Questions tagged [time-series]

Time series are data observed over time (either in continuous time or at discrete time periods).

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Temporary shock in VAR system

I hava the following bivariate VAR system $$z_t=a_{11} z_{t-1} + a_{12} v_{t-1} + b_{11} z_{t-2} + b_{12} v_{t-2}+u_{zt}$$ $$v_t=\gamma z_t + a_{21} z_{t-1} + a_{22} v_{t-1} + b_{21} z_{t-2} + b_{22} ...
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Compare the predictive capacity of multivariate models

I want to compare the prediction capacity of multivariate models (MGARCH, VAR, SVAR, VECM...). One option to do this is by comparing its error metrics: the mean square error or any other between the ...
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Time series data transformation for prophet model

I have a time series data that looks as follows The data has the following frequency distribution Here is the Q-Q plot It looks like the data is exponentially distributed. My assumption is that the ...
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How to obtain mean of a non-stationary, anti-correlated timeseres?

I have a velocity timeseries which is not stationary (Fig. 1). In other words, it is subject to trends and/or seasonality. I would like to report a mean velocity for this timeseries. A common way to ...
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Variance of a Straight line model [time series with deterministic mean]

I have been given the question - Consider the linear trend model: 𝑌𝑡 = 𝛽0 + 𝛽1𝑡 + 𝑒𝑡 + 0.5𝑒𝑡−1. You can assume 𝛽0=10, 𝛽1=0.2 and 𝜎𝑒^2=1. Find Var(𝑌𝑡). I tried solving this question by ...
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Measuring events in sales time series

I am trying to measure the effect of an event on some sales data. An event might be turning on a new payment method for customers, or a discount coupon promotion. Does it make sense to try a time ...
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Estimating of PD based on another model

my problem might not be easily solvable, but I am looking for some advices/ ideas as well. I have few bank segments(Corporate, SME, Retail) in which I estimate the probability of default based on some ...
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Studying inflation on my groceries, how to correctly show the increase of prices?

I have price data from the last two years from my online groceries purchases on an online supermarket for all the products I bought. I want to study the increase of prices for the products that I ...
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Input size vs hidden state in RNNs

Im using PyTorch to implement RNNs on univariate time series data. This is the documentation for the RNN class: link I think I'm understanding the math behind an RNN cell. But I have an specific ...
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Cycle detection on unsupervised time series data

i have some video data of production lines of some manufactories. In every video, an operator does the same 3-4 steps periodically for the entire video. Each periods of same steps is called cycle and ...
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How to check whether Yt is covariance stationary when A and B are random variables but not constants?

Suppose Suppose A and B are random variables that are independent of Xt. What are the steps to check whether {Yt} is covariance stationary?
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Estimate an ARMA disturbance model from measurement output data

Assume that we have a first order dynamical system $$G(s) = \frac{1}{0.2s + 2.1}$$ I run this with an input $u = 10sin(t)$ and with gaussian noise. ...
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How to train a Deep Neural Network to predict conditional probability distribution?

I am working with non-stationary time series data sampled at 128 Hz. I have segmented the entire time series into 1-second segments, meaning now I have a bunch of vectors, say $x_i$, where i = 1,2,3,.....
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Estimating input demand elasticities with time series data pooling

I want to find input demand elasticities of Labor, seed, agro-chemicals and fertilizer of 5 vegetables. Time series data are available from 1991-2019 for each crop for two growing seasons. When I'm ...
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How to calculate variance of AR(1) process

I have a stationary AR(1) process: $Z_t = \alpha_{1}Z_{t-1} + \nu_{t}$, where $\nu_t$ is white noise and $|\alpha_1| < 1$. I have to show that the variance of $\Delta Z_t$ is $$V[\Delta Z_t] = 2\...
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How to specify a VAR model in R with non-stationary, stationary, and trend-stationary variables?

I have a multivariate time series and I want to estimate a VAR model. I tested for unit roots with the ADF and KPSS test and concluded that some variables are non-stationary, while others are ...
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Can anyone provide me with reference to some lecture notes or an online lecture on Multiplicative Error Models?

As the title says, I am looking for some lecture notes or an online class going over Multiplicative Error Models. I have found a number of academic papers on the topic, but I am having trouble ...
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Border values at which timeseries decrease and increase

I have a timeseries data of signals in stock market ([-1, 1]) and I want to find mean values at which I have down trend and upwards trend. I already used Moving ...
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Testing the impact of a events on time series

Context I'm working with product data for a retail company. I have the daily impressions (number of times it was viewed online) for all products over a 30 day period (can get more data). Here is the ...
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Is this data time series or panel

I am working with a dataset of an online institution that is registered in one country, but has customers from across the world. I am working with a sample period of 5 months in 2022. I am unable to ...
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covariance matrix of any ARMA(p,q)

Assume I have an ARMA(p,q) weakly stationary process with the error term $\epsilon_{w}$ such that $\epsilon \sim WN(0,\sigma^2_w)$, can either be gaussian or non-gaussian. The covariance matrix,$M$ is ...
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Lagged regression with more than one predictor time-series

I have n + 1 different discrete time series. One of them is {Yt}, which I call ‘response time series’, and the other n are {Xt,i} (i = 1,…,n) which I call predictor series. I define n time lag ...
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Incorporate partial information about Y into predictions

I have a linear regression model predicting exports of toys from the United States on an annual basis. This initial model is based on a few factors: toy companies' demand projections, toy production ...
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Resampling a timeseries

I have a list of stock returns (say computed from the historical data) and would like to resample the historical return distribution. Naively doing bootstrapping means the samples are iid. I'm ...
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Shifting timeseries

See my timeseries below: Is there an easy way to detect if my timeseries keeps shifting between two y-values. In the figure this is for around -100 and -600. This especially occurs after the year ...
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Minimizing an objective function with input variables from a correlated error term

