Questions tagged [discrete-time]
The discrete-time tag has no usage guidance.
47
questions
1
vote
0answers
22 views
Determine order of events happening in discrete timespace
At $t=0$ I have a certain (active) population, lets say 1,000 customers. In each time step I expect a certain amount I have a probability of death of 1% and a prepayment rate of 5%. At the end of each ...
0
votes
0answers
20 views
Probability $X_n=k$ for a Markov Chain over the integers
Let $\{X_n\}$ be a Markov chain with state space $\mathcal{S}=\mathbb{Z}$, and $X_0=0,$ and $p_{0,1}=p_{0,-1}=1/2,$ and $p_{i,i+1}=1$ for all $i \ge 1,$ and $p_{i,i-1}=1$ for all $i\le -1.$ The ...
0
votes
0answers
19 views
Proving positive recurrence for a finite state space DTMC
Let $$P =
\begin{pmatrix}
0.3 & 0.5 & 0 & 0 & 0 & 0.2 \\
0 & 0.5 & 0 & 0.5 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 & 0 \\
0 & 0.3 & 0 & 0 &...
4
votes
1answer
95 views
Calculating the expected number of visits to a state by a DTMC
Suppose we have a DTMC $X$ : $\{X_n : n = 0, 1,2,\dots\}$, a transition probability matrix $P$, and state space $S = \{1,2,3\}$. Suppose I want to calculate the expected amount of times we visit state ...
3
votes
1answer
38 views
Conditional probabilities with Discrete Time Markov Chain non-perishable inventory
Suppose $\{X_n : n =0,1,2,\dots \}$ is a DTMC that represents the inventory level at the end of day $n$. We have inventory policy $(2,4)$, i.e., if $X_n < 2$, we order enough units to have ...
3
votes
1answer
128 views
What statistical tests allow for a comparison of the "roughness" of discrete functions?
I have a data set of the revenues of 10 different large companies from the years 2000 through 2019. Here they are all plotted in one graph. The y-axis has a unit of billions of Euros:
...
1
vote
1answer
33 views
Using test hypothesis to prove I ran a sufficient number of simulations
I simulated a system using discrete-events simulation, more particularly next-event simulation.
The system is M/M/1 (infinite FIFO waiting room). Whenever the system is jobless, the server shutdowns. ...
0
votes
0answers
15 views
Discrete Time Logistic
I'm trying to use panel survey data to determine married event in life using discrete logistic regression. However, some observations enter the survey not the same time as other i.e. some enter in ...
0
votes
0answers
12 views
Random effects for mixed 3-way (between x within x within) and 2-way (between x within) models in lmer and glmer
I conducted a study in which driving performance is measured among two groups (exposed to different manipulations) at two times (pre-manipulation and post-manipulation) in a simulator.
The data is ...
0
votes
0answers
45 views
Generating correlated discrete random variables
Suppose that we have $q_t \in \{-1, 1\}$ where $\mathbb{P}(q_t = -1) = \mathbb{P}(q_t = 1) = \frac{1}{2}$. Further, assume that
\begin{align}
Cor\left( q_t, q_{t-k} \right) =
\begin{cases}
...
3
votes
1answer
58 views
Z transform of $ 2^{-|n|} $
Dears,
I'm trying to compute the Z-transform of $$ x(n) = 2^{-|n|} $$.
My procedure is as follows:
Using definition of Z transform:
$$ X(z) = \sum_{n=-\infty}^{\infty}2^{-|n|} z^{-n} = \sum_{n=-\infty}...
2
votes
1answer
24 views
Variable data measured discretely with poor resolution
Is there an appropriate method for estimating variation when variable data is measured discretely where the resolution is poor. Here's an example: You are looking at how long it takes for a solid to ...
1
vote
0answers
37 views
Negative Binomial vs. Discrete Survival
I am trying to model a discrete duration variable (number of weeks) and I am not sure which model to use.
Many would argue that durations are modeled using survival models. However, in J. Hilbes ...
0
votes
0answers
23 views
Any methods for clustering short time series data
I have around 200 different sets of time series data with a semi-annual periodicity.
The length of each series varies from 1 to 6 years.
I essentially want to build unsupervised clusters by grouping ...
