scholarly journals Effect of Autocorrelation on Applying Central Limit Theorem to Air Pollutant Concentration Time Series

2002 ◽  
Vol 2 (1) ◽  
pp. 87-92
Author(s):  
Chung-Kung Lee ◽  
Ding-Shun Ho ◽  
Chung-Chin Yu ◽  
Cheng-Cai Wang ◽  
Yun-Hua Hsiao
Keyword(s):  
Time Series ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Air Pollutant ◽  
Pollutant Concentration ◽  
Concentration Time ◽  
Concentration Time Series

The asymptotic theory of linear time-series models

1973 ◽  
Vol 10 (01) ◽  
pp. 130-145 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Time Series ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Theory ◽  
Linear Time ◽  
Stationary Time Series ◽  
Linear Predictor ◽  
The Central Limit Theorem ◽  
Best Linear Predictor

A linear time-series model is considered to be one for which a stationary time series, which is purely non-deterministic, has the best linear predictor equal to the best predictor. A general inferential theory is constructed for such models and various estimation procedures are shown to be equivalent. The treatment is considerably more general than previous treatments. The case where the series has mean which is a linear function of very general kinds of regressor variables is also discussed and a rather general form of central limit theorem for regression is proved. The central limit results depend upon forms of the central limit theorem for martingales.

scholarly journals Spatial dissimilarities in seasonal cycle of PM10 particulate matters in Seoul, Korea

2019 ◽  
Author(s):  
Parth Bansal
Keyword(s):  
Time Series ◽  
Pm10 Concentration ◽  
Pollutant Concentration ◽  
Air Quality Monitoring ◽  
Comprehensive Understanding ◽  
Concentration Time ◽  
Spatial Differences ◽  
Concentration Time Series ◽  
Air Quality Monitoring Stations ◽  
Monitoring Stations

The increase in spatial and temporal resolution of pollution data has advanced the understanding of trend in pollutant concentration through time and space. However, this has also made inspection of time series and the relation between observations from different monitoring stations difficult to comprehend. In this study, we decompose PM10 concentration time series (2010 - 2018) from 40 Air Quality Monitoring Stations (AQMs) in Seoul and then cluster the seasonal cyclic components using K-Means and K-Shape algorithms. Firstly, the influence of diurnal, weekly and annual cycle on PM10 concentration is shown. Secondly, the clustering results illustrate that both algorithms are useful in determining AQMs with similar cycles, and together provide a comprehensive understanding of spatial differences in pollutant concentration.

CENTRAL LIMIT THEOREM FOR THE LOG-REGRESSION WAVELET ESTIMATION OF THE MEMORY PARAMETER IN THE GAUSSIAN SEMI-PARAMETRIC CONTEXT

Fractals ◽  
2007 ◽  
Vol 15 (04) ◽  
pp. 301-313 ◽  
Author(s):  
E. MOULINES ◽  
F. ROUEFF ◽  
MURAD S. TAQQU
Keyword(s):  
Time Series ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Variance ◽  
Spectral Density Function ◽  
Dependence Structure ◽  
Asymptotically Normal ◽  
The One ◽  
Gaussian Time

We consider a Gaussian time series, stationary or not, with long memory exponent d ∈ ℝ. The generalized spectral density function of the time series is characterized by d and by a function f*(λ) which specifies the short-range dependence structure. Our setting is semi-parametric in that both d and f* are unknown, and only the smoothness of f* around λ = 0 matters. The parameter d is the one of interest. It is estimated by regression using the wavelet coefficients of the time series, which are dependent when d ≠ 0. We establish a Central Limit Theorem (CLT) for the resulting estimator [Formula: see text]. We show that the deviation [Formula: see text], adequately normalized, is asymptotically normal and specify the asymptotic variance.

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