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

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How to perform seasonal adjustment to a time series?

Assume following data set representing each month of the year 2013 with the corresponding consumption of natrual gas to heat my flat and the respective mean temperature. How can I seasonal ...
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How to correctly concatenate time series data

I have this shifted time series data. For one set consists of features from week1-5 and labels at week6. Another set features from week2-6 and labels and week7 and so on. I have like four sets of ...
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Looking for definition: Granger Causality with a common explanatory process

I am looking for help in defining my problem. Essentially, I have two data processes (both continuous macroeconomic variables: $x$ and $y$). There is evidence of bidirectional causality between $x$ ...
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56 views

Additive vs Multiplicative decomposition

My question is a really simple one but those are the ones that really get me :) I don't really know how to evaluate if a specific time series is to be decomposed using an additive or a multiplicative ...
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45 views

Timeseries: Find points deviating from the mean

I haven't done much time-series modelling at all and now I have a dataset which screams "time series" at me and now I am hunting for a model. The data: Imagine a video watched by ~400 people, 100 ...
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51 views

Method for detecting anomalies in timeseries?

I am exploring creating alerts for anomalies in a timeseries. Say that I have a graph like this: There are two anomalies here that I would wanted to be alerted on: First, on April 7th with there ...
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Test whether there is a significant difference between two groups

I have some trouble with the last test I need to perform for my bachelor thesis. I have two variables and I need to test whether there is a significant difference. The first variable has all the ...
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75 views

Anderson-Darling test in 2D time series

Suppose two time series (of light flux). The goal is to determine whether the series are from the same distribution. It is usual to use the Kolmogorov-Smirnov (KS) test in this situation. However, ...
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restricting range of values for AR(1) process

We have a stationary AR(1) process defined as $A_{t}= d+ \rho A_{t-1}+ \epsilon_{t}$ with $d>0$; $-1<\rho<1$; $\epsilon_{t}$ is white noise and follows $N(0,\sigma^2)$. What conditions do we ...
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Test if advertising raised sales?

I have an (offline) advertising campaign that I'm running in one city. I'm trying to figure out how to answer the following questions: What are the chances that the advertising campaign has no ...
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Estimating a first order plus dead time model

The data generating process is given by the following differential equation: $y(t) = a + b u(t - \theta) + c \frac {dy} {dt}$ Now imagine having as data a long time series for both $y$ and $u$. If ...
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Dynamic time warping between more than two sequences

Dynamic time warping is a technique to find an optimal alignment between two given sequences. Is there a technique to find an optimal alignment between more than two sequences? Does it as an ...
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Is it true that values of parameters do not vary from sample to sample?

This is something I was told. However, it seems to me that parameters of a population can be functions of time, in certain situations, in which case the values of parameters could vary from sample ...
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59 views

Why could mean centering change results

I used centering for my variables due to multicolleanirity and surprisingly the results (from before to after centering) changed for two interacted variables; one from significantly negative to ...
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44 views

Consequences of modeling a non-stationary process using ARMA?

I understand we should use ARIMA for modelling a non-stationary time series. Also, everything I read says ARMA should only be used for stationary time series. What I'm trying to understand is, what ...
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27 views

Testing significance of correlation between two autocorrelated series

Say I collected the shin bones of N different skeletons; they are all around 30cm long, and I measured different properties P1, P2, P3, P4 and P5 along these bones every 3mm (so I have 100 data points ...
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38 views

Is the Moving Average of ARMA the same of Moving Average of Stock Market?

I'm studying time series prediction and I have some questions. Is the Moving Averages movel studied the methods of the ARMA family has the same concept as the methods studied in Moving Averages ...
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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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Getting a monthly time series from weekly data [migrated]

I've checked a few questions on time series aggregation, but haven't found what I was looking for. I have a zoo object of weekly data over 10 years, and I've ...
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26 views

Time Series Econometrics: Cointegration methods for series with mixed degree of integration

I am performing a time series analysis on dataset ranging from 1974-2008. I have performed Augmented Dickey Fuller tests and Phillips Perron tests to check the stationarity/ order of integration of my ...
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44 views

How do I detect state change in multivariate time series?

I have a multivariate time series . For each row in the data we have the values of inputs and a label for stability (0 or 1 ) . What are the algorithms that can detect the stability for an unlabelled ...
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26 views

Centering vs. Standarizing which one is better? [duplicate]

Two approaches have been proposed in order to overcome the issue of multicollinearity if we have interaction variables which are mean centering and standardizing (z scores). You can check No.2 in this ...
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35 views

How do I deal with asynchronous data in financial time series?

I have tick by tick data of two financial time series. I am trying to do online regression between the given two time series. But I am stuck due to asynchronic nature of given financial time series ...
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Correlation between sensors

Background: A home wired with multiple sensors, measuring attributes like temperature, light, motion etc. In addition, a multitude of actuators that can carry out an action like opening a door, ...
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110 views

How to compare time series with cyclical data, and describe any changes or trends

I have a bunch of time series where the data has a natural (known) cycle, for example daily or annual (or both). Here is an example (this is 6 years worth of temperature data sampled hourly): ...
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Analysis of proportions over time

My knowledge of statistics is limited and I am looking for resources to read on the matter if possible. Anyways, I am currently trying to estimate a confidence interval for a proportion over time. ...
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How to implement a metropolis hastings algorithm to find the posterior pdf of a time-dependent parameter?

