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### Why do stochastic processes involve time? [duplicate]

We define random variables as functions on a sample space $X(ω), ω ∈ Ω$. Here I do not see time being involved. A stochastic process is a family of random variables, but they also are functions of ...
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### What is a time-series signal? [duplicate]

Let's assume we have a CNC machine cutting an aluminium block and we are monitoring its RMS power consumption at a constant sample rate e.g. 1Hz (see figure below for example). Can this considered to ...
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### Definition of Stochastic Time-series Variable [duplicate]

I am seeking an exact mathematical definition of a stochastic time-series variable. Suppose we have a filtered probability space $(\Omega,(F_t)_{t\geq0},P)$. Then, a stochastic process is a ...
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### why independence assumption not applicable on time series analysis?

I just started my course in time series analysis. I saw a statement there: "Statistical methods that depend on independence assumption are no longer applicable in time series analysis". Why it so?
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### When is a data set a time series?

Time is a concept from the real world. In mathematics and statistics, however, we operate on numbers. When does a number, as a mathematical abstraction, correspond to "time"? Any data set ...
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### Definition of random walk as a summation of independent random processes

I have a complete beginner question on random walk. As per this paper ...
2k views

### Time series and random variable

I would like to know if the $n$ realizations of a variable, say $Y$ expressed in the form of a time series constitutes $n$ random variables or just a single random variable $Y$? For example, the ...
493 views

### Time series models (e.g. ARMA) a type or extension of GLM? Particular/stipulated forms of dependence in time series models

I am trying to understand the relationship between ARMA Time Series models and the GLM (Generalized Linear Model) family of models. As far I know, all GLMs have the following 3 components: 1) random ...
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### Relation and difference between time series and stochastic processes?

Partly inspired by the following post: Relation and difference between time series and regression? After thinking carefully into these two subjects, I kind of wondering for what kind of data/...
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### Definition of the dirichlet process: what is the sequence of random variables

Reference material by Dr. Teh Definition Given a measureable set S, a base probability distribution H and a positive real number $\alpha$, the Dirichlet process $DP(H, \alpha)$ is a stochastic ...
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### Understanding stationarity in stochastic processes and time series

I am having trouble fully grasping the concept of stationarity in time series. Here is what I have gathered so far. A stochastic process is a collection of random variables with mean $\mu$ and ...
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### What qualifies as a time series?

I have a simple question: does any data gathered over time could be treated as a time series? For instance, if I measure CPU load at certain intervals, would that be a time series? Actually, I'm not ...
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### Backshift Operator: Is it well-defined?

I have seen the backshift operator $B$ defined as $Y_{t-1} = BY_t$ in class. But I don't understand why this is a reasonable thing to do. Does the backshift operator exist for all discrete time ...