I've been reading into how to minimize objective functions and I am curious about the following, I have a model $y=X \beta +\epsilon$ where $E[\epsilon|X]=0$ and $Var[\epsilon|X]=\Sigma$ where $\Sigma$...
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Update to Box and Jenkins Air Passenger data? [closed]

A textbook example of a time series is the Box and Jenkins Air Passenger data. In R you can get it with the command data(AirPassengers). It has the number of ...
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Sum of $I(1)$ and WN

Is the process $\Delta Y$ an MA(1)? $Y_{t} = X_{t} + w_{t}$ with $X_{t} = X_{t-1} + e_{t}$ and $e_t$, $w_t$ both independent white noise a MA(1) process? What I did is the following: $(1-L)X_{t} = e_{...
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GARCH and need (or lack there of) for weak-stationarity of underlying data

For most applied examples I see they fit GARCH models directly to time series datasets with no underlying tests of stationarity beforehand. For example, a GARCH(1,1) has the assumption that the ...
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Do I need stationary time series data for Isolation Forest Model?

I am trying to predict anomalies using an isolation forest model with daily time series data. Do I need to make sure my data is stationary as I have observed weekly seasonality? I read that you need ...
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Is it OK to use multiple one-way ANOVA over a time course?

Dear CrossValidated community, I have time series data were the treatment decrease the visible tissue of the sample. I want to find the separation point between control and treatment curves. Initially ...
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Simulating multivariate time series with seasonality

Let's say I have a seasonal multivariate time series xyz with seasonal order 12: ...
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Time Series models vs Continuous time stochastic processes

By time series models, I mean typical frameworks like Box-Jenkins that are recommended in introductory forecasting books. When should one opt to model time-ordered data using the Box-Jenkins framework ...
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Is the Dickey Fuller test one-sided or two-sided?

The Dickey Fuller test tests whether a unit root is present in an AR model. Specifically, we have $$ X_t = \phi X_{t-1} + \varepsilon_t $$ where $\varepsilon_t$ is a Gaussian noise term. Now the ...
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Logistic regression(with Markov chain) on time series data?

I'm working with a biotech device's time series data to predict the replacement amount. The background is the battery of the device will die after the implant for a few years, and the battery will be ...
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What exactly does the Box-Cox transformation do to a time series?

If I were to try and rephrase the argument in the original Box-Cox paper in my own words, I would say something like the following: given a model $$ y = x \beta , $$ if the residuals do not appear to ...
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PCA on a matrix to produce a sequence

My dataset is organized as matrix with 6 variables (Each matrix shows a specific type of fault). I want to convert it to a sequence by applying PCA on matrix and choose the first principle component (...
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AR(1) Process and Infinite Geometric Series

I'm doing an assignment and I've been told that ln(real consumption) has a unit root and is an I(1) process and that real consumption is given by: I've also been told that: Part A I need to derive ...
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How can I predict a 2D array over time?

I've got a rectangular region that's composed of 1024 grid cells (32x32 cells). Each of these cells has an associated value, which then builds me a 2D array. For that 2D array, I've got 8 samples (...
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Deriving ADF unit root test form for the time series with quadratic deterministic trend

I have the following time series process $y_t $ $$\Delta y_t = \delta + \gamma t + \epsilon_t$$ where $e_t$ is white noise process with the variance of $\sigma^2$. I guess that whereas $\Delta y_t$ is ...
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Data Analysis for a Time Series Clinical Trial Dataset

I have a Clinical Trial dataset where, I have the values of Blood haemoglobin level for 40 patients for 6 weeks, after a particular treatment. For drawing some meaningful insights from this data set, ...
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Principle Component Analysis for Feature extraction from Voltage and Current Signals

I am doing research work on fault classification in power transmission lines. I generated fault datasets in MATLAB/Simulink and collected it in matrix format with 6 various i.e. 6 variables in 6 ...
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Unit root testing in AR(2) simulated data

I'm teaching a course in time series analysis, and using a lot of R simulation. I've come across the following situation. Consider an AR(2) process with $x_t = x_{t-1} - x_{t-2}+w_t$ where $w_t$ is ...
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Creating synthetic data for time series, Hidden Markov Model

Suppose that I have a task of classifying a time series. I decide to use Hidden Markov Model $\lambda(A, B, \pi)$, where $A$ is a transition matrix, $B$ is an emission probability, $\pi$ is an initial ...
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Interpret the conditional Sigma (vs Realized Absolute Returns) from DCC [duplicate]

I have estimated the DCC model and then plotted the model. Can someone help me understand how can I interpret the Conditional Sigma (vs Realized Absolute Returns) of the DCC model? ...
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Approaches for running separate monthly regressions on a time series

I have a time series with daily granularity. The time series under consideration depends on an independent variable x (say). In order to account for seasonality effects - I run a separate regression ...
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Interpret the Conditional Sigma (vs Realized Absolute Returns) of the DCC model

I have estimated a DCC model and now I have plot the dcc.fit of the model and now I would like to know if someone can help me to interpret this graph as I am new to ...
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Selecting AR($p$) order using cross-validation

I am playing around with some simulations to see if it is possible to select the order of an AR($p$) process using cross-validation. I simulate a number of observations of AR($2$) using ...
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Computing ``average'' PAC with panel data

How can a single partial autocorrelation function be computed when the dataset has a panel structure? Assuming that every ID follows the same data-generating process. One idea is to use only linear ...
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Applying Bayes Theorem to combine probability mass functions of time series changes

I apologize. I'm not well trained in formal statistics, so feel free to gently correct my terminology and methods. For a univariate continuous real-valued time series X, I've calculated probability ...
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