# Tagged Questions

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

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What is the intuition behind the finite sample adjustments in the Ljung-Box test: $Q = n\left(n+2\right)\sum_{k=1}^h\frac{\hat{\rho}^2_k}{n-k}$ Degrees of freedom adjustments usually involve ...
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### Improve fit by trend adjustment

I have data of daily observations for 35 years and I have modeled data for the same period. The coefficient of determination ($R^2$) between them is zero (no correlation at all!). I want to correct ...
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### How to do regression on a time series by learning from historical time series?

I have the following question: I have a data set of customer purchases from day their registration to 120 days. However, some new customers do not have 120 days yet, so that I want to predict how ...
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### What does “performing PCA on a timeseries” mean/do?

Yes, I already looked here but that's too high profile for my humble mind (and it's not exactly what I'm looking for). Imagine we have a timecourse with time on the x-axis and some value on the y-...
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### Interpreting coefficients that have been log transformed in a time-series

Let me apologize in advance for any lacking information or apparent cluelessness in the question, however I am by no means knowledgeable on the topic. Through unfortunate circumstances I find myself ...
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### Approaching a time series before building a predictive model

I have a big task at hand - building a predictive model that predicts the amount of fires in a certain region of a certain city tomorrow based on historical data. Currently the problem was narrowed ...
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### Testing whether a seasonal dip in a time series this year is abnormal compared to previous years

Let's say I have sales data for each month of the year for the last few years. Sales tend to dip in the summer, and I want to determine if the dip this year (or for a given month) is abnormal. ...
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### How to choose between plain vanilla RNN and LSTM RNN when modelling a time series?

What are the criteria used to choose between plain vanilla RNN and LSTM RNN when you have to model a generic time series?
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### Seasonal and autocorrelated regression residuals: difference raw data or residuals?

I have a multiple linear model for time series data for which the regression residuals are autocorrelated and display seasonal behavior. This seasonal behavior is induced deterministically by a cyclic ...
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### Explanation of what Nate Silver said about loess

In a question I asked recently, I was told that it was a big "no-no" to extrapolate with loess. But, in Nate Silver's most recent article on FiveThirtyEight.com he discussed using loess for making ...
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### Choosing regressors for inclusion in regression with ARMA errors

I would like to conduct a forecast based on a time series ARIMA-model with multiple exogenous variables. My time series is monthly unemployment data (in percentage) during several years and my ...
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### Ljung-Box statistic doesn't match to acf of ARIMAX

I'm afraid I basically missunderstand something in Ljung-Box-Pierce test. I actually estimate a ARMAX model with $y$ as seasonal responsevaribale with periodicity in lag 144, and ARMA(3,1)-process ...
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### periodogram, paired eigenvectors, scatterplot

I am reading up on spectrum analysis and am confused about the following terms (I have included the relevant language of different sources in brackets to further clarify the terms) Scatterplots of ...
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### Deciding the value of period in seasonal ARIMA (R)

I'm new to time series modeling and am trying to do seasonal ARIMA modeling here. I have figured out the p,d,q values but im not sure how to select the period in the below formula. There seem to be ...
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### How to aggregate data by the hour [on hold]

How could I get the hourly means of multiple columns of data? I have a large amount of trades data that is given by date/hour, and I would like to be able to get the hourly price & hourly trading ...
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### Double exponential smoothing alternative?

I am testing double EWMA smoothing on a time series of financial data to attempt to forecast the next point, xt+1 at time t. The original method I used (from wikipedia) is below: for t = 1 : s1 = x1 ...
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### Neglected nonlinearity in a VAR model

What happens if I estimate a simple linear VAR model and the data generating process is nonlinear? Do I get inconsistent estimates?
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### Weighted moving average for physiological data

I have a set of data representing a number of months. The x value is time. I want to compress this data into a single day, such that the x value becomes the hour of day for the y value. An hour = 1.0 ...
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### Inconsistent validation results (CARET and DNN)

G'day, I have a R script below which I run twice. ...
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### Multivariate time series clustering

I am collecting a group of multivariate time sequences. For example, there are 2000 time series. Each time series is of 12 dimensions. Are there any systematic models/algorithms that can cluster ...
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### ARIMA + day dummy model [on hold]

I am trying to fit an ARIMA model with weekdays dummy. I have managed to fit the model using the following commands in R: ...
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### Time Series Prediction using Machine Learning

I am trying to predict the request arrive time of some objects in network traffic. I have few features of the object like their type, size, previous arrival time, etc. So I was think that I should use ...
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### I'm using R to create a time series - having some difficulty understanding frequency

I'm working with a dataset of electrical submeter readings taken once per minute for 47 months. I'm trying to create a time series that covers meter readings from the kitchen during the week of ...
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### Time series object for hourly datat with daily seasonal in R

I have got hourly data from 2012.01.01 to 2016.06.13 and the data shows daily seasonal. I am trying to create a time series object with only daily seasonal in R. ...
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### What are periodic version of splines?

