Questions tagged [time-series]

Question 1

I have been studying the Koopman operator, which is an operator that transforms any dynamical system, even non-linear systems, into a linear system in a potentially infinite dimensional space. Suppose ...

Question 2

Is there a mathematical measure to calculate the validity of a long (i.e., nearly half the time series length) periodicity in a time series? See the graph below for an example. Is this meaningfully ...

Question 3

I have a time-series of events that go through a black box over a period of time. I need to determine if there is seasonality within the black box using these events, that are either True or False. ...

Question 4

I have a question when reading R. H. Shumway and D. S. Stoffer's Time Series Analysis and Its Application With R Examples, 5th edition. On page 181, section 4.1, it's said that Note that, if in (4.4),...

Question 5

In biostatistics it’s common to check residuals from survival or event-rate models (for example, a Cox PH fit or a Poisson/negative-binomial model on a regular time grid) for leftover structure. Let $...

Question 6

I think I don't understand the drift term in ARIMA models. This is what I did and my current understanding: I have a time series $Y_t$ of n observations with mean $\bar Y \approx 7.15.$ I wanted to ...

Question 7

The Allan Variance Sigma Tau Diagram allows one understand the different kinds of noise that are present in a time series; the following two images are taken from the wikipedia page related to Allan ...

Question 8

I am trying to find a distribution of a maximum value of the following process: \begin{align*} S_t &= S_{t-1} + \varepsilon_t, \quad \varepsilon_t \sim \ \mbox{i.i.d.} \ \mathcal{N}(0, 1) \...

Question 9

I have two time-series signals, say θ₁[n] and θ₂[n], sampled at constant time intervals. To analyze their relationship, I compute the Pearson correlation coefficient over batches of N samples using ...

Question 10

Suppose one aims to test $$H_0:X_1,\ldots,X_n\text{ is an i.i.d. sample from CDF }F.$$ Suppose that we observe data $X_1,\ldots,X_n$ that are such that $X_i\sim F$ for each $i\in[n]$, but such that ...

Question 11

Suppose I have a time-series prediction problem, where the loss between the model's prediction and the true outcome is some custom loss function $\ell(\hat{y}, y)$ Is there some theory of how the ...

Question 12

I have a question regarding training HMM and then applying it to new data: Is it possible to train a HMM with several time series as inputs? My point here is that it'd be convenient to have a ...

Question 13

Suppose that $\{X_t, t = 0, \pm1, \dots\}$ is a stationary process satisfying the equations $$X_t = \phi_1 X_{t-1} + \dots + \phi_p X_{t-p} + Z_t,$$ where $\{Z_t\} \sim \text{WN}(0, \sigma^2)$ and $...

Question 14

I'm analyzing a time series and estimating both the power spectrum exponent $ \beta $ and the Hurst exponent $ H $. According to the literature, these quantities are related by $ \beta = 2H - 1 $. ...

Question 15

In many books we can read that stock returns show no significant auto correlations. This can be easy verifyed by calculating Corr(r(t),r(t-d)). But there also AR models that claim there is auto ...

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Questions tagged [time-series]

Using Koopman Mode Decomposition: Are the Koopman Modes interpretable of relationships between system features?

Means to measure validity of long periodicities in time series

Any methods to find if a binary time series has seasonality OR NOT?

Why does Shumway & Stoffer use $a_k^2 + b_k^2$ to estimate $\sigma_k^2$ instead of $(a_k^2 + b_k^2) / 2$

Is $X^2$ scaling universal for residual spectra?

Does subtracting the mean from a time series generated from AR(1) model with drift make it stationary?

Generating and Interpreting the Allan Variance Sigma-Tau Diagram

Maximum of a Wiener process in discrete time

How Does Pearson’s coefficient Reveal Signals Derivatives?

Goodness-of-fit for i.i.d. null hypothesis against autocorrelated alternative

Time series with custom loss functions

Hidden Markov model (HMM) for multiple time series

Best linear predictor in an AR(p) process and relevance of Rao-Blackwellization

Connection Between Power Spectrum and Hurst Exponent [closed]

Understanding Auto Correlation and AR Model for Stock Returns

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