Linked Questions

1 vote
1 answer
285 views

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 ...
Nip's user avatar
  • 561
0 votes
0 answers
22 views

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 ...
DimP's user avatar
  • 236
0 votes
0 answers
14 views

Time series data [duplicate]

Is the following M4_regular_matrix time series data? I am a bit confused since The rows indicate locations although the columns consist of time. We actually ...
user149054's user avatar
6 votes
4 answers
976 views

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 ...
Igor F.'s user avatar
  • 9,069
4 votes
2 answers
3k views

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 I saw a statement there: "Statistical methods that depend on independence assumption are no longer applicable in time series analysis".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?
StatsMonkey's user avatar
5 votes
2 answers
2k views

Definition of random walk as a summation of independent random processes

I have a complete beginner question on random walk. As per this paper ...
Victor's user avatar
  • 6,565
4 votes
1 answer
958 views

How to show that an MA(2) process is strictly stationary?

I have a question about MA(2) model $X_t = e_t + 0.5e_{t−1} + 0.4e_{t−2}$ with $e_t \sim IID(0, σ^2_e $). I know by construction, MA process is (weakly) stationary, but can it be strictly stationary ...
Yana's user avatar
  • 41
4 votes
1 answer
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 ...
SKM's user avatar
  • 787
6 votes
1 answer
393 views

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 ...
ObnoxiousFrog's user avatar
3 votes
1 answer
563 views

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 ...
fool's user avatar
  • 2,440
7 votes
0 answers
821 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 ...
ColorStatistics's user avatar
0 votes
0 answers
666 views

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/...
Henry.L's user avatar
  • 2,450
3 votes
0 answers
593 views

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 ...
TheBaj's user avatar
  • 131
1 vote
1 answer
256 views

What is the difference between an AR process and autocorrelation?

Or is it maybe the same thing? I see that autocorrelation is when Yt is correlated with its lag Yt-1. But isn't that essentially what an AR process (say AR(1)) is? We are assuming that there IS ...
John's user avatar
  • 41
4 votes
1 answer
253 views

What is a Stochastic Process?

Online I found many definitions of stochastic processes, but none of them was intuitive or easy to understand. I was wondering if someone could provide me with some example and definition to deeply ...
Paolo Totaro's user avatar

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