In this What's wrong to fit periodic data with polynomials? post, I tried to use Fourier basis expansion and Polynomial basis expansion to fit a toy periodic data (daily temperature data set). I ...
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### Stationarity of a variable measured at irregular intervals

I have data collected on a meeting-by-meeting basis, where the change in time between two meetings is not constant, i.e., $\Delta t\ne1$. Are ordinary Augmented Dicky Fuller and Phillips-Perron tests ...
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### How to handle multiple seasonality in ARIMAX model?

x and y are two multiple seasonal time series and I want to check if the argument x has got influence on y. Both time series have the same multiple periodicity. I've read in some comments on the blog ...
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### Periodic splines to fit periodic data

In a comment to this question, user @whuber cited the possibility of using a periodic version of splines to fit periodic data. I would like to know more about this method, in particular the equations ...
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### Time interval prediction

I want to predict a specific time interval(ex. patient processing time in clnic) with some boolean value like whether this patient has cough or whether he/she has certain disease. I have tried using ...
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### Selection criteria select 0 lags for a VAR model

I am selecting the number of lags for a VAR model. Selection criteria and the LR statistic suggest 0 lags. Should I simply drop the VAR altogether, even if this goes against my intuition?
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### What is the difference between VAR, Dynamic Regressive, and ARMAX models?

All of these models seem to be used in predicting an endogenous time series variable, using several lagged exogenous time series variables. If it is so, how do we decide when to use which?
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### ARMAX or Dynamic Regression | regression of multiple timeseries

I have the following time series dataset (dependent | independent) : Sales | Income,Inflation, Interest Rates etc All of this is dynamic data pertaining to each ...
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### How to compare the variance of two time series?

I would like to answer whether two time series have the same variance. Initially, I used an F test to compare the two series variation. However, the two series appear to be skewed which would violate ...
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### Regression + Time series

I have time series data about sales/day, but i also want to include other data (static/dynamic) to forecast the time series. Is it possible to combine ARIMA model and regression models to achieve the ...
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### Diebold Mariano test (in R)

As I asked in my answer to this question: does anyone know if the DM test (in R in this case) is supposed to be made with h=h-1? If not, am I supposed to make several prediction sets (with h ...
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### measure the inter-relationship among a set of multi-variate data points

Given a group of multivariate data points, are there any ways to formalize/quantify the relationship of one given point comparing to other data points in this group. Clustering maybe one approach. But ...
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### When using a limited data set, how can I use excel to forecast future values?

To preface, I am a statistics novice, but I am faced with a problem that I cannot seem to be able to satisfactorily resolve. The problem is as follows: I am working to forecast future sales for one ...
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### Required sample size and degrees of freedom for a VAR

I have read in many textbooks that as the ratio between the number of coefficients to be estimated in a VAR and the number of time periods increases above a certain threshold, estimation becomes ...
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### Covariance matrix of the initial state vector. KFAS package

Any given ARIMA(p,d,q) model $y^*_t=\sum_{i=1}^pa_iy^*_{t-i}+e_t+\sum_{i=1}^qb_ie_{t-i}$,where $y^*_t=\Delta_dy_t$ - the difference of d$^{th}$ order, can be re-written as a dynamic linear model in ...
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### Test for significance of variation in time series data

Suppose a DMV office runs driving tests. Every week a number of people take the driving test, some pass and some fail. Looking at this data set, we notice that the pass rate varies from week to week. ...
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### Regression or time series model to predict trend

DATA I have the following data at hand: data about internet usage, per hour, per user, per part of the day (morning, afternoon, evening); the category of websites visited and their duration; ...
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### How can one create a time series object with multiple time series? [migrated]

How can I convert "A. Raw data" into "B. Time Series Objects" in R so I can perform time series analysis on multiple time series at a time? Please see to sample outputs below. A. Raw data month ...
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### Factoring out the effects of time in a predictive model

I have an ensemble model with a large number of independent variables, and one of those independent variables is time. The data was not generated/measured at regular intervals. There appears to be a ...
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### Detailed reference to facilitate manual implementation of ARIMAX

ARIMAX is implemented in SAS and R (function arimax in "TSA" package). I want to implement ARIMAX in an open source library in Scala and Python. Is there any ...
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### Kernel function between time series of different lengths

I'm studying a data set composed of time series of different lengths; some are up to an order of magnitude longer than others. (If it matters, the data aren't actually temporally related; it's just ...
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### I want to check the “affect of economic variables on the export of vegetable ” [closed]

I have used ARDL technique for that as I applied that technique following answer come to me. Value of Durbin Watson test (2.20). Please guide me how i can interpret that value?? In the long run ...
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### Relation linear regression and ARMA models

I have data from a time series which I am currently fitting with a linear model. For that Im using the data as cross-sectional data, where each response corresponds to the value of each variable on ...
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### Seasonal data deemed stationary by ADF and KPSS tests

I have got two time series and I want to evaluate a VAR model. For this, it is necessary that both time series are stationary. Using R, I have found periodicity ...