信噪比在AR模型定阶方法选择中的研究

Abstract

Abstract:

There are many methods can be used to determine the order of AR models. For specific time series, different method may provide different results. How to select method adaptively for particular series is an important problem, especially in big data era. In this paper, we introduce a method to estimate the signal-to-noise ratio (SNR) of the AR model in low-order noisy environments. It takes the influence of noise standard deviation, series length and eigenvalue of the model into consideration, which can be used as a criterion to evaluate the accuracy of AIC, BIC and FPE. The experimental results show that when the eigenvalue satisfies|λ₁|=|λ₂|=…=|λ_p|=|λ_max|, the order determination accuracy reaches the maximum under the condition of maximum eigenvalue. The accuracy is positively correlated with the series length and the distance of eigenvalue from origin, independent of noise standard deviation. Finally, based on the experimental results, we can select the order determination method of AR model according to the SNR of converted reference model, which provides a new perspective on the comparison of the advantages and disadvantages in different order determination methods.

Key words: Autoregressive model, Signal-to-noise ratio, Noise standard deviation, Series length, Eigenvalue, Reference model

CLC Number:

O212.1

Zhigang Wang,Yiming Ding. Research on Signal-to-Noise Ratio in Order Selection of AR Model[J].Acta mathematica scientia,Series A, 2020, 40(3): 811-823.

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Figures/Tables 18

References 9

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序列长度	$\lambda_{\max }=0.4$		$\lambda_{\max }=0.5$		$\lambda_{\max }=0.6$
	准确率(%)	信噪比	准确率(%)	信噪比	准确率(%)	信噪比
300	62.0	36.831	88.4	38.611	90.5	41.012
400	73.8	36.838	90.6	38.627	91.2	41.038
500	81.5	36.842	90.8	38.642	91.1	41.064
600	85.2	36.862	91.3	38.648	90.8	41.072
700	87.6	36.864	91.3	38.656	91.0	41.078

序列长度	$\lambda_{\max }=0.4$		$\lambda_{\max }=0.5$		$\lambda_{\max }=0.6$
	准确率(%)	信噪比	准确率(%)	信噪比	准确率(%)	信噪比
300	18.0	36.831	73.5	38.611	99.4	41.012
400	27.6	36.838	88.9	38.627	99.9	41.038
500	38.6	36.842	95.7	38.642	100.0	41.064
600	50.2	36.862	98.4	38.648	100.0	41.072
700	60.9	36.864	99.5	38.656	100.0	41.078

准确度	AR(2)		AR(3)		AR(4)		AR(5)
	上界	下界	上界	下界	上界	下界	上界	下界
$F>A>B$	$33.9_{0.0}$	$37.4_{29.1}$	$33.9_{0.0}$	$47.8_{32.4}$	$33.9_{0.0}$	$57.9_{25.4}$	$33.9_{0.0}$	$78.6_{31.9}$
$A>F>B$	$37.4_{29.1}$	$40.7_{73.0}$	$47.8_{32.4}$	$54.2_{71.0}$	$57.9_{25.4}$	$71.0_{71.5}$	$78.6_{31.9}$	$92.6_{69.3}$
$A>B>F$	$40.7_{73.0}$	$44.1_{88.5}$	$54.2_{71.0}$	$62.1_{88.2}$	$71.0_{71.5}$	$82.1_{88.6}$	$92.6_{69.3}$	$108.1_{86.0}$
$B>A>F$	$44.1_{88.5}$	$63.4_{99.1}$	$62.1_{88.2}$	$85.5_{99.3}$	$82.1_{88.6}$	$107.8_{99.2}$	$108.1_{86.0}$	$129.6_{99.9}$

准确率	AR(2)		AR(3)		AR(4)		AR(5)
	上界	下界	上界	下界	上界	下界	上界	下界
$F>A>B$	$33.9_{0.0}$	$36.1_{27.9}$	$33.9_{0.0}$	$43.7_{30.1}$	$34.0_{0.0}$	$55.3_{33.4}$	$34.1_{0.0}$	$70.8_{36.7}$
$A>F>B$	$36.1_{27.9}$	$38.6_{83.7}$	$43.7_{30.1}$	$49.2_{78.6}$	$55.3_{33.4}$	$64.0_{79.2}$	$70.8_{36.7}$	$83.3_{82.2}$
$A>B>F$	$38.6_{83.7}$	$40.8_{90.0}$	$49.2_{78.6}$	$54.1_{89.9}$	$64.0_{79.2}$	$71.6_{90.2}$	$83.3_{82.2}$	$94.0_{90.9}$
$B>A>F$	$40.8_{90.0}$	$52.0_{99.5}$	$54.1_{89.9}$	$89.5_{100.0}$	$71.6_{90.2}$	$113.7_{99.7}$	$94.0_{90.9}$	$137.8_{99.9}$

准确率	AR(2)		AR(3)		AR(4)		AR(5)
	上界	下界	上界	下界	上界	下界	上界	下界
$F>A>B$	$34.0_{0.0}$	$35.5_{34.5}$	$34.0_{0.0}$	$41.4_{33.6}$	$34.1_{0.0}$	$51.0_{34.7}$	$34.1_{0.0}$	$64.8_{38.4}$
$A>F>B$	$35.5_{34.5}$	$37.2_{84.1}$	$41.4_{33.6}$	$46.1_{86.2}$	$51.0_{34.7}$	$58.8_{86.3}$	$64.8_{38.4}$	$74.7_{85.1}$
$A>B>F$	$37.2_{84.1}$	$38.5_{92.0}$	$46.1_{86.2}$	$49.0_{90.7}$	$58.8_{86.3}$	$63.1_{91.4}$	$74.7_{85.1}$	$80.8_{92.8}$
$B>A>F$	$38.5_{92.0}$	$66.4_{99.5}$	$49.0_{90.7}$	$90.8_{100.0}$	$63.1_{91.4}$	$115.6_{99.9}$	$80.8_{92.8}$	$140.8_{100.0}$

Research on Signal-to-Noise Ratio in Order Selection of AR Model

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阶数	$SNR$	推荐方法	准确率1	准确率2
3	61.9	$BIC$	100%	100%
4	75.0	$BIC$	100%	100%
5	88.3	$BIC$	100%	100%

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