﻿ 几类预测模型对我国酒店行业的发展趋势分析

# 几类预测模型对我国酒店行业的发展趋势分析Analysis of the Development Trend of China’s Hotel Industry Based on Several Kinds of Prediction Models

Abstract: Based on the data of the number of chain hotels, the number of hotel rooms and the proportion of chain hotel rooms in the number of hotels in China from the year of 2015 to 2019, this paper establishes a single variable grey prediction model, a polynomial trend model and an exponential curve model. The computational results show that the three prediction models can get accurate numerical results. Based on this result, this paper further gives the number of chain hotels, the number of hotel rooms, and the proportion of chain hotel rooms in the number of hotels in China from 2020 to 2023. The calculation results can provide reference for the decision makers of China’s hotel industry.

1. 引言

2. 三类统计预测模型

2.1. 单变量灰色预测模型

$\frac{\text{d}{x}^{\left(1\right)}\left(t\right)}{\text{d}t}+a{x}^{\left(1\right)}\left(t\right)=b$(1)

${x}^{\left(0\right)}\left(k\right)+a{z}^{\left(1\right)}\left(k\right)=b$(2)

${\stackrel{^}{x}}^{\left(1\right)}\left(k\right)=\left[{x}^{\left(0\right)}\left(1\right)-\frac{b}{a}\right]{\text{e}}^{-a\left(k-1\right)}+\frac{b}{a},\text{\hspace{0.17em}}\text{\hspace{0.17em}}k=1,2,\dots$(3)

${\stackrel{^}{x}}^{\left(0\right)}\left(k\right)=\frac{{e}^{a}-1}{a}\left(b-{x}^{\left(0\right)}\left(1\right)\right){\text{e}}^{-a\left(k-1\right)},\text{\hspace{0.17em}}\text{\hspace{0.17em}}k=1,2,\dots$(4)

$\left(\begin{array}{c}a\\ b\end{array}\right)={\left({B}^{\mathcal{T}}B\right)}^{-1}{B}^{\mathcal{T}}Y$(5)

2.2. 多项式趋势曲线模型

${x}^{\left(0\right)}\left(t\right)={a}_{k}{t}^{k}+{a}_{k-1}{t}^{k-1}+\cdots +{a}_{1}t+{a}_{0}$(6)

${S}_{i}=\underset{t=\left(i-1\right)m+1}{\overset{im}{\sum }}{x}^{\left(0\right)}\left(t\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,2,\cdots ,k+1$(7)

$\left\{\begin{array}{l}{S}_{1}={a}_{k}\underset{t=1}{\overset{m}{\sum }}{t}^{k}+{a}_{k-1}\underset{t=1}{\overset{m}{\sum }}{t}^{k-1}+\cdots +{a}_{1}\underset{t=1}{\overset{m}{\sum }}t+{a}_{0}m\\ {S}_{2}={a}_{k}\underset{t=m+1}{\overset{2m}{\sum }}{t}^{k}+{a}_{k-1}\underset{t=m+1}{\overset{2m}{\sum }}{t}^{k-1}+\cdots +{a}_{1}\underset{t=m+1}{\overset{2m}{\sum }}t+{a}_{0}m\\ \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }⋮\\ {S}_{k+1}={a}_{k}\underset{t=km+1}{\overset{\left(k+1\right)m}{\sum }}{t}^{k}+{a}_{k-1}\underset{t=km+1}{\overset{\left(k+1\right)m}{\sum }}{t}^{k-1}+\cdots +{a}_{1}\underset{t=km+1}{\overset{\left(k+1\right)m}{\sum }}t+{a}_{0}m.\end{array}$ (8)

· 当 $k=1$ 时，求解线性趋势曲线 ${x}^{\left(0\right)}\left(t\right)={a}_{1}t+{a}_{0}$ 参数的表达式。首先，有

$\left\{\begin{array}{l}{S}_{1}={a}_{1}\underset{t=1}{\overset{m}{\sum }}t+{a}_{0}m,\\ {S}_{2}={a}_{1}\underset{t=m+1}{\overset{2m}{\sum }}t+{a}_{0}m.\end{array}$ (9)

$\left\{\begin{array}{c}{a}_{1}=\frac{{S}_{2}-{S}_{1}}{{m}^{2}},\text{ }\text{ }\text{ }\text{ }\text{ }\\ {a}_{0}=\frac{{S}_{1}}{m}-\frac{\left(m+1\right)\left({S}_{2}-{S}_{1}\right)}{2{m}^{2}}.\end{array}$ (10)

· 当 $k=2$ 时，求解线性趋势曲线 ${x}^{\left(0\right)}\left(t\right)={a}_{2}{t}^{2}+{a}_{1}t+{a}_{0}$ 参数的表达式。首先，有

