Questions tagged [continuous-time]
22 questions
9
votes
1 answer
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) vs "low traffic-high contact time" situation…
Polo Marco
- 93
- 4
5
votes
1 answer
Why are most epidemic models continuous-time?
Most classical epidemic models such as SIR and variants are formulated as differential equations. However, to me discrete-time models feel more natural to measure the evolution of a disease on a day-by-day basis:
human activity come in daily…
Federico Poloni
- 339
- 2
- 13
3
votes
0 answers
Split a two dimensional continuous time Markov chain into two independent ones?
Let's say we have a two dimensional MC defined on the state space $\mathbb{N}\times \mathbb{N}$ evolving as below:
$(i,j) \rightarrow (i,j+1)$ with rate $\lambda$ for all $i,j$.
$(i,j) \rightarrow (i-1,j+1)$ with rate $\alpha$ for $i > K$ $(K\ge…
Math. H
- 87
- 5
3
votes
1 answer
Continuous time Fourier representation
I have learned that the Fourier transform of a continuous-time unit-periodic stochastic process is:
$$x(t) = \sum\limits_{k=-\infty}^{\infty} a_k e^{i2\pi kt} \quad \quad \text{ where } \quad \quad a_k = \int \limits_{0}^{1} x(t) e^{-i 2\pi kt}…
Joy
- 313
- 1
- 16
3
votes
0 answers
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 $\{0,1,2,3,\ldots\}.$ Another convention defines it as…
Michael Hardy
- 7,094
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2
votes
1 answer
Continuous time distribution of autoregressive time series sampled in discrete time
If a discrete-time autogressive AR(p) model is fit to data x at t=1,2,..., what is the probability distributiom of x at time n+h, denoted x(n+h), where 0 < h < 1 and x(n) and x(n+1) are known?
Fortranner
- 586
- 2
- 12
2
votes
1 answer
Bayesian updating with continuous prior in continuous time
I am considering an example where a person flips his (unfair) coin to examine what is the probability of getting head.
I could find some posts saying that the posterior distribution follows Beta distribution in discrete time.
Would there be a…
김찬우
- 73
- 6
2
votes
0 answers
Continuous-Time Autoregressive process and RKHS
Consider a stationary Continuous-time AutoRegressive (CAR) process on
a bounded time-interval $(a, \, b)$. This article by Emmanuel
Parzen describes
the corresponding Reproducing Kernel Hilbert Space (RKHS) $\mathcal{K}$ and its inner product…
Yves
- 4,313
- 1
- 13
- 34
2
votes
0 answers
Continuous-time, non-recursive ARIMA Equation
In this question, I asked about validating the assumption of geometric Brownian motion in a analytic model using ARIMA. Here, I want to generalise this idea.
If I'm building a decision model that requires some assumption about how prices, say,…
Anthony
- 182
- 1
- 12
2
votes
0 answers
Infill likelihood for a continuously observed continuous-time process
Consider a continuous-time stochastic process $y(t)$ having the following linear
(Gaussian) state-space representation for $t \geq 0$
$$
\left\{
\begin{array}{c c l}
\text{d}{\boldsymbol{\alpha}}(t) &=& \mathbf{A} \boldsymbol{\alpha}(t)\,
…
Yves
- 4,313
- 1
- 13
- 34
1
vote
0 answers
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-Uhlenbeck process is mean-reverting while AR(1) does…
MilTom
- 289
- 1
- 8
1
vote
0 answers
ARIMA and Geometric Brownian Motion
I have read that Brownian motion, or more precisely, a Wiener process, is a scaling limit of a random walk. Hence, when attempting to model a real time-series of energy prices, if I discover that an $ARIMA(0,1,0)$ model fits my data well, I assume…
Anthony
- 182
- 1
- 12
1
vote
0 answers
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 to another (lets call it $a \to b$) don't occur…
Rizzeyish
- 11
- 2
1
vote
0 answers
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) from discrete time, list their counterparts in…
Richard Hardy
- 54,375
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1
vote
1 answer
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 \ln f + \ln \frac{-\beta \gamma}{\alpha} +…
InterwebIsGreat
- 53
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