Questions tagged [time-series]

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

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Link Anomaly Detection in Temporal Network

I came across this paper that uses link anomaly detection to predict trending topics, and I found it incredibly intriguing: The paper is "Discovering Emerging Topics in Social Streams via Link Anomaly ...
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1answer
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$ARIMA(p,d,q)+X_t$, Simulation over Forecasting period

I have time series data and I used an $ARIMA(p,d,q)+X_t$ as the model to fit the data. The $X_t$ is an indicator random variable that is either 0 (when I don’t see a rare event) or 1 (when I see the ...
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Getting started with bayesian structural models using MCMC

I'm trying to learn bayesian structural time series analysis. For a variety of reasons I need to use Python (mostly pymc3) not R so please do not suggest the ...
12
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937 views

Implementation of CoVaR (a systemic risk measure) in R

I'm trying to estimate CoVaR using bivariate DCC GARCH in R. The concept of CoVaR is the dependence adjusted of VaR, which was first introduced by Adrian and Brunnermeier (2011). However, this ...
10
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710 views

Picking block length in a block bootstrap

I am using the Mann-Kendall test to assess trends in a data time-series. I believe there is autocorrelation in my data and therefore need to use a block bootstrap to correct for it. I have plotted ...
10
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3answers
1k views

How to compare the accuracy of two different models using statistical significance

I am working on time series prediction. I have two data sets $D1=\{x_1, x_2,....x_n\}$ and $D2=\{x_n+1, x_n+2, x_n+3,...., x_n+k\}$. I have three prediction models: $M1, M2, M3$. All of those model ...
9
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615 views

Difference between Multivariate Time Series data and Panel Data

Recently I got mix response on the difference between multivariate time series data and panel data. I completely understand the difference between cross sectional data, time series data and panel data....
9
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608 views

Estimation of ARMA: state space vs. alternatives

I am interested in estimation of ARMA models. I understand that a popular approach is to write the model down in the state space form and then maximize the likelihood of the model using some ...
9
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198 views

What is tantile regression?

My question follows on this discussion of medials and tantiles vs medians and quantiles from earlier this year: When would we use tantiles and the medial, rather than quantiles and the median? As ...
8
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1answer
393 views

Markov Switching Forecast. How can I derive this?

Consider the autoregressive model, $\left[ \begin{array}{l} y^{\ast}_t\\ x_t^{\ast} \end{array} \right] = \left[ \begin{array}{l} a_{11}\\ a_{21} \end{array} \begin{array}{l} a_{12}\\ a_{...
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532 views

Clustering & Time Series

I have a multivariate dataset that changes over time. I have extracted (and normalised) some features and used k-means to generate clusters over the entire span of the dataset. Now I want to see ...
7
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449 views

Convolutional neural network for multi-variate time series?

I want to use CNN architectures for classification of multivariate time-series, where we apply one label to each sequence. I searched the net for the available designs in the literature and i found ...
7
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2answers
152 views

Is there a way to recover a temporal dependence structure in a time series from a regression against time?

Consider a time series: $X_1,X_2,...X_{n-1},X_n$ This series can also be written as a function of time $X(t)$, so that: $X_1,X_2,...X_{n-1},X_n = X(t_1),X(t_2),...X(t_{n-1}),X(t_n)$ Most ...
7
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127 views

Is autocorrelation not worth addressing with small N?

Consider a simple regression context in which there is a small set of response values, $Y$, and corresponding dates, $X$. (For simplicity, we can assume the dates are equally spaced.) We would like ...
7
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1answer
326 views

Nonstationary solutions for stationary ARMA equations

By "stationary" I mean "weakly stationary". Consider a "stationary" AR(1) equation: $$X_t=\varphi X_{t-1}+\varepsilon_t,$$ where $t\in\mathbb{Z}$ are discrete time moments, $\varepsilon_t$ a zero-...
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895 views

