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

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Isolating distinct components of a treatment effect

The effect of a drug on blood analytes is to be studied. Blood analytes are measured before and after administration of the drug, which shows that several of them have decreased after treatment. A ...
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Should outliers in a time series be removed before or after detrending?

I am doing a classical time series analysis. When do I remove outliers in the data? After detrend or before detrend?
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36 views

How to choose between VOMs and Predictive models, e.g., ARIMA?

In time series prediction, there is a lot of work that uses predictive models (e.g., ARIMA). On the other hand, there's also a lot of work that uses Variable Order Markov models (e.g., context ...
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32 views

Improving forecasting output obtained from Winter, ARIMA and TBATS method

I am trying to forecast commodity price for next year. I have collected and plotted monthly average prices from last 10 years.Plot has been attached. I used Holt's-Winter method on prices till 2014 ...
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13 views

Testing variation differences

I have a dataset on how two publications covered a conflict. One is considered liberal and the other is conservative. The dataset has about 10 variables and has been collected over 10 periods of time. ...
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1answer
52 views

Partitioning the sum of squares of a regression where Fourier coefficients are the regression coefficients

Given a finite realization from a time series, we can represent the n observations by the trigonometric polynomial Where does the equation (7.1.2) come from? what partitioning of the sum of ...
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How do I interpret weak exogeneity in an ADL model?

First year econ graduate student here; looking at an ADL (Autoregressive Distributed Lag) model for the first time. Consider $Y_t = \omega Z_t + \alpha Y_{t-1} + \beta Z_{t-1} + \mu + \epsilon_t$, ...
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32 views

Trend Visualization of N time series

I have about 500 time series with different trends, and each time series represents a given nb of transactions. (Volumes follow a long tail distribution). I would like to plot a summary graph on ...
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31 views

In time series analysis, is it a good idea to do the analysis using the factors describing intra-seasonal description

I hope my question is not vague. Suppose you are looking at the hourly sales of say Walmart/Dillons, with data given over a few months. It is clear that the data is a time series with frequency 24. ...
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32 views

loan default model

I have a loan dataset that includes all the loans originated from 2000 through the most recent quarter. For each loan, available are information at origination, such as loan size, FICO, LTV, LTI ...
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47 views

Examine historical demand data

I have to examine historical sales data in order to figure out which calendar events have an influence. I would like to ask for some feedback if it makes sense or what I could do better. What I have: ...
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37 views

Lag length selection for a VAR model

The model I am working on has 4 time series (X, X1, X2, X3). Lag lengths are 5, 1, 4 and 6, respectively. X1, X2 and X3 are stationary at level and X is stationary at second difference. I am applying ...
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43 views

Code for detrended cross-correlation in R

I want to code for Detrended Cross Correlation in R for time-series data but I'm still stuck. I don't know why the coefficient is not in range -1 : 1. I try to write following these equation below ...
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27 views

How do I test the stationarity of data using minitab? [closed]

I am working on a time series and trying to fit ARIMA to predict future values.However, I am facing trouble with finding out whether the data is stationary or not.
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31 views

Inverting a VAR - looking for a good resource

I am having trouble with something that should be pretty basic. I need to invert a VAR (vector autoregression). Everything I have read just brushes past the actual inversion process, taking for ...
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27 views

Unsmoothing of returns [migrated]

The following problem arises in the context of private equity, which typically report "smoothed" returns (think of it as a moving average). As you can imagine, "smoothed" returns would have a much ...
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39 views

Showing a Time Series is Regular

Note: this is not an assessed question, it is a practice question from a past exam. If we are given the following time series: $X_t=\alpha^2X_{t-1}+Z_t-\alpha Z_{t-1}+2\alpha^2$ I am asked to find ...
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41 views

Lag polynomial coefficients for integrated stationary processes

I'm following http://faculty.chicagobooth.edu/john.cochrane/research/papers/time_series_book.pdf to ramp up on time series (my background is Elec Eng). I'm having confusion about the meaning of some ...
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2answers
45 views

How to z-normalize multi-dimensional time series?

z-normalization for 1-dim time series is simple. $z_i = (x_i-m)/s$ Here, $x_i$ is the element of series for each time index $i$. $m$ is the mean, and $s$ is the standard deviation. For n-dim time ...
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23 views

Auto-covariance in a stationary time series

I am trying to calculate the auto-covariance of time series $Z_t$. Given a weakly stationary process $Y_t$; $t \in \mathbb{Z}$: $$Z_t=a+Y_t$$ Now, my goal is to show that $Z_t$ is also a stationary ...
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32 views

How to explain to laypeople that in a VAR model some variable explaines its own variance?

Background: I observed that people not familiar with vector autoregressive (VAR) models often struggle with the interpretation of a forecast error variance decomposition. I am frequently asked, why a ...
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1answer
53 views

Can I say that residuals are white noise?

