On the effect of deterministic terms on the bias in stable AR models

Giersbergen, N.P.A. van

doi:10.1016/j.econlet.2005.05.013

Cited by 18 publications

(6 citation statements)

References 8 publications

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“…where Z is the matrix of size (n − 1)·3 whose second column contains (n − 1) values equal to 1, and the third column contains the numbers 2 to n and y is a vector of size (n − 1)·1 containing the observations x 2 to x n . The bias-corrected serial correlation coefficient ρ * [45,86] is calculated using the formula mentioned in Equation (27). This value is used in bias-corrected pre-whitening and trend detection studies.…”

Section: Trend-free Pre-whiteningmentioning

confidence: 99%

Long-Term Homogeneity, Trend, and Change-Point Analysis of Rainfall in the Arid District of Ananthapuramu, Andhra Pradesh State, India

Patakamuri

Muthiah

Sridhar

2020

Water

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The objective of this study is to evaluate the homogeneity, trend, and trend change points in the rainfall data. Daily rainfall data was collected for the arid district of Ananthapuramu, Andhra Pradesh state, India from 1981 to 2016 at the subdistrict level and aggregated to monthly, annual, seasonal rainfall totals, and the number of rainy days. After quality checks and homogeneity analysis, a total of 27 rain gauge locations were considered for trend analysis. A serial correlation test was applied to all the time series to identify serially independent series. NonParametric Mann–Kendall test and Spearman’s rank correlation tests were applied to serially independent series. The magnitude of the trend was calculated using Sen’s slope method. For the data influenced by serial correlation, various modified versions of Mann–Kendall tests (pre-whitening, trend-free pre-whitening, bias-corrected pre-whitening, and two variants of variance correction approaches) were applied. A significant increasing summer rainfall trend is observed in six out of 27 stations. Significant decreasing trends are observed at two stations during the southwest monsoon season and at two stations during the northeast monsoon season. To identify the trend change points in the time series, distribution−free cumulative sum test, and sequential Mann–Kendall tests were applied. Two open−source library packages were developed in R language namely, ”modifiedmk” and ”trendchange” to implement the statistical tests mentioned in this paper. The study results benefit water resource management, drought mitigation, socio−economic development, and sustainable agricultural planning in the region.

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Section: Trend-free Pre-whiteningmentioning

confidence: 99%

Long-Term Homogeneity, Trend, and Change-Point Analysis of Rainfall in the Arid District of Ananthapuramu, Andhra Pradesh State, India

Patakamuri

Muthiah

Sridhar

2020

Water

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show abstract

“…where Z is the matrix of size ( − 1) x 3 whose second column contains ( − 1) values equal to 1, and the third column contains the numbers 2 to and is a vector of size ( − 1) x 1 containing the observations 2 to . Bias corrected serial correlation coefficient ρ * [42,78] is calculated using the formula mentioned in Equation (27). This value is used in bias-corrected pre-whitening and trend detection studies.…”

Section: Trend Free Pre-whiteningmentioning

confidence: 99%

Long Term Homogeneity, Trend and Change-Point Analysis of Rainfall in the Arid District of Ananthapuramu, Andhra Pradesh State, India

Patakamuri¹,

Muthiah²,

Sridhar³

2019

Preprint

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Daily rainfall data was collected for the arid district of Ananthapuramu, Andhra Pradesh state, India from 1981 to 2016 at the sub-district level and aggregated to monthly, annual and seasonal rainfall totals and the number of rainy days. The objective of this study is to evaluate the homogeneity, trend, and trend change points in the rainfall data. After quality checks and homogeneity analysis, a total of 27 rain gauge locations were considered for trend analysis. A serial correlation test was applied to all the time series to identify serially independent series. Non-Parametric Mann-Kendall test and Spearman’s rank correlation tests were applied to serially independent series. The magnitude of the trend was calculated using Sen’s slope method. For the data influenced by serial correlation, various modified versions of Mann-Kendall tests (Pre-Whitening, Trend Free Pre-Whitening, Bias Corrected Pre-Whitening and two variants of Variance Correction Approaches) were applied. A significant increasing summer rainfall trend is observed in 6 out of 27 stations. Significant decreasing trends are observed at two stations in the south-west monsoon season and at two stations in the north-east monsoon season. To identify the trend change-points in the time series, distribution-free Cumulative SUM test and sequential Mann-Kendall tests were applied. Two open-source library packages were developed in R language namely, ‘modifiedmk’ and ‘trendchange’ to implement the statistical tests mentioned in this paper. The study will benefit water resource management, drought mitigation, socio-economic development and sustainable agricultural planning in the region.

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“…However, it is vital to note that the ordinary least squares estimates of 1 are negatively biased [55], and bias corrected 1 ( * ) can be computed by [56] (2) Graphical CRD Approach to Identify Changes. The CRD plot (i.e., the cumulative sum from (A.20) versus the time of the data points) can be used to identify changes in the series over unknown periods as illustrated in Figure 7.…”

Section: (B) Correction Of Variance Inflation Due To Long-term Persismentioning

confidence: 99%

Statistical Uncertainty in Hydrometeorological Trend Analyses

Onyutha

2016

Advances in Meteorology

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This study demonstrates the existence of uncertainty in hydrometeorological trend analyses using historical rainfall from Kenya in East Africa. With respect to the influence of short- and long-term persistence on trend analyses, a total of 13 approaches of rank-based techniques including Mann-Kendall, Spearman’s Rho, and Cumulative Rank Difference (CRD) tests were employed. Graphically, CRD-based diagnoses of trends and subtrends were performed. To assess data-related uncertainty, a resampling procedure was applied. It was shown that at a selected significance level, the null hypothesisH0(no trend) can be rejected for trend direction while the evidence to rejectH0(zero trend magnitude) is statistically insufficient. Graphical and statistical approaches when combined yield more influential and comprehensive information for inference than relying purely on statistical results. Alongside an apparent linear trend, variations in the nonlinear (e.g., cyclical) component of the series may also not be due to natural randomness. Method-related uncertainty is not negligible especially for series with persistent fluctuations. These findings shed light on the need to assess uncertainty on trend results. Furthermore, it is recommended that the conclusiveness of trends be cautiously premised not only on statistical grounds but also on more considered physical and/or theoretical understanding of the hydrometeorological processes.

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On the effect of deterministic terms on the bias in stable AR models

Cited by 18 publications

References 8 publications

Long-Term Homogeneity, Trend, and Change-Point Analysis of Rainfall in the Arid District of Ananthapuramu, Andhra Pradesh State, India

Long-Term Homogeneity, Trend, and Change-Point Analysis of Rainfall in the Arid District of Ananthapuramu, Andhra Pradesh State, India

Long Term Homogeneity, Trend and Change-Point Analysis of Rainfall in the Arid District of Ananthapuramu, Andhra Pradesh State, India

Statistical Uncertainty in Hydrometeorological Trend Analyses

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