Journal Article10.1017/S1365100599013073
Sampling dynamical systems
TL;DR: In this paper, the Nyquist sampling rate is used to identify the discrete-time representation of a single-input-single-output (SISO) model, where all the variables of the system are sampled for a period using a fixed sample rate.
read more
Abstract: Linear dynamical systems are widely used in many different
fields from engineering to economics. One simple but important class of such
systems is called the single-input transfer function model . Suppose that all
variables of the system are sampled for a period using a fixed sample
rate. The central issue of this paper is the determination of the smallest
sampling rate that will yield a sample that will allow the investigator to
identify the discrete-time representation of the system. A critical sampling
rate exists that will identify the model. This rate, called the Nyquist
rate, is twice the highest frequency component of the system. Sampling at a
lower rate will result in an identification problem that is serious. The
standard assumptions made about the model and the unobserved innovation
errors in the model protect the investigators from the identification
problem and resulting biases of undersampling. The critical assumption that is needed to identify an undersampled system is that at least one of the
exogenous time series be white noise.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Time-scale transformations of discrete time processes
TL;DR: In this paper, the effects of temporal aggregation when the aggregation frequency is variable and possibly stochastic are investigated, and the results that they report include the well-known results on fixed-interval aggregation, such as when monthly data are aggregated into quarters.
Time-Scale Transformations of Discrete Time Processes
TL;DR: In this article, the effects of temporal aggregation when the aggregation frequency is variable and possibly stochastic are investigated, and the results that they report include the well-known results on fixed-interval aggregation, such as when monthly data are aggregated into quarters.
Modeling high-frequency foreign exchange data dynamics
TL;DR: In this article, an autoregressive conditional intensity model was proposed to model high-frequency irregularly spaced data based on the Poisson regression model, which has the advantage of being simple and maintaining the calendar timescale.
6
References
•Book
Time series analysis, forecasting and control
George E. P. Box,Gwilym M. Jenkins +1 more
- 01 Jan 1970
TL;DR: In this article, a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970 is presented, focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject.
19.7K
Time Series Analysis: Forecasting and Control
TL;DR: Time Series Analysis and Forecasting: principles and practice as mentioned in this paper The Oxford Handbook of Quantitative Methods, Vol. 3, No. 2: Statistical AnalysisTime-Series ForecastingPractical Time-Series AnalysisApplied Bayesian Forecasting and Time Series AnalysisSAS for Forecasting Time SeriesApplied Time Series analysisTime Series analysisElements of Nonlinear Time Series analyses and forecastingTime series analysis and forecasting by Example.
19.6K
Time series analysis, forecasting and control
P. Young,S. Shellswell +1 more
TL;DR: Time series analysis san francisco state university, 6 4 introduction to time series analysis, box and jenkins time seriesAnalysis forecasting and, th15 weeks citation classic eugene garfield, proc arima references 9 3 sas support, time series Analysis forecasting and control pambudi, timeseries analysis forecasting and Control george e.
14.1K