# Questions tagged [continuous-time]

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### When are continuous-time models important?

In Econometrics, majority of the models are in discrete-time setting, whereas when you move on to quantitative finance, continuous-time models are most prevalent. I get the theory and idea behind ...
• 1,030
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### Variance estimate in a gillespie simulation

Lets say I simulate a immigration-death process: $P(X(t + \delta t) = x+ 1 | X(t) = x) = \lambda \delta t$ $P(X(t + \delta t) = x-1 | X(t) =x) = v x \delta t$ using a Gillespie simulation - I pick a ...
• 251
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### Modelling irregularly sampled observations of a continuous time signal with a discrete state space model

I need to model time series whose observations are sampled at arbitrary points in time. By modelling, I mean that I would like to fit a generative (probabilistic) model that can approximately ...
• 1,125
1 vote
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### What would be a continuous-time version of a VAR process?

It is often said that a AR(1) process can be viewed as a discretized version of the continuous-time Ornstein-Uhlenbeck process. Can we really claim this to be valid considering that the Ornstein-...
• 299
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### Continuously occurring true negatives

How can I handle discrete events in a continuous time stream in the context of an F1 metric? To give an example, let's say the Earthquake Forecasting Bureau would report the following for their ...
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• 252
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### Is there a way to calculate the riskiest places to be infected by COVID-19?

Is there a way to calculate the riskiest places to be infected by COVID-19? My friends and I are having an argument of whether being in a "high traffic-short contact time" situation (public transport) ...
1 vote
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### Can the interarrival times of a continuous time markov chain be distributed with 2 parameter (scale,location) exponential distributions?

I'm trying to model data with a time-homogenous CTMC with a number of states with corresponding constant transition rates $\lambda_{i}$ when I notice that much of the transition times from one state ...
1 vote
143 views

### Correspondence between time series models in continuous vs. discrete time

I am interested in an overview over the connection and correspondence between time series models in continuous vs. discrete time in finance. E.g. take ARMA(p,q) or GARCH(s,r) or ARMA(p,q)-GARCH(s,r) ...
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### Generate PDF from CTMC

I have an irreducible continuous-time Markov chain (CTMC) with a finite state space. The CTMC also does not have any one-step transitions from any state to itself. I have the transition rate matrix $Q$...
• 73
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### Modeling by means of a negative binomial process

The negative binomial distribution with parameters $p\in(0,1)$ and $t>0$ is sometimes defined as the distribution of the number of failures before the $t$th success. This is supported on the set \$\{...
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1 vote
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### Derivation Harvey (1984) Logistic Curve

Given a logistic function of the form. \begin{align*} f(t) = \frac{\alpha}{1 + \beta e^{\gamma t}} \end{align*} Harvey (1984) differentiates this and takes logs to yield: \begin{align*} \ln f' = 2 ...