Forecasting time-series ahead by multiple time horizons

Suppose that I have daily data on the population of a small village, given by $Y(t)$, as well as daily data on various factors that are relevant to the size of the population in the future, given by ...
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Measure score change over time while accounting for baseline differences

I'd like to test for and estimate group differences in NIHSS (National Institute of Health Stroke Scale) change between hospital discharge and three months after hospital discharge. Because the score ...
6
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152 views

What guarantees the existence of a finite representation of the Wold decomposition? Mechanics and Intuition

Every covariance stationary process can be written as a linear, infinite distributed lag of white noise. In other words, every covariance stationary process has a Wold representation. Then we go on to ...
6
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1answer
820 views

forecast::auto.arima() is not returning a model with a differencing parameter when it should

I'm experiencing an issue in which it seems forecast::auto.arima() isn't returning a model with a differencing parameter when it should. Read through my reproducible example to arrive at the question. ...
6
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0answers
2k views

Which loss function to use when training LSTM for time series?

I'm experimenting with LSTM for time series prediction. The example I'm starting with uses mean squared error for training the network. I know that other time series forecasting tools use more "...
6
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4answers
1k views

Choice of time-series model for store sales prediction

I have a data set of weekly sales for a range of stores (all belonging to one company). I am trying to predict weekly/monthly use of several ingredients in the individual stores. The choice for what ...
6
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0answers
530 views

Should I use a seasonal arima or stl decomposition and model residuals only?

I have a basic question in time series modeling. (using r but the question is not particularly about r) For a time series with obvious seasonality, shall I use stl (Seasonal and Trend decomposition ...
6
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2k views

Stationary vs Stability

I am searching for an example of an unstable VAR($p$) process (its reverse characteristic polynomial has no roots inside and on the complex unit circle) which is stationary. I come up with this ...
6
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0answers
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Empirical Prediction interval for time series forecast based on quantile regression

As Gardner notes "almost all point forecasts are wrong", so prediction intervals (PI) are necessary to quantify uncertainty and help us make informed decisions. There exists theoretical PI, and in ...
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338 views

Empirical distribution function of overlapping time series data

If we model asset return volatility for periods of more than one (say more than one day) there is the square-root rule which holds true under some assumptions. On the other hand practitioners ...
6
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735 views

Fisher's test of periodicity

I have evenly sampled time series on which I applied Fourier transform. I am trying do determine if the signal contains statistically significant periodic components. I have succeeded with determining ...
6
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0answers
908 views

Better understanding of GARCH and ARCH models

I want to make a function that does GARCH and ARCH in python for calculating variance. But I only have a general understanding of the model. Are there any good papers that can be recommend to give me ...
6
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0answers
3k views

Time series clustering: Fourier transform and PCA

I have biological time series (9 years long) of the biomass of species which logically exhibit a seasonal pattern. I would like to cluster them into a few groups based on their typical seasonal ...
6
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107 views

How to form a confidence band around the trend fitted from time series data

I have a time series data set. I can decompose it and get the trend but I would like to put confidence ranges around the trend (past) not the forecast-ed component. The decompose function also doesn'...
6
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269 views

Forecasting a complex time series by splitting into subseries

I have finance data that I need to forecast out for 7 years. My data is generally debits and credits, and those are split into a number of sub-series which share common traits (e.g. similar ...
6
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782 views

Classification of multiple time series and case level attributes

I'm pretty new to machine learning so wondering whether someone can help check my thinking or point me in the right direction! I need to create a classifier which can predict an outcome for a person ...
6
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303 views

How to denoise a “Poissonous” time series

I have $N$ time series each of which can be modeled as $$y_{kt}=Ax_{kt}+b+\varepsilon_{kt}\quad(1\le k\le N,1\le t\le T),$$ where $x_{kt}\sim\text{Pois}(\lambda\Delta t)$ and $\varepsilon_{kt}\sim N(0,...
6
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1answer
131 views

Detecting changes in large number of time-series that share seasonality

I have large number of time-series that are independent of each other, but share some seasonality patterns. I need to detect anomalies/changes (increased volume, change in mean), that appear in the ...
6
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1answer
2k views

How run Random Forest when there is temporal structure in the data

I am used to data sets that dont have a time component. In In reading up on time series data i learned the importance of transforming the data into stationary data before applying the ARIMA model to ...
6
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1answer
694 views

How do I compare date-ranges from a time series?