$\left\{\begin{array}{l}{S}_{1}={a}_{2}\underset{t=1}{\overset{m}{\sum }}{t}^{2}+{a}_{1}\underset{t=1}{\overset{m}{\sum }}t+{a}_{0}m,\\ {S}_{2}={a}_{2}\underset{t=m+1}{\overset{2m}{\sum }}{t}^{2}+{a}_{1}\underset{t=m+1}{\overset{2m}{\sum }}t+{a}_{0}m,\\ {S}_{3}={a}_{2}\underset{t=2m+1}{\overset{3m}{\sum }}{t}^{2}+{a}_{1}\underset{t=2m+1}{\overset{3m}{\sum }}t+{a}_{0}m.\end{array}$ (11)

${a}_{2}=\frac{\left(6{S}_{1}-6{S}_{3}\right)m\left(3m+1\right)-\left(6{S}_{1}-6{S}_{2}\right)m\left(5m+1\right)-6m\left(m+1\right)\left({S}_{2}-{S}_{3}\right)}{2{m}^{3}\left(-12{m}^{2}+m+1\right)}$

$\begin{array}{c}{a}_{1}=\frac{2m\left({S}_{1}-{S}_{2}\right)\left(38{m}^{2}+15m+1\right)-2m\left({S}_{1}-{S}_{3}\right)\left(14{m}^{2}+9m+1\right)}{2{m}^{3}\left(-12{m}^{2}+m+1\right)}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+\frac{4m\left({S}_{2}-{S}_{3}\right)\left(m+1\right)\left(m+\frac{1}{2}\right)}{2{m}^{3}\left(-12{m}^{2}+m+1\right)}，\end{array}$

$\begin{array}{c}{a}_{0}=\frac{-m\left[{S}_{1}\left(3m+1\right)-{S}_{2}\left(m+1\right)\right]\left(38{m}^{2}+15m+1\right)}{2{m}^{4}\left(-12{m}^{2}+m+1\right)}+\frac{m\left[{S}_{1}\left(5m+1\right)-{S}_{3}\left(m+1\right)\right]\left(14{m}^{2}+9m+1\right)}{2{m}^{4}\left(-12{m}^{2}+m+1\right)}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}-\frac{2{m}^{2}\left[{S}_{2}\left(5m+1\right)-{S}_{3}\left(3m+1\right)\right]\left(m+1\right)\left(m+\frac{1}{2}\right)}{2{m}^{4}\left(-12{m}^{2}+m+1\right)}。\end{array}$

2.3. 指数曲线模型

${x}^{\left(0\right)}\left(t\right)=a{b}^{t}$(12)

$\mathrm{ln}{x}^{\left(0\right)}\left(t\right)=\mathrm{ln}a+t\mathrm{ln}b$(13)

$\left\{\begin{array}{l}\sum \mathrm{ln}{x}^{\left(0\right)}\left(t\right)=n\mathrm{ln}a+\left(\sum t\right)\mathrm{ln}b\\ \sum t\mathrm{ln}{x}^{\left(0\right)}\left(t\right)=\left(\sum t\right)\mathrm{ln}a+\left(\sum {t}^{2}\right)\mathrm{ln}b\text{\hspace{0.17em}}，\end{array}$ (14)

2.4. 模型精度的评价准则

· 百分比误差(APE)

$\text{APE}\left(k\right)=|1-\frac{{\stackrel{^}{x}}^{\left(0\right)}\left(k\right)}{{x}^{\left(0\right)}\left(k\right)}|×100%,\text{\hspace{0.17em}}k=1,2,\cdots ,n$(15)

· 平均绝对百分比误差(MAPE)

$\text{MAPE}=\frac{1}{n-1}\underset{k=2}{\overset{n}{\sum }}|1-\frac{{\stackrel{^}{x}}^{\left(0\right)}\left(k\right)}{{x}^{\left(0\right)}\left(k\right)}|×100%$(16)

· 均方根误差(RMSPE)

$\text{RMSPE}=\sqrt{\frac{1}{n-1}\underset{k=2}{\overset{n}{\sum }}{\left(1-\frac{{\stackrel{^}{x}}^{\left(0\right)}\left(k\right)}{{x}^{\left(0\right)}\left(k\right)}\right)}^{2}}×100%$(17)

3. 我国酒店行业发展趋势分析

Table 1. Historical data of the number of chain hotels in China, the number of hotel rooms in the hotel industry in China, and the proportion of the number of chain hotel rooms in the number of hotels in China

3.1. 我国连锁酒店数量发展趋势分析

Table 2. Calculation results of the number of chain hotels in China by the three prediction models

3.2. 我国酒店业客房数量发展趋势分析

Table 3. Calculation results of the number of guest rooms in China’s hotel industry by the three prediction models

3.3. 我国连锁酒店客房数量占全国酒店数量的比重发展趋势分析

Table 4. Calculation results of the proportion of the number of guest rooms of chain hotels in the total number of hotels in China by the three prediction models

4. 结束语

NOTES

*通讯作者。

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