Univariate Tests for Time Series Models

Cromwell, Jeff; Labys, Walter C.; Terraza, Michel

doi:10.4135/9781412986458

Cited by 98 publications

(87 citation statements)

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“…CROMWELL et al, 1994), it can be seen from their data and from their graphical presentation in Figure 2 that they probably do not represent a sample from a stationary stochastic process. At the same time, data and their time series representation show that time series from boreholes BV-1 and BV-2 are dissimilar and that they do not originate from the same time series generating stochastic process.…”

Section: Discussionmentioning

confidence: 98%

Unevenly spaced time series analysis:Case study using calcimetry data from BV-1 and BV-2 boreholes in Ljubljansko barje (central Slovenia)

Brenčič¹

2009

Geologija

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Statistical analyses of calcimetric data from boreholes BV-1 (north of Podpe~) and BV-2 (south of ^rna vas) on Ljubljansko barje in central Slovenia are given. The original data are represented as unevenly spaced time series that are translated into evenly spaced time series. To calculate the interpolation weighted influence function, a model based on the power correlated influence is defined. Parameter selection is performed based on the maximum entropy principle. In the reconstructed time series, autocorrelation and Fourier power spectrum analyses are performed. In both time series, a transition from white noise to red noise was detected. Such behaviour can be described by a Lorentz process. Red noise is the result of a stochastic process with long-term memory. This effect can be seen predominantly in the autocorrelation function of borehole BV-1. In the calcimetric time series of borehole BV-2, periodicity with a period between 10.0 m and 12.5 m was also detected. We suppose that this period reflects climatic fluctuations during the Quaternary Period.

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Section: Discussionmentioning

confidence: 98%

Unevenly spaced time series analysis:Case study using calcimetry data from BV-1 and BV-2 boreholes in Ljubljansko barje (central Slovenia)

Brenčič¹

2009

Geologija

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“…The procedure for the univariate time-series analysis, defined by Cromwell et al (1994), was followed. The first thing provided were the descriptive statistics.…”

Section: Methodsmentioning

confidence: 99%

An Analysis of Sex Ratio at Birth in Croatia 1946 – 2007

Pavić¹

2011

Drustvena istrazivanja

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Section: Runs Testmentioning

confidence: 99%

“…let T be the number of observations, T a be the number above the mean, T b be the number below the mean and R be the observed number of runs. Then the test statistic for this test is given as Cromwell et al [22]:The test of series randomness is rejected if the calculated Z N value exceeds the selected critical value obtained from the standard normal distribution table. …”

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confidence: 99%

Prediction of Long-term Pattern and its Extreme Event Frequency of Rainfall in Dire Dawa Region, Eastern Ethiopia

Solomon¹

2015

J Climatol Weather Forecasting

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Rainfall is the most critical and key variable both in atmospheric and hydrological cycle. Its patterns usually have spatial and temporal variability. Its variability is assumed to be the main cause for the frequently occurring climate extreme events such as drought and flood. In this study, spectrum analysis, cross-spectral analysis as well as seasonal auto-regressive integrated moving average (SARIMA) model were used in intending to predict the pattern and its extreme event frequency of rainfall in Dire Dawa Region based on data obtained from Dire Dawa and adjacent stations: Dengego and Haramaya. The result indicated that the amount of rainfall at Dengego and Haramaya are more or less the same on average in all seasons and much higher than that of Dire Dawa during last 30 year study period. The variability of annual rainfall in Dire Dawa during the study period is a bit larger than neighboring station's rainfall (Dengego and Haramaya), indicating that climate instability is high in Dire Dawa than other nearby stations. The result also indicates that relatively there is a tendency of increasing pattern in average annual rainfall of Dire Dawa in forecasted period. In the region, the rainfall extreme event like flood predicts or inferred to be recurring at about 4.17 years. Moreover, the rainfall periodicities of Dengego and Dire Dawa are found to be more likely associated, which implies that rainfall extreme event frequency in two districts is statistical significantly associated. It is proposed that assessing the factors that cause the fluctuation in the pattern and frequency of rainfall distribution in the region is needed to be study. The impacts of climate variability and climate change are evident on almost all socio-economic sectors. The output of this study can play an important role in the design of hydrological structures in the area of study and help the policy makers in improve their decisions by taking into consideration the available and future water resources. Prediction of Long-term Pattern and its Extreme Event Materials and Methods Data and variable of the studyA time series of monthly 30 years rainfall data in mm for the period January, 1984 to January, 2014 collected by the National Meteorological Agency of Ethiopia were used in the study. The data were collected from the synoptic stations of Dire Dawa and adjacent station: Dengego and Haramaya for further investigation. MethodologyThe development of climatology as a science has given rise to growing statistical applications on climatic information. Conducting investigations using standard statistical methodologies is an essential step in the development of climatology [13]. For instance, time series analysis is used in order to evaluate the temporal and spatial behavior of rainfall [14]. In this study a univariate Box-Jenkins Methods, in particular, Seasonal Autoregressive Integrated Moving Average (SARIMA) methods and spectral analysis and cross-spectral analysis are employed [15].Seasonal autoregressive integrated moving average (SA...

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Univariate Tests for Time Series Models

Cited by 98 publications

References 0 publications

Unevenly spaced time series analysis:Case study using calcimetry data from BV-1 and BV-2 boreholes in Ljubljansko barje (central Slovenia)

Unevenly spaced time series analysis:Case study using calcimetry data from BV-1 and BV-2 boreholes in Ljubljansko barje (central Slovenia)

An Analysis of Sex Ratio at Birth in Croatia 1946 – 2007

Prediction of Long-term Pattern and its Extreme Event Frequency of Rainfall in Dire Dawa Region, Eastern Ethiopia

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