I have a time series which contains monthly readings for air pollution in a city. The seasonality from this time series has been removed. Given two date ranges, for example Jan-Aug 2008 and Jan-Aug ...
5
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1answer
116 views

Time Series Regressor Selection

I am interest in a (multivariate) algorithm to identify relevant regressors (which are itself time series) to forecast a time series of interest. The question is worded in general terms because this ...
5
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1answer
79 views

Evaluating if time series need differencing

I am a total beginner with time series analysis. I use R. I understand that time series data need to be stationary for analyses like cross-correlation or modeling. I am, however, struggling with ...
5
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136 views

Is there a theoretical reason why simple models perform better than complex models on time series forecasting tasks?

Empirically, simple forecasting methods such as damped trend exponential smoothing, STL, or even random walks typically outperform more complex models such as higher order ARIMA models or ML based ...
5
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626 views

Time Series forecasting with Gaussian Processes

I am trying to forecast various time-series with Gaussian Processes, using the functional approach like in the Mauna Loa example in section 5.4.3 of "Gaussian Processes for Machine Learning". (X = ...
5
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389 views

Multitask Gaussian Process on multiple multivariate time series

I am in the process of working with multitask gaussian processes (the ones introduced by Bonilla et al in this paper). I am now interested in applying the MGP to multiple multivariate time series. ...
5
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1answer
305 views

How does Canonical Time Warping help in time alignment?

Canonical Time Warping is a state-of-the-art technique for time alignment. According to the original paper, it helps account for individual varieties when aligning sequences derived from different ...
5
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177 views

Linear regression with overlapping observations

Suppose we're doing univariate linear regression between X and Y. Let's say X are daily observations, and Y reflects how some variable changes 1 year into the future. So Y observations will be ...
5
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0answers
1k views

Hierarchical time-series forecasting with complex aggregation constraints

I'm trying to forecast multiple time-series with a hierarchical structure using the hts package by prof. Hyndman. However, the aggregation constraints are not sums ...
5
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1answer
2k views

Using Rolling Forecast Origin Resampling in R for Neural Network Time Series

I am new to time series prediction and forecasting with neural networks and am having trouble with cross validation. I am fitting a multivariate time series. I have 236 monthly observations. I am ...
5
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1answer
465 views

What is the difference between ARMA+Fourier and TBATS model?

I am just wondering that, in terms of the multi-seasonal time series forecast, what is the difference between using auto.arima find the ARMA order, then fit ...
5
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0answers
2k views

Is it possible to do a time series analysis with more than one explanatory variable?

I am working on a project, and I am absolutely new to forecasting and not so strong in statistics. I have an employee data for the last 7 years, along with the other variables like economic growth, ...
5
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0answers
708 views

Seasonally adjusted data used in time series forecasting

I am looking at two time series, from 01/01/2000 to the present: The ISM Manufacturing: New Orders Index, only available seasonally adjusted The manufacturing industry unemployment rate, only ...
5
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0answers
397 views

Ideal statistical or machine learning technique to model highly cross-correlated data

I'm trying to build a model that can predict streamflow for an alpine (snowmelt-fed) watershed using snow albedo (roughly, the energy reflectance of the snow) data. Albedo controls the melt of the ...
5
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0answers
632 views

Seasonal Kendall test and the Mann-Kendall test

I am trying to detect trends using non-parametric methods but I'm a little confused as to when you should apply the Seasonal Kendall test. Don't get me wrong I know you apply it when you have ...
5
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1answer
1k views

ARIMA, adjustments and intervention analysis

I have very little knowledge of time-series analysis (despite my stat master - didn't do anything else than an introductory course) but now I'm facing a statistical problem whose answer is this very ...