带有时间序列错误的回归模型-MATLAB和SIMULINK金宝app - 金宝app,下载188bet金宝搏,金宝搏官方网站

带有时间序列错误的回归模型

什么是时间序列错误的回归模型？

Regression models with time series errors attempt to explain the mean behavior of a response series (y_t,t= 1,...,T）考虑预测因子的线性效应（X_t）使用多线性回归（MLR）。但是，错误（u_t）unconditional disturbances，是时间序列而不是白噪声，这与线性模型假设背道而驰。与包括外源预测因子的Arima模型不同，带有时间序列误差的回归模型保留了回归系数的敏感性解释（β)[2].

这些模型对于计量数据特别有用。使用这些模型：

分析新政策对市场指标的影响（干预模型）。
Forecast population size adjusting for predictor effects, such as expected prevalence of a disease.
Study the behavior of a process adjusting for calendar effects. For example, you can analyze traffic volume by adjusting for the effects of major holidays. For details, see[3].
估计混乱关系nd by including time (t) in the model.
Forecast total energy consumption accounting for current and past prices of oil and electricity (distributed lag model).

在计量经济器工具箱中使用这些工具到：

Specify a regression model with ARIMA errors (seeregARIMA).
使用指定模型以及响应和预测数据估算参数（请参阅estimate).
Simulate responses using a model and predictor data (seesimulate).
Forecast responses using a model and future predictor data (seeforecast).
Infer residuals and estimated unconditional disturbances from a model using the model and predictor data (see推断).
filterinnovations through a model using the model and predictor data
Generate impulse responses (seeimpulse).
Compare a regression model with ARIMA errors to an ARIMAX model (seearima).

Conventions

A regression model with time series errors has the following form (in lag operator notation):

\begin{matrix} y_{t} = c + X_{t} β + u_{t} \\ a (L) A (L) {(1 - L)}^{D} (1 - L^{s}) u_{t} = b (L) B (L) ε_{t}, \end{matrix}

(1)

where

t= 1,...,T.
y_tis the response series.
X_tis rowt的X, which is the matrix of concatenated predictor data vectors. That is,X_tis observationt的each predictor series.
c是回归模型截距。
βis the regression coefficient.
u_t是干扰系列。
ε_tis the innovations series.
$L^{j} y_{t} = y_{t - j} .$
$a (L) = (1 - a_{1} L - ... - a_{p} L^{p}),$ 哪个学位p, nonseasonal autoregressive polynomial.
$A (L) = (1 - A_{1} L - ... - A_{p_{s}} L^{p_{s}}),$ 哪个学位p_s, seasonal autoregressive polynomial.
${(1 - L)}^{D},$ 哪个学位D, nonseasonal integration polynomial.
$(1 - L^{s}),$ 哪个学位s, seasonal integration polynomial.
$b (L) = (1 + b_{1} L + ... + b_{q} L^{q}),$ 哪个学位q, nonseasonal moving average polynomial.
$B (L) = (1 + B_{1} L + ... + B_{q_{s}} L^{q_{s}}),$ 哪个学位q_s，季节性移动平均多项式。

以下框和詹金斯方法论，u_tis a stationary or unit root nonstationary, regular, linear time series. However, ifu_tis unit root nonstationary, then you do not have to explicitly difference the series as they recommend in[1]. You can simply specify the seasonal and nonseasonal integration degree using the software. For details, seeCreate Regression Models with ARIMA Errors.

Another deviation from the Box and Jenkins methodology is thatu_t没有恒定项（条件均值），因此其无条件的平均值为0。但是，回归模型包含截距项，c.

Note

If the unconditional disturbance process is nonstationary (i.e., the nonseasonal or seasonal integration degree is greater than 0), then the regression intercept,c, is not identifiable. For details, seeIntercept Identifiability in Regression Models with ARIMA Errors.

该软件可实施ARMA流程的稳定性和可逆性。那是，

$ψ (L) = \frac{b (L) B (L)}{a (L) A (L)} = 1 + ψ_{1} L + ψ_{2} L^{2} + ...,$

where the series {ψ_t} must be absolutely summable. The conditions for {ψ_t} to be absolutely summable are:

a(L) andA(L）是稳定的(i.e., the eigenvalues ofa(L) = 0 andA(L）= 0位于单元圆内）。
b(L) andB(L）是invertible(i.e., their eigenvalues lie ofb(L) = 0 andB(L) = 0 inside the unit circle).

该软件使用最大可能性进行参数估计。您可以选择高斯或学生的t分布的创新,ε_t.

该软件将预测因子视为估计和推理的非障碍变量。

参考

[1]Box, G. E. P., G. M. Jenkins, and G. C. Reinsel.Time Series Analysis: Forecasting and Control. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.

[2] Hyndman，R。J.（2010年10月）。“ Arimax模型混乱。”Rob J. Hyndman. Retrieved May 4, 2017 fromhttps://robjhyndman.com/hyndsight/arimax/.

[3] Ruey, T. S. “Regression Models with Time Series Errors.”Journal of the American Statistical Association.卷。79，编号385，1984年3月，第118-124页。