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