# Questions tagged [time-series]

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

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### How to generalize shrinkage to fully-bayesian models?

I've got a time series that I'm modelling as an exponential; growth rate, with the rate following a logistic distribution:
$$
y_t = e^{x_t r_t}
$$
where
$$
r_t = \frac{L}{1-e^{-k(x_t-x_0)}}
$$
I've ...

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### What is the ACF plot of $x_t = 0.9 x_{t-2} + w_t$

I am just learning time series,
and I am wondering about the following AR(2) model:
$x_t = 0.9 x_{t-2} + w_t, w_t \sim N(0, \sigma_w^2)$
Please show me the plot of its Autocorrelation Function,
or ...

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### First-difference and lags

I am newbie to time-series econometrics. I want to estimate a model for the association between greenhouse gas emissions and new green technologies. The estimation equation I want to use is $$CO_{t} = ...

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### How to compare change in regression

I am trying to determine the effect of a program on a single measurable value over time. I am a computer programmer with only a very elementary understanding of statistics, so please forgive me for ...

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### Statistical test for forecasting models

I developed many forecasting models over the same dataset (multiple iteration of simulated time series data). My dataset basically is a multivariate timeseies so the forecasting models forecast many ...

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### Parameter estimation for time-varying autoregressive processes in R

I want to estimate the parameters of an autoregressive process with time-dependent coefficients. For example TVAR(1) model with 1 lag: $$ X_t = \phi_t X_{t-1} + \sigma_tW_t $$ where $\phi_t$ and $\...

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### Determining standard error of the mean from a correlated, stationary time series using known autocorrelation without block averaging

I'd like to determine the SEM of measurements taken from a stationary time series. SEM calculation using all measurements isn't accurate because adjacent measurements may be highly correlated, so the ...

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### Confusing results from Granger Causality Analysis

I am currently doing a (university related) longitudinal analysis of online comments to find out if there is predictive power of financially related Reddit comments on movements in stock closing ...

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### Time Series Stationarity Proof

I am new to Time Series, please help with showing why the equation below by taking the second order differencing it will be stationary? $$ Z_t =\beta_0+\beta_1t+\beta_2t^2+\epsilon_t $$

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### $z_t=x_{t+7}/x_t$. Solve back for x. model is $z_t=alpha*z_{t-1}$

I want to create a model of x,
Now my issue is that to get this fit I need to transform the original data such that $z=x_{t+7}/x_t$ the absolutely best fit I could get is
by regressing $z_t=alpha*...

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### At what point during ARIMA series model building should log transformation be considered for variance stabilization?

Data: http://fred.stlouisfed.org/series/ECOMPCTNSA
Model Build: Seasonal ARIMA Model
Program: R
I am building a Seasonal ARIMA Model to model the quarterly time series data which can be downloaded ...

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### Interpretation of Johanson co-integration test results

if the Max-eigenvalue test indicates no cointegration at the 0.05 level, while the Trace test indicates 2 cointegrating eqn(s) at the 0.05 level, how do i interpret the results?

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### Correlating noisy time series with a phase difference (lag)

I am trying to find the correlation (or any other indicator of "similarity") between a real-world time series (example: monthly sales of tractors - seasonal over the year) and some market index, like ...

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### Daily timeseries decomposition into seasonal, trend, remainder?

I have time series for each day, that captures the time(s) of the day where a certain event $E$ happens (or alternatively, when it certainly isn't happening). This looks like the following:
...

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### How to emphasize a sudden drop in time series for the purpose of clustering?

I would like to cluster uni-variate daily time series so that an emphasis is put on sudden drops in time series. Series that contain such uncommon drops should be in one cluster (drops should ...

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### bs.bootstrap function confusion in arch package python

After applying bs.bootstrap function in bs.apply(), sharp_ratio() function is applied with 2500 reps . So here analysis is done taking mean of block length or 1 full dataset
http://arch.readthedocs....

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### How to approach Feature Extraction and Feature Selection part in machone learning in python?

I am a bit new to machine learning and I have the following questions:
Question 1:
When dealing with feature extraction with signals from sensors, what is the typical approach to extract features ...

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44 views

### Correlation between two variables as time series with multiple samples

Main objective
I have two variables ($A$ and $B$) as two time series for $n$ samples, and I would like to test if $A$ and $B$ are correlated. Let's first assume that these $n$ samples are independent ...

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### How to estimate a single AR model for multiple time series?

I have ACF of a time series data, I want to interpolate the ACF using AR model for which I need to calculate the coefficient of the AR model The problem is I have (6000x6000) matrix of ACF and I cant ...

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### Is it valid to use company/year combinations for (financial) data analysis?

I want do to a multiple regression analysis on some financial data. Sadly I only have 30 observations (the 30 different companies) and I would like to have more. My friend asked me why I don't add the ...

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### Low memory time series input for deep learning

Background
I have some data that looks like this:
...

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### Model selection based on Jarque-Bera, Shapiro-Wilk and Ljung-Box tests

I am kinda new to econometrics
I have six models with Jarque-Bera, Shapiro-Wilk and Ljung-Box results. How can I choose the best model using the tests mentioned above?
Thank you

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### Improving ARIMA forecasts

I am trying to use ARIMA to forecast stock returns. The problem is that variance is time-varying but ARIMA assumes that it is constant. As I understand, GARCH is only used for forecasting volatility (...

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### TSFRESH - features extracted by a symmetric sliding window [closed]

As raw data we have measurements m_{i,j}, measured every 30 seconds (i=0, 30, 60, 90,...720,..) for every subject ...

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### Is Gaussian process model impacted by order of variable index?

