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不忘初心 · 2024年01月29日

最后一步是什么意思？

NO.PZ2020011101000025

问题如下：

A log-linear trend model is estimated on annual euro-area GDP using data from 1995 until 2018. The estimated model is $ln RGDP_t = -18.15 + .0136 t + \widehat\epsilon_t$ , and the estimated standard deviation of $\epsilon_t$ is 0.0322. Assuming the shocks are normally distributed, what are the point forecasts of GDP for the next three years? How do these compare with a linear model $RGDP_t = -234178.8 + 121.3 * t + \widehat\epsilon_t$ ?

选项：

解释：

In this case,

$E_T[Y_T]=exp(E_T[ln Y_T]+\sigma^2/2)$

And the error bounds on the ln are +/-1.96*0.0322, so the bounds are given in proportional terms rather than fixed values.

$Bounds_Multiplier = exp({1.96 * 0.0322) = exp(\pm 0.0631) = 0.939,1.065$

Calculating $E [ln RGDP_t]$ :

$E[ln RGDP_{2019}] = -18.15 + 0.0136 * 2019 = 9.308$

$E[ln RGDP_{2020}] = -18.15 + 0.0136 * 2020 = 9.322$

$E[ln RGDP_{2021}] = -18.15 + 0.0136 * 2020 = 9.336$

Furthermore,

$\sigma^2/2=0.0322^2/2=0.0005$

(which will only make a small impact in this example)

So:

E[RGDP2019] = exp(9.308 + 0.0005) = 11,031.4

E [RGDP2020] = exp(9.322 + 0.0005) = 11,186.9

E[RGDP2021] = exp(9.336 + 0.0005) = 11,344.6

And the 95% confidence bands are given as:

$95\%_{CB_{RGDP2019}}= [0.939 * 11031.4,1.065 * 11031.4] = [10,358.5,11,748.4]$

$95\%_{CB_{RGDP2020}}= [10,504.5,11,914.0]$

$95\%_{CB_{RGDP2019}} = [10,652.6,12,082.0]$

In comparison with the linera model, the bands are growing in size and overall the results are a bit bigger.

下面这步骤没看懂，

And the 95% confidence bands are given as:

95%��2019=[0.939∗11031.4,1.065∗11031.4]=[10,358.5,11,748.4]

为什么是乘e+_0.0631?

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1 个答案

pzqa27 · 2024年01月30日

嗨，爱思考的PZer你好：

因为残差项是个随机变量，而前面的-18.5+0.136*t，其实不是随机变量。所以lnRGDPt可以看做服从 N(-18.15+0.136*t, 0.0322^2）。之所以有置信区间，是由残差项这一个随机变量带来的。而这个残差项随机变量，又在指数上。所以左边端点是，E[RGDP2019]*e^(-1.96*标准差0.0322)

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2024-03-09 10:30 1 · 回答

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2022-06-28 16:04 1 · 回答

您好，请问算95%confininterval的时候为什么用forecast*0.939而不是+/-1.96stanrviation呢？这个0.939又是怎么算出来的呢？谢谢

2020-02-05 19:44 1 · 回答

这题的答案中标准差的平方除以2，是在哪个地方的知识点？

2020-02-03 23:26 1 · 回答