2
votes
0answers
119 views
Proving/showing that the Markov property holds in discrete time Markov chain example
I am currently studying the textbook Introduction to Modeling and Analysis of Stochastic Systems, Second Edition, by V. G. Kulkarni. In a section on discrete-time Markov chains, the author presents ...
1
vote
1answer
330 views
Rows and columns of the one-step transition probability matrix
I am currently studying the textbook Introduction to Modeling and Analysis of Stochastic Systems, Second Edition, by V. G. Kulkarni. In a section on discrete-time Markov chains, the author introduces ...
0
votes
1answer
389 views
Regression analysis with small data set
We've performed a regression analysis with 14 data points (Y's) that originate from 9 X's (plant batches were split up).
I'm well aware that this is a small data set and there are caveats. However, ...
2
votes
1answer
89 views
Statistical modeling multidimensional discrete system
I have a system which its state is described by a vector $v=(a, b, c)$, where $a$, $b$ and $c$ can take any value between $0$ and $100$ and where $a+b+c <= 100$.
I have observations of the state ...
0
votes
1answer
48 views
Detecting Significant Changes in Time Series
I’m hoping someone might be able to point me in the right direction for this problem. I’ve anonymised the problem by describing it in terms of supermarket purchase data rather than the real context so ...
1
vote
1answer
175 views
Posterior distribution from piecewise likelihood
Consider a hierarchical Bayesian model for analysing data from an inhomogeneous Poisson process that we observe in discrete time. Let $Y_i, i = 1,...,n$, be the number of events occurring in the time ...
1
vote
0answers
69 views
Modeling Time in the Discrete Time Analysis using Left-truncated Data
I am doing multiple-spell, discrete-time analysis to examine factors shaping time to exiting a renter spell, with time-varying covariates at monthly interval. My data has left-truncated spells, ...
-1
votes
1answer
382 views
INAR(1) simulation in R [closed]
How do we simulate values of $Y_t$ for a maximum value of $t=60$ when we have an INAR(1) process as follows:
$Y_t=ρ^*Y_{(t-1)}+R_t$
where $t$ takes values from 1 to 60, $ρ=0.3,0.8$, $ρ^*$ is ...
0
votes
1answer
245 views
Simulating a (discretized) Cox process via binomial sampling
Let X be a Cox process (doubly-stochastic Poisson process) driven by a Poisson process with fixed intensity(rate) $\lambda=50$ , and choose some small time interval $dt=0.01$ . Is the proper way to ...
0
votes
1answer
93 views
How to recognize an ARMA process?
By looking at the autocovariance, how could you recognise what discrete model (MA(q), AR(p), or ARMA(p,q)) is more appropriate to describe your data?
4
votes
2answers
370 views
Simulation -Discrete Time Hazard model
How we can simulate the survival times for fitting discrete time hazard model?
5
votes
1answer
2k views
How to forecast integer time series in R?
For a while now I used to forecast integer/count time series as I would do for any other continuous time series, meaning : I use models like ARIMA, ETS, THETA, TBATS ... And then I simply round the ...
3
votes
0answers
62 views
best statistical approach to study the time evolution of clustering in a data set
I am using a stochastic method for the clustering of a data set. The number of clusters that this approach returns, can differ in each iteration. On the other hand, I would like to study the evolution ...
6
votes
0answers
69 views
Is average stopping time a continuous function of Bernoulli parameter?
Consider an infinite sequence $X = (X_i)_{i \in \mathbb N}$ of i.i.d Bernoulli random variables with (unknown) parameter $p \in (0,1)$, and let $N$ be a stopping time on $X$. Is it always the case ...
2
votes
0answers
28 views
Gaussian random variable over multiple periods
Let's assume that :
$$X_0=X_0$$
$$X_1=(1+R_1)*X_0$$
$$...$$
$$X_N=(1+R_N)*X_{N-1}$$
where $R_i \sim \mathcal{N}(0,u^2)$.
I am trying to compute the probability $P(X_N < a)$.
How accurate is it to ...
0
votes
1answer
1k views
Linear mixed model: Time as continuous or discrete variable?