I'm learning about Gaussian Process through this video by Richard Turner (University of Cambridge, link below). In the video, it was explained that GP is a generalization of multivariate Gaussian ...

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### R Dataset Tree Ring - Analysis ideas

I am trying to fit an appropriate model to the "treering" data-set (available in R). No simple ARIMA model seems to fit particularly well: for example, as remarked on p13 of http://people.stat.sfu.ca/...

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### Analysing seasonal variations in time series?

I have to analyze NDVI time series over 17 years. NDVI is ...

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### MASE Statistic: Comparing Across Time Series

I've read that the Mean Absolute Scaled Error (MASE) can be used to compare forecasting accuracy across datasets with different scales. I'm unclear on what this means.
The MASE is a ratio of the ...

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### Time series object with multiple station data with different time periods?

How can make a time series object from a set of data. I have data set from a number of regional meteorological stations. And I don't know how to create a time series object that includes time series ...

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### Time Series Analysis and Forecasting of Astronomical data having a sinusoidal trend

I have data of an orbital parameter of a satellite for 456 days. I am treating this data as univariate time series data and wish to use time series models to forecast future values. However, this data ...

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### AR(1) with known initial and terminal condition: how to draw the innovations?

Suppose I have the following stationary $AR(1)$ process:
$$ y_{t}=\alpha_{0}+\alpha_{1}y_{t-1} + u_{t} $$
where $u_{t} \sim \mathbb{N}(0,\sigma^{2})$, with $\sigma^{2}$ known. Suppose I have an ...

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### forecasting percentage change with uncertainty

I used a machine learning model to predict the percentage change of a time series with upper and lower bounds of the change (see figure_1). here are the results:
...

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### Fitting a VEC model: suggestions on procedure and results

I'm having some hard times trying to do a simple but statistically sound analysis on 4 cointegrated daily time series which I analyzed through VEC. I ask the community:
is the procedure I followed ...

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### The covariance function of a stochastic process is positive semidefinite

Let $\{X_t, t \in \mathbb{Z}\}$ a real-valued stochastic process and $\gamma : \mathbb{Z} \times \mathbb{Z} \to \mathbb{R}$ the autocovariance function. I would like to show it is a positive ...

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### Using support vector regression to estimate GARCH model

I would like to estimate GARCH (1,1) model with support vector regression and I want to use asset returns series. I want to use python. Can anybody help me to explain the process with example step-by-...

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### Temporal resampling effects on linear trend estimation

I'm looking to determine rate of change of a noisy seasonal time series with linear regression.
In the first figure, there is daily data for 30 years. The second figure is the same data aggregated ...

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### Drivers that should be positively correlated to Y have a negative correlation with the residuals?

In my data set it's clear that X,Y, and Z are positively correlated with A, since they have a strong correlation (close to 1) when I test the correlation in Excel. However, I took the regression of ...

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### R: Compare two time series

I have two time series Time Series Plot . Red line is the public data and the blue one is the predicted data.
I found these lines look very similar.
Is there a way to statistically compare the two ...

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### AR model estimated with Yule-Walker equation is poor

Hello :) I am an undergraudate student studying time series analysis as a way to kill time during the Covid-19 self-quarantine. I write this to ask you, what could be the possible reasons behind my ...

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**1**answer

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### causal economic research [closed]

I want to analyse the relationship between the level of globalization,and the level of income inequality between two specific countries. however, I'm quite lost as to which method is good to use. I'm ...

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### Getting the error of a mean curve compared to multiple original time series

I have a 5 days of time series of an individual's steps in 15 min intervals. What I have done is fitted a curve to estimate the individual's general day steps profile. So this curve has a span of one ...

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### Should I impute the missing values of timeseries data?

I have the following task - predicting the next 12 hours of PM10 particles based on historical data of previous 24 hours of PM10, O3 (ozone), CO (carbon monoxide), and others (not included) using RNN'...

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### How to identify the dissimilar points between multiple time series having almost similar patterns?

I have multiple time series that are quite similar to each other in terms of pattern. I Clustered all them to get similar time series under a cluster.
This is what the cluster looks like:
Now I'd ...

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### How can I implement a 1D CNN in front of my LSTM network

At the moment I reshape my X_train like this:
X_train = input.reshape(1,1,12)
...

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### Non linear parametric time series vs non linear non parametric time series

I am new to non linear time series modelling. Can Any tell me difference between parametric and non parametric models.

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### BiLSTM (Bidirectional Long Short-Term Memory Networks) with MLP(Multi-layer Perceptron)

I am trying to implement the network architecture of this paper Speaker Change Detection in Broadcast TV using Bidirectional Long Short-Term Memory Networks, by Ruiqing Yin, Herve Bredin, Claude ...

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### Time series split to avoid data leakage when lag variables are created for a univariate forecast model. Please help me in preparing the python code [closed]

I am doing a time series split for a univariate forecast model. Basically I am developing a regression prediction by creating Lag variables. When Lag variables are created then there is a high chance ...

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### Can someone explain how data leakage occurs if you randomize time series data?

I am a bit dense and I am not understanding the intuition behind why data leakage would occur if we don't "respect" the temporal order of time series data when doing sample splitting or cross ...

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### Autocorrelation in large panel of short time series (large N, small t)

Context: I have a large panel of short time series that represent entities of the same type. They are autocorrelated in that I get nice correlations if I take the (Pearson) correlation between (...

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### Are ARIMA coefficients bounded?

I don't have a lot of background in TS analysis and I haven't found references that are clear on this. Hopefully someone here can help me understand this.
I'm optimising ARIMA coefficients for a ...