# 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.

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### Estimating the current reliability of a flawed detector

I have a detector that tries to evaluate if a given measurement in our system indicated urgent intervention is required. I have quite a bit of historical data. This can tell me the historical ...
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### How to find the current time when a vinyl is dragged up

I am trying to create a DJ Mixer, i have this so far: When the mouse moves up how do i calculate the new current time of the vinyl rewinding. This is my code so far: ...
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### Show that a certain stochastic process is not linear

Let $Y=(Y_t)_{t \in \mathbb Z}$ be a stochastic process defined on $(\Omega, \mathcal{F}, P)$. We say that $Y$ is a linear process if: \begin{equation}\label{I}\tag{I} Y_t = \sum_{j=0}^\infty \psi_j \...
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### How to determine numerically that a fluctuating curve (which depends on random variables) is stationary, i.e. has no upward or downward tendency?

I need to determine if and when curves like the following are stationary: My idea so far is to perform linear fits in different parts of the curve (see example) When the modulus of the slope of a ...
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### Testing predictability of a predictor of expected weekely returns on the stock market

say I have a T daily observations for the last ten years on a new predictor $x_t$ which I think is a predictor of the expected weekly return on the stock market, $r_{t,t+5} = r_{t+1}+...+r_{t+5}$, ...
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### Inequality involving changing order of limits and probability

I read this paper, in Corollary 1 the author claims that $$\underset{\pi \in [0, 1]}{\sup}\ W_T(\pi) \overset{p}{\to} \infty$$ as $T \to \infty$. Where $W_T(\pi)$ is Wald statistics but I think it ...
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### What is the definition of "periodicity of the data"?

I'm reading a research paper where it says. Here $m$ is the periodicity of the data (e.g., 12 for monthly series). I understand: There are twelve months in a year. So I suspect periodicity relates to ...
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### Can you use combinatorics to determine the average time needed for something?

So im building an graffitiprinter and I use a matrix so could it be possible if I know the time of one spray to calculate the avarege time to complete a picture. If I also knew the total amoents of ...
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1 vote
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### Is the product of independent white noise also white noise?

Assume that the random vector $(u_t, v_t)$ is sampled iid over time and that $E[u_t v_t] = 0$. We also assume that $E[u_t] = E[v_t] = 0$ and that $E[u_t^2] = \sigma^2_u$, $E[v_t^2] = \sigma^2_v$. ...
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### Comparing sample mean of a month X to the distribution of points during month X last year

Let's say $M$ is a metric of interest in the context of time series. We are interested to see if the average $A$ of $M$ computed during month $M$ this year makes sense.I had many ideas: compare $A$ ...
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1 vote
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### Why do the bivariate vectors $(X_t, X_s)$ and $(X_s, X_t)$ from strictly stationary $X_t$ not have the same distribution?

from homework I got some weeks ago, we were asked if the bivariate vectors of $(X_t, X_s)$ and $(X_s, X_t)$ from strictly stationary Time Series$X_t$ do not have the same distribution. I thought they ...
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### Fourier transform of time series by diagonalising matrix

Does there exist a case where the Fourier transform of a time series is found via diagonalising a matrix? Ideally, I am looking for cases where the eigenvalues correspond to frequencies. Any leads are ...
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### How to determine whether a reduced-form VAR is covariance-stationary or not?

I know how to determine whether a vector is covariance-stationary or not but I do not know how to determine whether a reduced-form VAR is stationary or not. For example, the expression is shown below, ...
1 vote
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### What is the limit of autocorrelation of ARIMA(1,1,0) series

Consider the causal AR(1) time-series $y_t = \phi y_{t-1} + w_t$ such that $x_{t} - x_{t-1} = y_t$. I want to compute the limit $\lim_{t \to \infty} corr(x_t, x_{2t})$. It is easy so see that the ACF ...
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### How to plot autocorrelation vs time instead of autocorrelation vs number of lags?

If I consider a stochastic process given by the monthly sunspots and I calculate the autocorrelation by using this Python code: ...
1 vote
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### Autoregressive Time Series in Continuous Time?

I have seen that AR(1) process in discrete time corresponds to Ornstein–Uhlenbeck process in continuous time, is there a general analog of AR(n) process in continuous time?
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### Finding drops in timeseries - excluding spikes

I am trying to find drops that do not happen after spikes in a time series. This needs to be done without code (the platform supports min and max though). I can detect drops already using this ...
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### Calculating rates of change of a curves on a graph in a time interval

I have a situation where I have continuous glucose response measurements and I would like to know the rate of change of the curve once it begins to change (i.e., how fast glucose rises and falls). AUC ...
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Not being a mathematician, I still need to understand this equation. I apologise in advance for the possibly trivial nature of this question. Here is the equation:  \mathbf t_i = (t_{i, 1}, \ldots, ...