I am analysing a dataset from a randomised controlled trial (2 treatment groups) with measurements at 3 time points (weeks 0, 1 and 8). I am struggling with whether to analyse this with the three time ...
0
votes
1answer
120 views
Probability distribution for day of the year [closed]
"Day of the year" is an integer from 1 to 365, indicating the day within the year. I'd like to model the day of the year that a particular event occurs. The event must occur between day 100 and day ...
4
votes
1answer
2k views
discrete time survival analysis
I would greatly appreciate if you could let me know how to do discrete time survival analysis with time varying covariates.
Some part of my data set is as follows:
...
0
votes
1answer
1k views
parametric survival regression and discrete time survival regression
I would greatly appreciate if you could let me know how to choose among different parametric distributions including gama, Weibull, lognormal, loglogistic and etc for panel (time series cross ...
0
votes
0answers
27 views
Looking for suitable method to update predictions
consider an e-commerce website which daily updates their transaction data. I take interest in predicting the revenue an account generates over a certain time range, say until the fifth year after the ...
2
votes
0answers
158 views
Difference between count time and discrete time survival analysis
Is there a practical or theoretical difference between count time survival analysis (e.g. ctset/cttost in Stata), where counts ...
3
votes
0answers
399 views
Interpreting a (integer valued) discrete predictor as a continuous variable?
I am currently working on a multiple linear regression in order to evaluate the impact of some variables on a contract's length, which can only take integer values (years). As I am only interested in ...
5
votes
0answers
329 views
Describe AR process with additive white noise using ARMA process
Disclaimer: This is a homework problem
This is a problem from "Adaptive Filter Theory" by Haykin. Problem 2.10 (2nd edition).
Problem
A discrete-time stochastic process $\{x(n)\}$ that is real-...
1
vote
1answer
197 views
Algorithms for extracting moving average intervals
I have a series of discrete events and a global clock.
Whenever an event happens, I record a timestamp and do some processing. Specifically, I am trying to compute "moving average" (not really) ...
0
votes
0answers
203 views
How to check assumptions for a discrete time survival analysis
What tests are required before and after estimating a discrete time survival model? In other words, how the assumptions should be tested and how the generalization of results should be investigated ...
1
vote
1answer
102 views
Coefficients in discrete proportional hazards model
I am aware of the rationale behind taking the exponentiated coefficients in a proportional hazards model as representing change in hazard per unit change in the corresponding predictor. This also ...
1
vote
1answer
227 views
I have a discrete-valued time series and would like to analyse it, but dont know where to start
Due to some health issues, each day at about the same time, I give myself a score which represents the state of my health: specifically, fatigue, with 1 being the worst and 10 the best. In practice, ...
0
votes
1answer
317 views
How to calculate the probability of death between two discrete time periods using survival curves
I was hoping somebody could help, I am trying to work out the probability of death between two time points on a survival curve.
i.e. I have my survival curve as follows (this is an example Kaplan-...
0
votes
2answers
1k views
When is time treated as a discrete variable?
Time is usually treated as a continuous variable but in some cases it is discrete. An example would be with a drug study and measurements are taken at 1, 2 and 3 hours. Am I right to think an ...
1
vote
2answers
204 views
Resource request : How to prove the output of a process is random variables?
I am reading through articles which present the spectral properties of chaotic systems such that they can be candidates for generating pseudo random binary sequences. One such article, is http://...
1
vote
0answers
92 views
Difference between Cox Proportional Harzards Model and interval-based logistic model for survival regressions
I have a dataset of timestamped trader transactions (to the second). I want to conduct a survival analysis on the trades where a trade is started at startTime and ...
0
votes
2answers
125 views
Discrete survivor function expressed in terms of hazard
Let $T$ can take on values $t_1,t_2,\ldots,$ with $0\le t_1\le t_2,\ldots,$ and let the probability function be
$$f(t_j)=Pr(T=t_j),\quad j=1,2,\ldots$$
The survivor function is then
$$S(t)=Pr(T\ge ...
3
votes
0answers
237 views
Discrete time generator of stochastic process
While looking at one paper about Metropolic Hasting optimal convergence rates, I came accross a discrete time generator of Markov chain. It is defined as follows:
$$G V(x)=nE\left [ \left( V(y)-V(x)\...
