Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation

Exact Simulation of Time-Varying Fractionally Differenced Processes

Time-varying fractionally differenced (TVFD) processes can serve as useful models for certain time series whose statistical properties evolve over time. A TVFD process can be taken to have a spectral density function that obeys a power law at low frequencies with a time-varying exponent. In contrast to locally stationary or locally self-similar processes, the power law exponent for a TVFD proce...

Exact Simulation of Time-Varying Fractionally Differenced Processes

Time-varying fractionally differenced (TVFD) processes can serve as useful models for certain time series whose statistical properties evolve over time. The spectral density function for a TVFD process obeys a power law whose exponent can be time dependent. In contrast to locally stationary or locally self-similar processes, the power law exponent for a TVFD process is not restricted to certain...

Wavelet-Based Parameter Estimation for Trend Contaminated Fractionally Differenced Processes

A common problem in the analysis of time series is how to deal with a possible trend component, which is usually thought of as large scale (or low frequency) variations or patterns in the series that might be best modeled separately from the rest of the series. Trend is often confounded with low frequency stochastic fluctuations, particularly in the case of models such as fractionally differenc...

Short-Term Forecasting with ARIMA Time Series Models

Continuous-time Modelling of Hydrologic Time Series: Shot Noise Models

To simulate the runoff process at short-term aggregation scale (typically one day) the shot noise model has gained considerable reputation. In this paper, the model developed by Murrone et al. (1997) is taken as a notable example of physically-consistent framework to discuss the different aspects related to the building and estimation of a stochastic tool for time-series generation. In particul...