Automatic trend estimation

By: CË?alin VamosÂ¸, Maria CrË?aciun

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Paperback | 15 September 2012

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144 Pages

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Discrete stochastic processes and time series.- Trend definition.- Finite AR(1) stochastic process.- Monte Carlo experiments. - Monte Carlo statistical ensembles.- Numerical generation of trends.- Numerical generation of noisy time series.- Statistical hypothesis testing.- Testing the i.i.d. property.- Polynomial fitting.- Linear regression.- Polynomial fitting.- Polynomial fitting of artificial time series.- An astrophysical example.- Noise smoothing.- Moving average.- Repeated moving average (RMA).- Smoothing of artificial time series.- A financial example.- Automatic estimation of monotonic trends.- Average conditional displacement (ACD) algorithm.- Artificial time series with monotonic trends.- Automatic ACD algorithm.- Evaluation of the ACD algorithm.- A paleoclimatological example.- Statistical significance of the ACD trend.- Time series partitioning.- Partitioning of trends into monotonic segments.- Partitioning of noisy signals into monotonic segments.- Partitioning of a real time series.- Estimation of the ratio between the trend and noise.- Automatic estimation of arbitrary trends.- Automatic RMA (AutRMA).- Monotonic segments of the AutRMA trend.- Partitioning of a financial time series.

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You Can Find This Book In

Non-Fiction Mathematics Probability & Statistics Computing & I.T.Graphical & Digital Media Applications 3D Graphics & Modelling Science Physics Mathematical Physics Calculus & Mathematical Analysis Numerical Analysis Statistical Physics

Introduction	p. 1
Discrete Stochastic Processes and Time Series	p. 1
Trend Definition and Estimation	p. 4
AR(1) Stochastic Process	p. 7
References	p. 12
Monte Carlo Experiments	p. 15
Monte Carlo Statistical Ensembles	p. 15
Numerical Generation of Trends	p. 18
Numerical Generation of Noisy Time Series	p. 21
Statistical Hypothesis Testing	p. 26
References	p. 30
Polynomial Fitting	p. 31
Polynomial Fitting	p. 31
Polynomial Fitting of Artificial Time Series	p. 34
An Astrophysical Example	p. 38
References	p. 42
Noise Smoothing	p. 43
Repeated Central Moving Average	p. 43
Smoothing of Artificial Time Series	p. 49
A Financial Example	p. 53
References	p. 58
Automatic Estimation of Monotonic Trends	p. 61
Average Conditional Displacement (ACD) Algorithm	p. 61
Automatic ACD Algorithm	p. 65
Evaluation of the ACD Algorithm	p. 70
A Climatological Example	p. 74
Monotonic Components of Nonmonotonic Trends	p. 76
References	p. 80
Estimation of Monotonic Trend Segments from a Noisy Time Series	p. 81
Time Scale of Local Extrema	p. 81
Local Extrema of Noisy Time Series	p. 85
Local Extrema of RCMA Trends	p. 89
Significant Local Extrema of a Real Time Series	p. 92
References	p. 97
Automatic Estimation of Arbitrary Trends	p. 99
Automatic RCMA (AutRCMA)	p. 99
Statistical Significance of the Local Extrema of the AutRCMA Trend	p. 105
References	p. 110
Statistical Properties of the Linear Regression	p. 111
Spurious Serial Correlation Induced by MA	p. 113
Continuous Analogue of the ACD Algorithm	p. 117
Standard Deviation of a Noise Superposed over a Monotonic Trend	p. 121
Construction of a Partition of Scale n	p. 127
Estimation of the Ratio Between the Trend and Noise Magnitudes	p. 129
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Automatic trend estimation

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