# 计量经济学 Econometrics ECON20110T

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Consider a generic diffusive process governed by
$$d x=\mu(x) d t+\sigma(x) d w$$
for some vector-valued process $x$. We typically have a set of observations denoted by
$$x\left(t_{0}\right), x\left(t_{1}\right), \cdots, x\left(t_{N}\right)$$
for some set of $N$ times, usually equally spaced, e.g., $t_{i}=i h$ for some time step $h$. Following Yu (2014), we distinguish the following two limiting cases:
\begin{aligned} &N \rightarrow \infty, h \text { fixed } \ &h \rightarrow 0, N \text { fixed } \end{aligned}

## ECON20110TCOURSE NOTES ：

for $i=1, \ldots, N$ and (instantaneous) covariance structure given by $d w_{i} d w_{j}=$ $\rho_{i j} \sigma_{i} \sigma_{j} d t \equiv X_{i j} d t$. Consider now the sample covariance of $T+1$ discretely observed realizations:
$$\bar{v}=\frac{1}{T} \sum_{i=1}^{T} \Delta z_{i} \Delta z_{i}^{T}-\bar{\mu} \bar{\mu}^{T}$$
where $\Delta z_{i} \equiv z_{i}-z_{i-1}$ and the sample mean $\bar{\mu}$ is given simply by
$$\bar{\mu}=\frac{1}{T} \sum_{i=1}^{T} \Delta z_{i}=\frac{1}{T}\left(z_{T}-z_{0}\right)^{71}$$

# 计量经济学代写Econometrics 代考

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## 代写计量经济学作业代写Econometrics

### 控制理论Control theory代写

• Regression analysis回归分析
• Quasi-experiment准实验
• Simultaneous equations model同步方程模型
• Natural logarithm自然对数

## 计量经济学的相关

Econometrics uses economic theory, mathematics, and statistical inference to quantify economic phenomena. In other words, it turns theoretical economic models into useful tools for economic policymaking.

## 计量经济学相关课后作业代写

Specifically, we will focus on SV of order one $\left(L_{w}=1\right)$. Set
$$\begin{gathered} \theta=\left(a, r_{y}, r_{w}\right)^{\prime} \ v_{l}(\theta) \equiv \exp \left(\frac{a w_{l-1}+r_{w} v_{l}}{2}\right) r_{y} z_{t}, \quad \forall t \end{gathered}$$
Models (2.1) and (2.2) may then be conveniently rewritten as the following identity:
$$y_{t}-x_{t}^{\prime} \beta=v_{R}(\theta), \quad \forall t$$

# 计量经济学作业代写Econometrics代考

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## 代写计量经济学作业代写Econometrics

### 应用计量经济学Applied Econometrics代写

• 时间序列分析Time-series analysis
• 控制理论Control theory
• 数学方法Mathematical methods
• 优化理论 optimazation
• 横截面数据Cross-sectional Data

## 计量经济学Econometrics的研究对象

Econometrics may use standard statistical models to study economic questions, but most often they are with observational data, rather than in controlled experiments. In this, the design of observational studies in econometrics is similar to the design of studies in other observational disciplines, such as astronomy, epidemiology, sociology and political science. Analysis of data from an observational study is guided by the study protocol, although exploratory data analysis may be useful for generating new hypotheses. Economics often analyses systems of equations and inequalities, such as supply and demand hypothesized to be in equilibrium. Consequently, the field of econometrics has developed methods for identification and estimation of simultaneous equations models. These methods are analogous to methods used in other areas of science, such as the field of system identification in systems analysis and control theory. Such methods may allow researchers to estimate models and investigate their empirical consequences, without directly manipulating the system.

One of the fundamental statistical methods used by econometricians is regression analysis.Regression methods are important in econometrics because economists typically cannot use controlled experiments. Econometricians often seek illuminating natural experiments in the absence of evidence from controlled experiments. Observational data may be subject to omitted-variable bias and a list of other problems that must be addressed using causal analysis of simultaneous-equation models.
In addition to natural experiments, quasi-experimental methods have been used increasingly commonly by econometricians since the 1980s, in order to credibly identify causal effects.

where
$$I=1,2,3, \ldots, N \text { and } t=1,2,3, \ldots, T$$
Then the empirical implications of the ICAPM are as follows. $K-1$ represents the number of the priced state variables. In a system with $S$ state
122 M. MAITI
variables if each factor portfolio is multifactor minimal variance, then $\alpha_{i}=0$ foralli, and the minimal variance boundary is crossed by a lincar combination of factor portfolios. The above statements can be tested statistically using the GRS test. The GRS examines whether the joint alphas value cqual to zero that is $\alpha_{i}=0$ foralli.

Empirically GRS test $F$ statistics can be calculated by using the following Eq. 5.14.
$$\left(\frac{T}{N}\right)\left(\frac{T-N-K}{T-K-1}\right)\left[\frac{\alpha^{\prime} \sum^{-1} \alpha}{1+\mu^{\prime} \Omega^{-1} \mu}\right] \sim F(N, T-N-K)$$
where
T sample size
$N$ number of assets/portfolios returns
$K$ number of risk factors
$\alpha$ is a $N \times 1$ vector of the estimated intercepts
$\Sigma$ is residual covariance matrix
$\mu$ is a $K \times 1$ vector of the factor portfolios’ sample means
$\Omega$ is the factor portfolios covariance matrix
$\alpha^{\prime} \sum^{-1} \alpha$ and $\mu^{\prime} \Omega^{-1} \mu$ are scalar terms.

## 计量经济学Econometrics课后作业代写

Selection of Variables
Based on the study statement wisely selects the study variables. Selection of variables is the another important task in financial econometrics study. Most of the financial econometrics study deals with the closest proxy variables available as it is very difficult to obtained the real variables data. For example, it is very difficult to obtain the real estimates for the market returns. Influential Stock Index benchmarks (S\&P 500; BSE 30; NSE 50, and others) are often used as the proxy for market returns. For the study statement “To examine the performance of Capital Asset Pricing Model (CAPM) in Indian context”, study variables could be as follows: individual stocks or portfolio excess returns (dependent variable); risk free rate (91 days T-bills); market returns (BSE 30 or BSE-200 index monthly excess returns). For financial econometrics studies, data could be obtained from both paid and unpaid databases or data sources. Bloomberg, Thomson Reuters Eikon, Capitaline, Compustat, Datastream, CMIE Prowess, and others are some of the leading providers of financial data or databases based on subscriptions. Likewise Yahoo finance, central banks, World bank, IMF, Stock exchanges, Google finance, SEC, CoinMarketCap (Cryptocurrency), and others are some of the leading providers of public or free financial data or databases. Once variables are chosen next study period and frequency of data (daily, weekly, monthly, yearly or others) has to be specified.