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金融计量经济学Financial Econometrics的一个基本工具是多元线性回归模型。计量经济学理论使用统计理论和数理统计来评估和发展计量经济学方法。计量经济学家试图找到具有理想统计特性的估计器,包括无偏性、效率和一致性。应用计量经济学使用理论计量经济学和现实世界的数据来评估经济理论,开发计量经济学模型,分析经济历史和预测。
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经济代写|计量经济学代写Econometrics代考|Data and Sample
We focus on both the U.S. and developed Europe ${ }^{26}$ REIT markets, REIT markets, proxied by the daily excess log-returns on the FTSE EPRA Nareit United States USD Total Return Index and the FTSE EPRA Nareit Developed Europe EUR Total Return Index. The FTSE EPRA Nareit data are from Thomson Reuters Eikon.
We explore the sensitivity of the two REIT indices to (1) the bond market factor as proxied by the daily excess log-returns on the S\&P US Treasury Bond Index and the S\&P Eurozone Developed Sovereign Bond Index respectively, and to (2) the stock market factor proxied by the daily excess log-returns on the S\&P500 index and the EUROSTOXX600 index respectively. The bond market data are obtained from Standard and Poor’s and the stock market data are from Thomson Reuters Eikon.
The risk-free rate is the one-month T-bill rate for the USA and the one-month Euribor rate for developed Europe computed on a daily basis. The data are from the Federal Reserve Economic Data (FRED) and the European Money Markets Institute (EMMI), respectively.
Assuming that beta can be influenced by risk aversion, we use three risk aversion indicators commonly used in the literature (Bank 2007) as exogenous variables that may affect the evolution of the bond market beta and the stock market beta. In particular, we use implied volatility as an indicator of the volatility that is expected by the market, the Ted Spread as an indicator of credit risk in the interbank money market, and the High Yield Option-Adjusted Spread as an indicator of credit risk.
The volatility indices, i.e., the VIX for the USA and the VSTOXX for developed Europe, respectively measure the 30-day expected volatility of the US stock market based on the S\&P500 option prices and the 30-day expected volatility of the European stock market based on the EUROSTOXX50 option prices. We hereafter both call them VIX for simplicity. The Ted Spread is the difference between the three-month Treasury bill and the three-month USD LIBOR rate. ${ }^{27}$ The US High Yield Index Option-Adjusted Spread is the difference between a computed option-adjusted spread (OAS) index of all bonds in the Bank of BofAML US High Yield Master II Index and a spot Treasury curve. As for the EUR High Yield Index Option-Adjusted Spread of BofAML, it is the European equivalent of the US High Yield Index Option-Adjusted Spread.
The full sample runs from October 02, 2009, to October 01, 2019, which amounts to 2554 daily returns.
经济代写|计量经济学代写Econometrics代考|Empirical Results
The aim of our empirical study is to compare the performance of the competing models from two perspectives: in-sample beta estimates on the one hand and out-ofsample beta forecasts on the other hand. The in-sample analysis is meant to assess how well the different models fit the data while the out-of-sample analysis is useful in assessing what modeling technique provides the best beta forecasts in a tracking exercise. A better beta forecast can then be used as an input within many financial applications.
We use the first 2304 observations of our sample as the in-sample period and the remaining 250 observations as the out-of-sample period. Having performed a sensitivity analysis on the same sample by increasing the number of out-of-sample period observations (to 500 and 750 observations respectively) and having found that the results were qualitatively the same, we do not report them to save space.
tional bond market betas $\left(\beta_{B, t}\right)$ and the conditional stock market betas $\left(\beta_{M, t}\right)$ for both the USA and developed Europe. We estimate the following two-factor model:
$$
\widetilde{r}{\mathrm{REIT}, t}=\alpha_t+\beta{B, t} \tilde{r}{B, t}+\beta{M, t} \tilde{r}_{M, t}+\varepsilon_t .
$$
The seven competing models are the following:
OLS model:
$$
\begin{aligned}
& \alpha_t=\alpha, \beta_{B, t}=\beta_B, \beta_{M, t}=\beta_M \forall t, \
& \varepsilon_t \stackrel{\text { i.i.d. }}{\sim} N\left(0, \sigma^2\right) .
\end{aligned}
$$
Univariate GARCH model:
$$
\begin{aligned}
\alpha_t & =\alpha, \beta_{B, t}=\beta_B, \beta_{M, t}=\beta_M \forall t, \
\varepsilon_t & =\sigma_t z_t, \quad z_t \stackrel{\text { i.i.d. }}{\sim} N(0,1), \
\sigma_t^2 & =\lambda_0+\lambda_1 \sigma_{t-1}^2+\lambda_2 \varepsilon_{t-1}^2 .
