Questions tagged [time-series]

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

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Best method for short time-series

I have a question related to modeling short time-series. It is not a question if to model them, but how. What method would you recommend for modeling (very) short time-series (say of length $T \leq 20$...
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Using k-fold cross-validation for time-series model selection

Question: I want to be sure of something, is the use of k-fold cross-validation with time series is straightforward, or does one need to pay special attention before using it? Background: I'm ...
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Books for self-studying time series analysis?

I started by Time Series Analysis by Hamilton, but I am lost hopelessly. This book is really too theoretical for me to learn by myself. Does anybody have a recommendation for a textbook on time ...
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Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey

I am used to seeing Ljung-Box test used quite frequently for testing autocorrelation in raw data or in model residuals. I had nearly forgotten that there is another test for autocorrelation, namely, ...
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Simple algorithm for online outlier detection of a generic time series

I am working with a large amount of time series. These time series are basically network measurements coming every 10 minutes, and some of them are periodic (i.e. the bandwidth), while some other aren'...
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How do I write a mathematical equation for ARIMA (2,1,0) x (0,2,2) period 12

I would appreciate if someone could help me write the mathematical equation for the seasonal ARIMA (2,1,0) x (0,2,2) period 12. I'm a little confused with how to go about this. I would prefer an ...
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Period detection of a generic time series

This post is the continuation of another post related to a generic method for outlier detection in time series. Basically, at this point I'm interested in a robust way to discover the periodicity/...
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What method can be used to detect seasonality in data?

I want to detect seasonality in data that I receive. There are some methods that I have found like the seasonal subseries plot and the autocorrelation plot but the thing is I don't understand how to ...
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Dynamic Time Warping Clustering

What would be the approach to use Dynamic Time Warping (DTW) to perform clustering of time series? I have read about DTW as a way to find similarity between two time series, while they could be ...
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Transfer function in forecasting models - interpretation

I am occupied with ARIMA modelling augmented with exogenous variables for promotional modelling purposes and i have hard time explaining it to business users. In some cases software packages end up ...
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Interpretation of mean absolute scaled error (MASE)

Mean absolute scaled error (MASE) is a measure of forecast accuracy proposed by Koehler & Hyndman (2006). $$MASE=\frac{MAE}{MAE_{in-sample, \, naive}}$$ where $MAE$ is the mean absolute error ...
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Moving-average model error terms

This is a basic question on Box-Jenkins MA models. As I understand, an MA model is basically a linear regression of time-series values $Y$ against previous error terms $e_t,..., e_{t-n}$. That is, the ...
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What is the long run variance?

How is long run variance in the realm of time series analysis defined? I understand it is utilized in the case there is a correlation structure in the data. So our stochastic process would not be a ...
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Endogeneity in forecasting

I know that omitted variable bias isn't a major problem in forecasting, but are other endogeneity issues (such as simultaneity or measurement error) going to be a problem if I am only interested in ...
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Resources/books for project on forecasting models

My professor suggested a comparison of various forecasting models as a topic for my semester project. Given that my only experience in statistics is the intro course in probability and statistics ...
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What is wrong with extrapolation?

I remember sitting in stats courses as an undergrad hearing about why extrapolation was a bad idea. Furthermore, there are a variety of sources online which comment on this. There's also a mention of ...
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Data has two trends; how to extract independent trendlines?

I have a set of data that is not ordered in any particular way but when plotted clearly has two distinct trends. A simple linear regression would not really be adequate here because of the clear ...
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Estimating same model over multiple time series

I have a novice background in time series (some ARIMA estimation/forecasting) and am facing a problem I don't fully understand. Any help would be greatly appreciated. I am analyzing multiple time ...
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Are explosive AR(MA) processes stationary?

According to Theorem 8.8 in Time Series by A.W. van der Vaart, an ARMA process $$\phi (L)X_t=\theta(L)\epsilon_t$$ has a unique stationary solution $X_t=\psi(L)\epsilon_t$ with $\psi=\theta/\phi$ ...
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How is the augmented Dickey–Fuller test (ADF) table of critical values calculated?

Could you please explain in simple terms how the table of critical values for the augmented Dickey–Fuller (ADF) test is created?
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Is there any standard / criteria of good forecast measured by SMAPE and MASE?

I have built a forecasting model for a company. Since it is dedicated to practical usage, I prefer to use the relative error parameter (like MAPE, SMAPE, & MASE) as a measurement for my model ...
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What is the difference between a stationary test and a unit root test?

What is the difference between the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test and the augmented Dickey-Fuller (ADF) test? Are they testing the same thing? Or do we need to use them in different ...
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Seeking certain type of ARIMA explanation

This may be hard to find, but I'd like to read a well-explained ARIMA example that uses minimal math extends the discussion beyond building a model into using that model to forecast specific cases ...
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Is it possible to automate time series forecasting?

I would like to build an algorithm that would be able to analyze any time series and "automatically" choose the best traditional/statiscal forecasting method (and its parameters) for the analyzed time ...
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How do you do bootstrapping with time series data?

I recently learned about using bootstrapping techniques to calculate standard errors and confidence intervals for estimators. What I learned was that if the data is IID, you can treat the sample data ...
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Detecting Outliers in Time Series (LS/AO/TC) using tsoutliers package in R. How to represent outliers in equation format?

Comments: Firstly I would like to say a big thank you to the author of the new tsoutliers package which implements Chen and Liu's time series outlier detection which was published in the Journal of ...
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Can PCA be applied for time series data?

I understand that Principal Component Analysis (PCA) can be applied basically for cross sectional data. Can PCA be used for time series data effectively by specifying year as time series variable and ...
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AIC versus cross validation in time series: the small sample case

I am interested in model selection in a time series setting. For concreteness, suppose I want to select an ARMA model from a pool of ARMA models with different lag orders. The ultimate intent is ...
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Does it make sense to use a date variable in a regression?

I'm not used to using variables in the date format in R. I'm just wondering if it is possible to add a date variable as an explanatory variable in a linear regression model. If it's possible, how can ...
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Cross-validation techniques for time series data

What is an appropriate cross-validation technique for time series data? I have a daily 4 years time series data and fitting a SVM model by MATLAB R2015b: ...
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How do I write a mathematical equation for ARIMA (0,2,1) x (0,0,1) period 12 [duplicate]

I would appreciate if someone could help me write the mathematical equation for the seasonal ARIMA (0,2,1) x (0,0,1) period 12. I'm a little confused with how to go about this. I would prefer an ...
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Why does a time series have to be stationary?

Would like to understand primary reasons for making a data stationary? I understand that a stationary time series is one whose mean and variance is constant over time. Can someone please explain why ...
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Regularization for ARIMA models

I am aware of LASSO, ridge and elastic-net type of regularization in linear regression models. Question: Can this (or a similar) kind of penalized estimation be applied to ARIMA modelling (with a non-...
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stochastic vs deterministic trend/seasonality in time series forecasting

I have moderate background in time series forecasting. I have looked at several forecasting books, and I don't see the following questions addressed in any of them. I have two questions: How would I ...
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Binary time series

I have a binary time series: We have 2160 data (0=didn't happen, 1=happened) for one-hour period in 90 days. I want to forecast after these 90 days, where the next 1 will happen, and also Extend ...
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What are the assumptions for applying a quantile regression model?

The question has been asked (one time) on CV before, but the answer is really imprecise and does not really answer the question in my opinion. So: What are the assumptions for estimating a linear ...
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