Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models

Box, George E. P.; Pierce, David A.

doi:10.1080/01621459.1970.10481180

Cited by 1,540 publications

(343 citation statements)

References 14 publications

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“…Second, we did not consider other tests of autocorrelations such as the Box-Pierce test, the Ljung-Box test and their extended versions (e.g., Box & Pierce, 1970;Horowitz, Lobato, Nankervis, & Savin, 2006;Ljung & Box, 1978;Lobato, Nankervis, & Savin, 2001. The Box-Pierce and Ljung-Box tests examine whether the autocorrelations up to lag l are all zero.…”

Section: Discussionmentioning

confidence: 99%

Testing autocorrelation and partial autocorrelation: Asymptotic methods versus resampling techniques

Zhang

2017

Brit J Math & Statis

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Autocorrelation and partial autocorrelation, which provide a mathematical tool to understand repeating patterns in time series data, are often used to facilitate the identification of model orders of time series models (e.g., moving average and autoregressive models). Asymptotic methods for testing autocorrelation and partial autocorrelation such as the 1/T approximation method and the Bartlett's formula method may fail in finite samples and are vulnerable to non-normality. Resampling techniques such as the moving block bootstrap and the surrogate data method are competitive alternatives. In this study, we use a Monte Carlo simulation study and a real data example to compare asymptotic methods with the aforementioned resampling techniques. For each resampling technique, we consider both the percentile method and the bias-corrected and accelerated method for interval construction. Simulation results show that the surrogate data method with percentile intervals yields better performance than the other methods. An R package pautocorr is used to carry out tests evaluated in this study.

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Section: Discussionmentioning

confidence: 99%

Testing autocorrelation and partial autocorrelation: Asymptotic methods versus resampling techniques

Zhang

2017

Brit J Math & Statis

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“…This will affect the trend of the curve, sometimes causing fatal error when performing slope estimation. Using a short term moving average (Box and Pierce 1970) should overcome this problem. Equation (5) shows the moving average process convolution procedure:…”

Section: Entropy Determinationmentioning

confidence: 99%

Monitoring Debris Flows Using Spatial Filtering and Entropy Determination Approaches

Kao¹,

Ren²,

Lee³

et al. 2013

Terr. Atmos. Ocean. Sci.

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We developed an automatic debris flow warning system in this study. The system uses a fixed video camera mounted over mountainous streams with a high risk for debris flows. The focus of this study is to develop an automatic algorithm for detecting debris flows with a low computational effort which can facilitate real-time implementation. The algorithm is based on a moving object detection technique to detect debris flow by comparing among video frames. Background subtraction is the kernel of the algorithm to reduce the computational effort, but non-rigid properties and color similarity of the object and the background color introduces some difficulties. Therefore, we used several spatial filtering approaches to increase the performance of the background subtraction. To increase the accuracy entropy is used with histogram analysis to identify whether a debris flow occurred. The modified background subtraction approach using spatial filtering and entropy determination is adopted to overcome the error in moving detection caused by non-rigid and similarities in color properties. The results of this study show that the approach described here can improve performance and also reduce the computational effort.

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“…Portmanteau white noise test developed by Box & Pierce (1970) is computed to test for normal distribution of the residual within the sample. The test relies on the fact that if χ(1) ,…, χ(n) is the realization from white noise process (Baum, 2005).…”

Section: Normal Distribution Testmentioning

confidence: 99%

Assessing the Exchange Rate Volatility as an External Shock to Chinese Economy

Azimi¹

2016

IJEF

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Theoretically, the rate of exchange is one of the major drivers of inflation that influences the wholesale price index (WPI) in countries where significant emphasis is put over import and export like China. In this paper, the exchange rate's clustering volatility and its impulsiveness as an external shock to WPI is investigated on a set of time series data which represents 4,067 daily observation of Chinese Economy from August 12, 2004-September 30, 2015. The ordinary least square and weighted regression analysis reveal significant p-values of 0.000 for exchange rate that explain the WPI throughout the stated period. The autoregressive conditional heteroskedasticity and generalized autoregressive conditional heteroskedasticity model exhibit significant probability value of 0.000 and 0.044 respectively for WPI and the exchange rate. It is found that the previous days' volatility of WPI influences the future volatility of WPI as an internal shock in addition to the previous days' impulsiveness of the exchange rate which influences the future volatility of the WPI as an external shock. The testing models are thoroughly applied and their stability and validity are evidenced thereto.

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Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models

Cited by 1,540 publications

References 14 publications

Testing autocorrelation and partial autocorrelation: Asymptotic methods versus resampling techniques

Testing autocorrelation and partial autocorrelation: Asymptotic methods versus resampling techniques

Monitoring Debris Flows Using Spatial Filtering and Entropy Determination Approaches

Assessing the Exchange Rate Volatility as an External Shock to Chinese Economy

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