\end{aligned}
$$
Univariate GARCH model with interaction variables (GARCH-Z):
$$
\begin{aligned}
& \alpha_t=\alpha \forall t, \
& \beta_{B, t}=c_B+\theta_{B, \mathrm{TED}} \mathrm{TED}{t-1}+\theta{B, \mathrm{HY}} \mathrm{HY}{t-1}, \ & \beta{M, t}=c_M+\theta_{M, \mathrm{VIX}} \mathrm{VIX}{t-1} \text {, } \ & \varepsilon_t=\sigma_t z_t, \quad z_t \stackrel{\text { i.i.d. }}{\sim} N(0,1), \ & \sigma_t^2=\lambda_0+\lambda_1 \sigma{t-1}^2+\lambda_2 \varepsilon_{t-1}^2 \text {, } \
&
\end{aligned}
$$
计量经济学代考
经济代写|计量经济学代写Econometrics代考|Data and Sample
我们专注于美国和欧洲发达国家${ }^{26}$房地产投资信托基金市场,房地产投资信托基金市场,以富时EPRA Nareit美国美元总回报指数和富时EPRA Nareit欧洲发达国家欧元总回报指数的每日超额对数回报为代表。富时EPRA Nareit数据来自汤森路透Eikon。
我们探讨了两个REIT指数对(1)分别以标普美国国债指数和标普欧元区发达国家主权债券指数的日超额对数收益为代表的债券市场因素,以及(2)分别以标普500指数和EUROSTOXX600指数的日超额对数收益为代表的股票市场因素的敏感性。债券市场数据来自标准普尔,股票市场数据来自汤森路透Eikon。
无风险利率是指美国的一个月国库券利率和欧洲发达国家的一个月欧元银行同业拆借利率,按日计算。数据分别来自美联储经济数据(FRED)和欧洲货币市场研究所(EMMI)。
假设贝塔可以受到风险厌恶的影响,我们使用文献中常用的三个风险厌恶指标(Bank 2007)作为可能影响债券市场贝塔和股票市场贝塔演变的外生变量。特别是,我们使用隐含波动率作为市场预期波动率的指标,泰德价差作为银行间货币市场信用风险的指标,高收益期权调整价差作为信用风险的指标。
波动率指数,即美国的VIX指数和欧洲发达国家的VSTOXX指数,分别以标准普尔500期权价格衡量美国股市30天的预期波动率,以EUROSTOXX50期权价格衡量欧洲股市30天的预期波动率。为了简单起见,我们以后都叫它们VIX。泰德价差是3个月期国库券和3个月期美元伦敦银行同业拆息之间的差额。${ }^{27}$美国高收益指数期权调整价差是美国银行美国高收益综合指数中所有债券的期权调整价差(OAS)指数与现货国债曲线之间的差额。至于美银的欧元高收益指数期权调整价差,它相当于美国的高收益指数期权调整价差。
完整的样本从2009年10月2日到2019年10月1日,相当于2554个日收益。
经济代写|计量经济学代写Econometrics代考|Empirical Results
我们的实证研究的目的是从两个角度比较竞争模型的性能:一方面是样本内β估计,另一方面是样本外β预测。样本内分析旨在评估不同模型对数据的拟合程度,而样本外分析用于评估哪种建模技术在跟踪练习中提供了最佳的beta预测。然后,一个更好的beta预测可以用作许多金融应用程序的输入。
我们使用样本的前2304个观测值作为样本内周期,其余250个观测值作为样本外周期。通过增加样本外周期观测值的数量(分别为500和750个观测值)对同一样本进行敏感性分析并发现结果在质量上是相同的,我们不报告它们以节省空间。
美国和欧洲发达国家的传统债券市场beta $\left(\beta_{B, t}\right)$和有条件股票市场beta $\left(\beta_{M, t}\right)$。我们估计如下的双因素模型:
$$
\widetilde{r}{\mathrm{REIT}, t}=\alpha_t+\beta{B, t} \tilde{r}{B, t}+\beta{M, t} \tilde{r}_{M, t}+\varepsilon_t .
$$
这7款车型分别是:
OLS模型:
$$
\begin{aligned}
& \alpha_t=\alpha, \beta_{B, t}=\beta_B, \beta_{M, t}=\beta_M \forall t, \
& \varepsilon_t \stackrel{\text { i.i.d. }}{\sim} N\left(0, \sigma^2\right) .
\end{aligned}
$$
单变量GARCH模型:
$$
\begin{aligned}
\alpha_t & =\alpha, \beta_{B, t}=\beta_B, \beta_{M, t}=\beta_M \forall t, \
\varepsilon_t & =\sigma_t z_t, \quad z_t \stackrel{\text { i.i.d. }}{\sim} N(0,1), \
\sigma_t^2 & =\lambda_0+\lambda_1 \sigma_{t-1}^2+\lambda_2 \varepsilon_{t-1}^2 .
\end{aligned}
$$
具有交互变量的单变量GARCH模型(GARCH- z):
$$
\begin{aligned}
& \alpha_t=\alpha \forall t, \
& \beta_{B, t}=c_B+\theta_{B, \mathrm{TED}} \mathrm{TED}{t-1}+\theta{B, \mathrm{HY}} \mathrm{HY}{t-1}, \ & \beta{M, t}=c_M+\theta_{M, \mathrm{VIX}} \mathrm{VIX}{t-1} \text {, } \ & \varepsilon_t=\sigma_t z_t, \quad z_t \stackrel{\text { i.i.d. }}{\sim} N(0,1), \ & \sigma_t^2=\lambda_0+\lambda_1 \sigma{t-1}^2+\lambda_2 \varepsilon_{t-1}^2 \text {, } \
&
\end{aligned}
$$
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