# Questions tagged [time-series]

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

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### Autocovariance and spectral density of time-varying Markov switching AR model [closed]

I want to know how to calculate the autocovariance and spectral density at frequency = 0 of time-varying Markov switching AR model, the model is described below Best, Wendy
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### Generating White Noise with rnorm() vs. arma.sim() in R [closed]

I’ve been working on generating white noise for a statistical task and found that the rnorm() function in R is a straightforward way to create it. Here’s a simple ...
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### Get relative excess risk do to interaction for DLNM [closed]

I'm working on quasi-poisson model combined with DLNM. My aim is to calculate relative excess risk do to interaction. However, I get error message when running crosspred function. Like below. What ...
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### Dealing with autocorrelation in GAMs with proportional response data and categorical predictors

I'm new to GAMs and am trying to figure out how to parameterize and interpret models where the response variable is percent of salmon migrating through a given route and I think there might be ...
1 vote
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### State Space Model with All Observed Factors

I have seen state space models implemented when we have latent/unobserved factors we want to uncover that jointly explain the dynamics of a time series of dependent variables. I have also seen state ...
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1 vote
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### AR(1) model predictions: Are the predictions shifted by one period?

I am estimating AR(1) one step ahead forecasts for the following data using the following code. The AR(1) predictions seem to perform quite well. However, they seem to be shifted by one period in to ...
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### Predicting financial asset returns using a vector autoregressive (VAR) model

I have trade data for 10 assets (assume stocks). The data is on 5-minute interval since 2007. A sample of the data rows and columns looks like this, where 'ivv', 'iwm', and 'xlf' are 3 of the 10 ...
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### How can I create latent classes in different cross-sectional data if certain variables are only present in one part of the cross-sectional data?

I have cross-sectional data from several years (6 in total). Only in two of these years 4 variables were queried. I would like to form latent classes on the basis of these and other socio-economic ...
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### Difficulties in tree-based learners for long-horizon / multiple time series forecasting

I'm currently building a massive (20000+ series) framework for forecasting and noticing a struggle when using XGBoost for long horizon (18 month) forecasting, as they are rough for detecting certain ...
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### multivariate time series forecasting

I have a dataset of 200,000 rows. Each row contains the song ID, the number of streams today (day_0), the number of streams yesterday (day_1), etc. up to the number of streams 21 days ago (day_21). My ...
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### Meaning of asymptotic in the context of stochastic process

So for a fractional Brownian motion, I define $k^{th}$ variation as $$S_n = \frac{1}{n}\sum_{i = 1}^{n}{|B_{H}(i\times\frac{T}{n}) - B_{H}((i - 1)\times\frac{T}{n})|^k}$$ where T is fixed and $B_H$ ...
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### R – Model specification for TWO TIME variables AND PAIRED design in repeated measures generalised linear mixed model (GLMM) (in lme4 package)?

This question has already been suggested to be reposted here from stackoverflow. I have a dataset similar to below: Fixed effects of interest Hour (4-level factor) Response (continuous) Treatment (2-...
1 vote
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I am estimating a VAR-model, which I then use for Monte Carlo simulations. However, for some of the variables there is a clear downward trend in the data which we don't want to include in our ...
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### How to deal with missing data when performing a BSTS analysis

Data Description I am using data from the Worldwide Governance Indicators (WGI), gathered by the World Bank. This dataset is a combination of multiple indicators from various sources, each with their ...
1 vote
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### What is the forecasting approach about "weird" data

I have a hourly time series dataset consists of 4000 rows and 3 columns (they are also my target columns). What im trying to do is using XGBoost to predict future. I've used ARIMA-SARIMA-ETS but to no ...
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### Predicting Target Variable in Time Series Data from Multiple Experiments Using Statistical Models

I am working on a project where I aim to predict a specific target variable using time series panel data collected from multiple experiments conducted on the same equipment. The challenge involves ...
1 vote
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### Long horizon recursive forecasting using XGBoost/Random Forest

I'm currently working on a large-scale time series framework at my job and encountering some frustration when it comes to XGBoost/Random Forest. The goal of this effort is to be able to forecast 18 ...
1 vote
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### Use latest data in training a timeseries model

I am training a global timeseries deep learning model. I have split the data for training, validation(to select the best hyperparameters), and test(to test on out of sample data). There are only 3 ...
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### What statistical test can I use? If any?