I want to check whether residuals are white noise or not. When I look at the plot, all lags do not pass(exceed) the significance band except for fourth lag. However, fourth lag's p-value of 0.228 is ...
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Stationarity after differencing

I have the following two processes: \begin{align} x_t &= x_{t-1} + u_t \tag{1} \\ x_t &= {\beta}_0 + {\beta}_1t + u_t \tag{2} \end{align} Differencing once leads to: \begin{align} \Delta ...
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Which model approach for data with timings and signals

I have a data set of times, signals and their values. The signals have values from A1 to A6. The first 25 data points of the record are as follows: ...
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Dectect White noise ACF - PACF Eviews

I found PACF and ACF like the following table . But, how can I decide whether there exists white noise? And what is white noise? If there is white noise, how can i build my best fit model with ...
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Identify outliers with median-absolute-deviation for timeseries data

I am having trouble understanding this particular method of detecting outliers in a time series. Below is the problem: I have a region-of-interest containing 15 voxels. Each voxel contains values ...
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Time series model [duplicate]

I have been give a task for this: "Construct the best-fit time series model for the mean and variance process underlying the portfolio returns, use the best time series model to forecast the mean and ...
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28 views

Suggestions for Time Series Exercises

Do you know of a good set of exercises, preferably with solutions, that would help me learn Time Series by myself? I was searching for solutions to the exercises of Shumway and Stoffer's «Time Series ...
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54 views

Interpretation of VAR and causality

I have two time series(X1 and X2) each having 900 records. I wanted to establish relationship between them and put it in ...
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51 views

Residuals Interpretation:Time Series Data

I am trying to use multiple regression for a time series dataset. I have values corresponding to a variable measured by 24 hrs for 4 months. Since there was a pattern which repeated every 24 hours I ...
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42 views

Least squares regression of NPS

I would like to monitor customer satisfaction over time and would ideally like to use NPS for that. Specifically, I would like to see if there's an overall trend over time. Could I regress Net ...
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33 views

Time Series: testing significance

Assume we follow a single companies stock over several years. This stock has a steady upward trend over the years we are recording its value. Then in the current year it takes a hard downward trend in ...
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29 views

Dealing with seasonality in time series with no trend

I'm working with quarterly time series data. The series does not have a trend but fluctuates around more or less a constant mean. I observe weak seasonality such that the values are somewhat lower on ...
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Dealing with spikes in data

A company sells chocolates. Demand is recorded weekly. The future demand is estimated using the sales for every week in the previous 3 years. But the sales pattern is corrupted by promotions that have ...
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Does this ARMA-inspired time process have a name?

I have to estimate a price time series for my thesis. We found that the price is reasonably well described by a process on this form, which looks like an ARMA(p, q) process but has an extra term: ...
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What are valid ways of analysing predictors for a response variable that changes with time?

I have a cohort of similar patients who are likely to get a certain disease over time. I am trying to find out how some continuous health markers (e.g. weight) at time 0 are related to their disease ...
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How do I choose the correct model for a regression? [migrated]

So the central question of my project is to what extent does a country's level of export contibution towards GDP (i.e. exports as a % of total GDP) affect its GDP growth. I'm comparing this ...
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48 views

Interpreting VECM result

X1 , X2 , X3 and X4 are time series which are stationary at level. I want to establish long term relation between them. I am planning to use it as forecasting model for my work. I want to create this ...
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62 views

Time series Analysis - VAR or VECM

I have 4 time series. One of them is stationary and rest of them are not. I need to find relation between them. I will use AIC to decide lag length. Should I use VAR or VECM to find relation between ...
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How to represent an ARIMA(p,d,q) with dlm package in R? [closed]

I've been using DLM package for modeling my timeseries in state-space format, and then use Kalman Filter to get better 2 step-ahead forecasts. Even though I've read the vignette and parts of their ...
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Need to extrapolate missing monthly data from annual data; the monthly/seasonal index is reasonably well-known

I have a revenue dataset for various businesses. For about half of those businesses, monthly data is available. For the other half, only annual revenue data is present. I know the seasonality of the ...
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rsquared relation in regression with ma(1)

Hi: I'm fitting a time series regression model with ma(1) errors so $ z_t = \beta_0 + \beta_1 * x_{t-1} + \beta_{2} * y_{t-1} + \epsilon_{t} - \alpha * \epsilon_{t-1} $ Although there are ways to ...
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Contemporaneous regression in R (VAR model)

I have two time series and I want to check the relation between them. I am using a VAR(3) model. I would also like to include the contemporary variable, something like this: Can we do this ...
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19 views

Best way to fit an ARIMA model when the values of the variables don't change

I have a time series with various features that record sensor data. It can be the case that the values are recorded although they did not change compared to the previous observation. Hence, the series ...
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1answer
22 views

Modelling turnovers by a random walk. Is it right?

I need to analyse a bunch of weekly time series that reflect the turnovers of various companies. I already read that return rates or share prices show stochastic patterns that can be modelled by a ...
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11 views

resources for temporal count data

I am currently in the middle of analyzing count data. The count data is gathered once per day for more than 100 days. There are two populations that are counted everyday. Is this type of count data ...
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How to tell in Panel Data how the independent variables affect the dependent for specific countries instead of the whole sample in total?

I am working on my Master Thesis on how some specific independent variables (like inflation) can affect a specific index which is the dependent variable. I am taking 25 annual values for 12 countries. ...
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Does a stationary process necessarily have to be mean-reverting?

I wonder about if a stationary process is by definition mean-reverting too. I know the formal definition of a stationary process, but I'm not sure about the definition of a mean-reverting process. ...
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forecast(method ='arima') ; auto.arima() function, how to avoid forecast not in line with history?

I am working on an alogorithm in R to automatize a monthly forecast calculation. I am using, among others, the forecast(method='arima') function from the forecast package to calculate forecast. It is ...
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The results and specifics from the 'qs' function in R

I'm not entirely familiar with the results of the qs() function in R's package seasonal. But, by what I understand roughly, the ...