Questions tagged [time-series]
This tag is used for question related to time series models such as AR, ARMA, ARCH, GARCH and their properties and techniques used for inference.
980 questions
0 votes
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21 views
Optimal lags in neuralprophet model [closed]
I am using neuralprophet model in time series data having 2 columns( ds and y). ds is timestamp and y is numerical column. As I am using hyperparameter tuning , so how to select optimal n_lags value ...
-1 votes
0 answers
39 views
Finance: Expected Growth of a Company
I have recently started to dive into financial models, and the very first I encountered was the discounted cash flow analysis. In this model, there is a parameter called the expected growth of a ...
0 votes
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57 views
Using Koopman Mode Decomposition: Are the Koopman Modes interpretable of relationships between system features?
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 ...
0 votes
0 answers
15 views
Means to measure validity of long periodicities in time series
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 ...
0 votes
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43 views
Any methods to find if a binary time series has seasonality OR NOT?
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. ...
2 votes
0 answers
61 views
Why does Shumway & Stoffer use $a_k^2 + b_k^2$ to estimate $\sigma_k^2$ instead of $(a_k^2 + b_k^2) / 2$
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),...
1 vote
0 answers
64 views
Is $X^2$ scaling universal for residual spectra?
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 $...
1 vote
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41 views
Does subtracting the mean from a time series generated from AR(1) model with drift make it stationary?
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 ...
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40 views
Generating and Interpreting the Allan Variance Sigma-Tau Diagram
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 ...
1 vote
0 answers
79 views
Maximum of a Wiener process in discrete time
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) \...
0 votes
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33 views
How Does Pearson’s coefficient Reveal Signals Derivatives?
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 ...
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46 views
Goodness-of-fit for i.i.d. null hypothesis against autocorrelated alternative
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 ...
0 votes
0 answers
118 views
Time series with custom loss functions
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 ...
1 vote
1 answer
92 views
Hidden Markov model (HMM) for multiple time series
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 ...
1 vote
1 answer
110 views
Best linear predictor in an AR(p) process and relevance of Rao-Blackwellization
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 $...