I'm currently investigating mortality rates in my local area compared to England. Mortality rates in my local area have always been higher than England however recently I've noticed a widening gap ...
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### Suggested techniques to model forward moving averages

I want to start a personal project, but i'm failing to formulate my business problem into a model. I would love inputs on how to better look into this issue and what type of models/techniques i should ...
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### Pls Help! AR(1) Covariance derivation query [closed]

Can someone pls explain to me why they can do this when deriving the autocovariance of AR(1) Why can they just add a $\phi$ in front of μ ? Shouldn't it be: $\phi y_{t-1} + \epsilon_t - \mu$ Much ...
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### Time Series Cross Validation by skicit learn and Cross Validation by Prophet

I have confusion between time series cross validation by skicit learn and cross validation by Prophet. So I'm trying to compare lstm algorithm with prophet and method The split data used for LSTM is ...
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### On assumptions of local projection method

It is well known that Jorda(2005) proposed the following model called local projection: $$y_{t+h} - y_{t-1} = \beta_h shock_{t} + \gamma_h ctr_{t-1} + \epsilon_{t,h}, h = 0,1,2,\dots,H.$$ I am trying ...
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### Gaussian Process Literature suggestion

I'm quite new to Gaussian Process and hope to get some help regarding the materials to read up on here. Suppose I have the following 2d time series data table: \begin{bmatrix}s_{t_1}^{v_1} & s_{...
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### Dickey Fuller test: confusion about the alternative hypothesis

I am rather confused about the alternative hypothesis of the Dickey-Fuller test (at least from a practical perspective). I understand the mathematical details behind the DF test, but I am struggling ...
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### How to Improve performance of deep learning timeseries forecasting model like LSTM? [duplicate]

I have historical data of 5 years (June 2019- June 2024). Data is in daily & csv file format. I have 4 features: Data, AQI, Raw Concentration, NowCast Concentration. I am trying to forecast only ...
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### Perfusion Analysis Counts as Survival Analysis?

In perfusion analysis, the patient is injected with some dose of medicine. A machine detects, over time, the dose of medicine in the patient's body. In other words, the data for each patient is time ...
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### Confused about the stationarity and unit root concepts

Say that I consider a white noise process, which by definition is stationary. I'm confused by the fact that if I use the Dickey-Fuller test, technically speaking I should fail to reject the null ...
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### How to correlate two variables together with lag

I am curious to know about measures of correlation for the frequency of an event against a continuous variable (I am aware this question is similar to this one). In this case, I've plotted my weight ...
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### Variance of the estimator of unconditional mean of AR(1) process

AR(1) process is defined as: $y_t=c+\phi y_{t-1}+\varepsilon_t$ where $\varepsilon_t$ is IID with mean zero and variance $\sigma^2<\infty$. For a stationary process, i.e. $\phi\ne 0$, the ...
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### Defining clinical follow-up: Fixed Period vs. Maximum Duration

We are retrospectively analyzing data of around 1100 patients operated between 2017 and 2023. We analyzed follow-up documentation until 2024. This means that patients operated at a later date will ...
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1 vote
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### Combine back- and forecast errors for cross-validation

Suppose I have a procedure to predict the timeseries value $Y_{t+k}$, where $t$ is the current period and $k \geq 1, 2, \dots$. Now, I want to estimate the procedure's out-of-sample performance. The ...
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### Dickey-Fuller Unit Root test, Deterministic Terms

I'm learning about unit root tests and i'm trying to implement these tests in python. I have some doubts about the theory underlying the deterministic terms inside the regression. Some textbooks ( ...
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