Description Usage Arguments Details Value Author(s) References See Also Examples
Generate a random time series of the 1-dimensional stationary Ornstein-Uhlenbeck state space (OUSS) process.
1 2 | generate_ouss(times, mu, power_o, sigma,
lambda, power_e, epsilon)
|
times |
Numeric vector of times for which to evaluate OUSS model. Times need to be strictly increasing. |
mu |
Single number. Deterministic equilibrium of OU process, i.e., the expected value of the time series at any particular time. |
sigma |
Single number. Standard deviation of OU fluctuations around equilibrium. |
power_o |
Single non-negative number. Power spectrum at zero-frequency generated by the OU process. Either |
lambda |
Single non-negative number. Resilience (also known as relaxation rate) of the OU process. This is the inverse of the OU correlation time. |
epsilon |
Single number. Standard deviation of Gaussian measurement error. Setting this to zero will yield a time series from the classical OU process. |
power_e |
Single non-negative number. Asymptotic power spectrum at large frequencies due to the Gaussian measurement errors. Setting this to zero will yield a classical OU process. Either |
The OUSS model describes the measurement of an Ornstein-Uhlenbeck (OU) stochastic process at discrete times with additional uncorrelated Gaussian measurement errors. The OU process itself is a continuous-time random walk (Brownian motion) with linear stabilizing forces, described by the stochastic differential equation
dX = λ(μ-X) dt + s dW,
where W is the standard Wiener process and s^2=2λσ^2. The OUSS model is obtained by adding uncorrelated Gaussian numbers with zero mean and variance ε^2 to the time series.
A numeric vector of same length as times
, containing sampled values of the OUSS process. These values will all have the same expectation (mu
) and variance (sigma^2+epsilon^2
) but will be correlated.
Stilianos Louca
Louca, S., Doebeli, M. (2015) Detecting cyclicity in ecological time series, Ecology 96: 1724–1732
Dennis, B., Ponciano, J.M. - Density dependent state-space model for population abundance data with unequal time intervals, Ecology (in press as of June 2014)
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