价格变动随机过程的观点。后来,几位著名的学者,即尤金·法玛、伯顿·马尔基尔和其他人,也确立了同样的观点。

金融代写|金融计量经济学Financial Econometrics代考|What Is Random Walk Hypothesis and Its Implications

随机游走假设假设股票市场中单个证券的价格变动遵循随机游走,并且连续的价格变动相互独立。因此,随机游走假设假设不可能预测股票价格的变动。随机游走假设还表明,从长远来看,市场参与者不可能击败市场。只有承担额外的风险,投资者才有可能超越市场表现。随机游走假设因几个原因而受到严厉批评,例如市场参与者在金融市场上花费的时间不同。然后,一些已知和未知的因素推动了股价(Maiti,2020)。由于存在几个这样的不同因素,通常不太可能检测到股票价格变动中可能存在的相关趋势或模式。为在实践中检验随机游走假设,华尔街日报(WSJ)于 1988 年发起了“投掷飞镖投资大赛”,形成了两组:一组属于专业投资者,另一组属于虚拟投资者。专业投资者组由与 NYSE 合作的专业人士组成,而 WSJ 员工组则为虚拟对象。换句话说,专业投资者代表“技能”,而虚拟投资者代表“运气”。专业投资者根据他们的技能选择股票,而虚拟投资者根据投掷飞镖的结果(运气)选择股票。经过100场比赛,结果如下:专业投资者赢了 61 次或技巧赢了 61 次与运气。然而,专业投资者(技能)能够在 100 次中击败市场 (DJIA) 51 次。Dart Throwing Investment Contest 并未就“运气与技能”达成任何最终共识。目前的共识是随机游走假说与有效市场假说(EMH)相关联。在数学上,带有漂移的简单随机游走模型由以下等式表示。(2.1): 在数学上,带有漂移的简单随机游走模型由以下等式表示。(2.1): 在数学上,带有漂移的简单随机游走模型由以下等式表示。(2.1):

 价格 吨= 价格 吨−1+一个吨
价格吨表示当时的股票价格 (吨)

金融代写|金融计量经济学Financial Econometrics代考|Efficient Market Hypothesis

有效市场假设假设证券价格反映了所有可用信息并遵循随机游走。然而,这些假设的强度取决于 Fama (1970) 解释的 EMH 的形式。因此,EMH 的直接含义是,仅仅通过采取特定的风险调整策略是不可能稳定地击败市场的。Fama(1970)根据相关信息的水平将有效市场假设分为三种类型,分别为EMH的弱、半强和强形式。EMH 的弱形式假设所有历史股票价格信息都包含在股票的当前价格中。然后,半强形式的 EMH 假设除了那些历史股票价格信息之外的所有公开可用信息都很好地保留在股票的当前价格中。最后,强大的 EMH 形式假设所有可用的私人信息(内幕信息)和公共信息都完全包含在股票的当前价格中。联合假设问题使 EMH 难以检验。作为 EMH 提出的论点只能在市场均衡模型(资产定价模型)的帮助下进行检验。EMH 主要测试假设的市场均衡模型(资产定价模型)所建议的预期收益的属性是否在实际收益中被注意到。如果测试拒绝,那么很难解释拒绝是由于市场效率低下还是市场均衡模型(资产定价模型)不好。Fama (1970) 强调 EMH 总是与市场均衡模型一起测试,反之亦然。此后,对 EMH 和资产定价进行了大量研究。所有这些研究都一致强调,和米H原则上非常简单,但测试它被证明是困难的。随机游走假设和有效市场假设在应用金融计量经济学研究中都具有重要意义,因为它们都可以提供有关相对市场效率的一些相关信息。关于市场是否真的有效,仍然存在不同的观点吗?有几项研究表明,支持 EMH 的证据,例如平均而言共同基金无法跑赢市场。然后“投掷飞镖投资大赛”结果显示,在击败市场方面,技巧与运气的表现相当相似。另一方面,有一组研究表明反对 EMH 的证据如下:股票市场异常的存在、股票市场过度波动的存在、行为金融学理论等。

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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。