Questions tagged [discrete-time]

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14 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 &...
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1answer
26 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 ...
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1answer
20 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 ...
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36 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:                  ...
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1answer
29 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. ...
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14 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 ...
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9 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 ...
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37 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} ...
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1answer
38 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}...
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1answer
23 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 ...
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29 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 ...
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12 views

Computing discrete survivor functions

I am trying to understand the survivor function for a discrete point process, but I am finding two conflicting definitions. Any clarification would be much appreciated. For illustration purposes, ...
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11 views

Average of the product of two autocorrelated variables

I am not expert in statistics, so I hope this question doesn't sound too trivial. I have a discrete random variable that evolves in discrete time, . The stochastic process behind this variable has ...
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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 ...
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85 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 ...
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1answer
165 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 ...
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1answer
222 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, ...
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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 ...
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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 ...
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1answer
150 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 ...
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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, ...
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1answer
298 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 ...
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1answer
193 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 ...
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1answer
69 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?
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2answers
335 views

Simulation -Discrete Time Hazard model

How we can simulate the survival times for fitting discrete time hazard model?
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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 ...
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59 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 ...
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67 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 ...
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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 ...
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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 ...
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1answer
108 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
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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: ...
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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 ...
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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 ...
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0answers
153 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 ...
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0answers
393 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 ...
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0answers
302 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-...
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1answer
183 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) ...
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202 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 ...
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1answer
89 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
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1answer
198 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, ...
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1answer
292 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-...
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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 ...
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2answers
160 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://...
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0answers
90 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 ...
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2answers
119 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 ...
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226 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)\...