Assume that I have a time series observations denoted by Yi where i is from 1-5000. yi=β1 x1i + β2 x2i + β3 x3i + Ci; Here x is the input. I have to find the values of Betas. But, I'm taking all ...
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How accurate is F test in panel data

I heard that the F-test is to advice you whether to use fixed effects or pooled OLS. However, I didn't find any details about it in books. Only in a very few studies. What is the hypothesis of the ...
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Is it ok to transform a logarithm variable to z score

I have a variable that has 57 kurtosis, so I decided to transform it to log. However, I have multicolleanirity problem due to interacting this variable and others with another variable so I am using z ...
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37 views

temperature prediction algorithm

I found an interesting problem in a contest on temperature prediction: https://www.hackerrank.com/contests/expansion-challenge/challenges/temperature-predictions It is not about forecasting the ...
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check for players undergoing the maximum/minimum change in time course data?

I have time series data of many variables (This data comes from high throughput biological experiments, which measure the amount of particular biological components such as RNA content of a cell etc., ...
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57 views

Forecasting in R using forecast package

I'm trying to forecast hourly data for 30 days for a process. I have used the following code: ...
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25 views

Characterizing trend of time series in R

I have a fairly basic statistics application question. Lets say I have a set of four fold-change values, representing the abundance of a factor as it passes through four consecutive time points: ...
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Cluster analysis on time series samples

In the follow-up to this Ways to understand 2-dimensional time-series data I'm working on 2D time series data where two attributes are depth and temperature. When I plotted depth-vs-temp curve and ...
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Whitening Transformation using a Hadamard product Variance Matrix

I want to whiten a vector $X$ by transforming the variance-covariance matrix so the variance-covariance matrix of the transformed series will be the identity matrix $I$. $X$ is a time-series column ...
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73 views

Difference between series with drift and series with trend

A series with drift can be modeled as $y_t = c + \phi y_{t-1} + \epsilon_t$ where $c$ is the drift(constant), and $\phi=1$ A series with trend can be modeled as $y_t = c + \delta t + \phi y_{t-1} + ...
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Difficult to understand the meaning of ergodicity and ensemble averaging

Chaotic Signal Processing, pg147--148 describes how a signal (output of laser) operating in chaotic regime is ergodic. Literature says that a stationary signal is ergodic, if its ensemble average = ...
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How to conduct the two sample test with extra data to eliminate between-subjects variability

I am stuck with the correlated and independent data combined in one study. Here's my dilemma: Say X is a drug(explanatory variable) and Y is a gene expression(response variable). Normally, you ...
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How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$? [duplicate]

Suppose we have a time series $X_t$ s.t. $X_t \sim^{iid} (0,1)$. How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$? Or, I guess, if ...
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Ways to understand 2-dimensional time-series data

I'm working on 2D time series data where two attributes are depth and temperature. When I plotted depth-vs-temp curve and saw its variation over time, the fluctuation occurs at few places only. I'm ...
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42 views

Imputing missing observation in multivariate time series

Suppose I have a dataframe consisting of six time series. In this dataframe, some observations are missing, meaning at some timepoints all time series contain a NA-value. In R, one possible imputation ...
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Repeated measures with multiple time points for the predictor and dependent variable: Does Xt-1 predict Yt better than Yt-1 predict Xt?

I have a question on what type of analysis I should be looking into to analyze some data I have: Suppose you have 2 runners X and Y, and they take turns sprinting 100 meters, with runner X going ...
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How many quarters of observations are suggested before and after an event to determine the events significance in a time series analysis?

I'm reviewing a multiple regression time series analysis, and I'm concerned about the (possibly insufficient) sample size. The goal of the analysis is to determine whether an event during the time ...
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42 views

Repeated measures ANOVA design/structural issue

As part of my PhD work, I've conducted an inoculation experiment concerned with marine phytoplankton community productivity (dependant variable, as 'no. of cells') vs nutrient availability. I have two ...
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Markov Chain State Transition Probability in R

I have a dataset which shows the states (3 states) across 11 time points for each participant. I wanted to estimate the Markov Chain state transition probability matrices for time points 2-11 using R. ...
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Time Series on Oil Filter Pressure

I am not really strong with time series but I have a project I am working on.. I have a problem where I am trying to model a time series of the difference in pressure before and after oil has passed ...
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$R^2$ correspondence for nonlinear time series

Is there a statistical measure for nonlinear time series data that is comparable to $R^2$ value in linear regression (giving an idea of how well the fit is)? The data is not monotonic, so I cannot ...
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53 views

Creating a composite rank of restaurants with some missing data

I have monthly sales data of 500 restaurants for one year. For the same restaurants, I also have customer defection or dissatisfaction rates. I want to create a composite score that can rank ...
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Machine-Learning algorithms for Forecasting

For work, I'm working on an app where you essentially forecast the failure rate of the overall machine through different factors such as the historical failure rates for the components used to build ...
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Need clarity on alpha, beta, gamma optimization in Triple Exponential Smoothing Forecast

I asked a variation of this question, but I want to be more direct. Take the exact same Triple Exponential Smoothing Model (Holt-Winters with a moving level, trend, and seasonal component)--- Would ...