Prediction in moving average processes

Schίck, Anton; Wefelmeyer, Wolfgang

doi:10.1016/j.jspi.2007.01.007

Cited by 5 publications

(3 citation statements)

References 31 publications

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“…Moving averages are commonly used for time series to smooth out short‐term fluctuations and highlight longer term trends or cycles (Schick and Wefelmeyer, 2008). The signals can be actually regarded as being composed of a large number of frequencies, short‐term fluctuations are smoothed out and long‐term trends are reserved with the size of the subset being averaged growing.…”

Section: Resultsmentioning

confidence: 99%

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles

Bolliger

Blacque

Frech

2008

Chemistry A European J

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The aminophosphine-based pincer complexes [C6H3-2,6-(XP(piperidinyl)2)2Pd(Cl)] (X=NH 1; X=O 2) are readily prepared from cheap starting materials by sequential addition of 1,1',1''-phosphinetriyltripiperidine and 1,3-diaminobenzene or resorcinol to solutions of [Pd(cod)(Cl)2] (cod=cyclooctadiene) in toluene under N2 in "one pot". Compounds 1 and 2 proved to be excellent Heck catalysts and allow the quantitative coupling of several electronically deactivated and sterically hindered aryl bromides with various olefins as coupling partners at 140 degrees C within very short reaction times and low catalyst loadings. Increased reaction temperatures also enable the efficient coupling of olefins with electronically deactivated and sterically hindered aryl chlorides in the presence of only 0.01 mol % of catalyst. The mechanistic studies performed rule out that homogeneous Pd 0 complexes are the catalytically active forms of 1 and 2. On the other hand, the involvement of palladium nanoparticles in the catalytic cycle received strong experimental support. Even though pincer-type Pd IV intermediates derived from 1 (and 2) are not involved in the catalytic cycle of the Heck reaction, their general existence as reactive intermediates (for example, in other reactions) cannot be excluded. On the contrary, they were shown to be thermally accessible. Compounds 1 and 2 show a smooth halide exchange with bromobenzene to yield their bromo derivatives in DMF at 100 degrees C. Experimental observations revealed that the halide exchange most probably proceeded via pincer-type Pd IV intermediates. DFT calculations support this hypothesis and indicated that aminophosphine-based pincer-type Pd IV intermediates are generally to be considered as reactive intermediates in reactions with aryl halides performed at elevated temperatures.

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Section: Resultsmentioning

confidence: 99%

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles

Bolliger

Blacque

Frech

2008

Chemistry A European J

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“…Correlation analysis. Moving averages are commonly used for time series to smooth out short-term fluctuations and highlight longer term trends or cycles (Schick and Wefelmeyer, 2008). The signals can be actually regarded as being composed of a large number of frequencies, short-term fluctuations are smoothed out and long-term trends are reserved with the size of the subset being averaged growing.…”

Section: Time-varying Response Characteristicsmentioning

confidence: 99%

Response analysis of rainfall–runoff processes using wavelet transform: a case study of the alpine meadow belt

Liu

Bao

Chen

et al. 2011

Hydrological Processes

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Abstract:Rainfall-runoff processes appear to be highly nonlinear in Bayinbluk watersheds of the northwestern China. In this study, the time-scale wavelet transform has been used for the analysis of this nonstationary system. The Haar and Morlet wavelet transform were used to analyse the rainfall-runoff conversion relationship. Wavelet power spectrum and change point methods are also employed to analyse rainfall rates and runoffs measured at daily to half-hourly sampling rate. The four experimental sites (Luoto, Haer, Kuce and Shengl) are located in the Tianshan Mountains (Xinjiang province, China). Correlation analysis and wavelet transform are first applied to runoff process in different underlying surfaces. Wavelet analyses of rainfall rates and runoffs also give meaningful information on the temporal variability of the rainfall-runoff relationship. Change point and wavelet power spectrum analysis provide simple interpretation of energy distribution between different scales. The results indicate that wavelet transform is a good method for analysing the nonlinear relationship of temporal-spatial responses between rainfall and runoff. This method allowed quantification of the processes affecting runoff and provided an insight into their implications in surface water management.

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“…For the MA(1) model X t = ε t − ϑε t−1 with |ϑ| < 1 and innovations ε t , t ∈ Z, that are i.i.d. with finite variance, Schick and Wefelmeyer (2006b) construct root-n consistent estimators for the random variable q(h) when m = 1. We generalize their result to arbitrary invertible linear processes and to arbitrary m.…”

Section: Introductionmentioning

confidence: 99%

Prediction in invertible linear processes

Schίck

Wefelmeyer

2007

Statistics & Probability Letters

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We construct root-n consistent plug-in estimators for conditional expectations of the form E(h(X n+1 , . . . , X n+m )|X 1 , . . . , X n ) in invertible linear processes. More specifically, we prove a Bahadur type representation for such estimators, uniformly over certain classes of not necessarily bounded functions h. We obtain in particular a uniformly root-n consistent estimator for the m-dimensional conditional distribution function. The proof uses empirical process techniques.Keywords. Von Mises statistic, kernel smoothed empirical process, residual-based kernel density estimator, stochastic expansion, infinite-order moving average process, infinite-order autoregressive process.

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Prediction in moving average processes

Cited by 5 publications

References 31 publications

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles

Response analysis of rainfall–runoff processes using wavelet transform: a case study of the alpine meadow belt

Prediction in invertible linear processes

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Prediction in moving average processes

Cited by 5 publications

References 31 publications

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: PdIV Intermediates and Palladium Nanoparticles

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: PdIV Intermediates and Palladium Nanoparticles

Response analysis of rainfall–runoff processes using wavelet transform: a case study of the alpine meadow belt

Prediction in invertible linear processes

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Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles