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Questions tagged [time-series]

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

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16 views

Prediction of $X_{n+1}$ with Yule-Walker estimate

Consider a causal AR(1) process $X_t = \phi X_{t−1} + Z_t$ with $(Z_t)$ iid with mean 0 and finite variance. I am reading in a book, that $\phi X_n$ is the best predictor for $X_{n+1}$ because it ...
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14 views

Prove stationarity

It can be easy question, but it is a part of bigger exercise. I have problem with lack of statement "uncorrelated" Prove that if ${X_t,t \in T}$ is stationary, then $Y_t = X_t - X_{t-1}$ is also ...
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17 views

What statistical techniques can I use to model improvement over time?

Say you have a group of 30 students and you measure each individual's performance on a test at 4 intervals throughout the year. (For the purpose of this investigation, assume the tests taken are ...
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1answer
27 views

Why is Out of sample R^2 inappropriate for Time Series Forecasting?

I've been reading a few posts from distinguished members of this community about R^2 and time series forecasting: 1.What is the problem with using R-squared in time series models? 2.R-squared to ...
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13 views

How to adjust data labels to alluvium instead of axis for bump time series chart (R ggalluvial)? [on hold]

How can the data labels in this example be made to appear centered on the alluvia?: ...
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7 views

Singular spectrum analysis - classification and/or clustering [on hold]

I have several time series plots/datat that I wish to perform on them classification and/or clustering? Any method that can be recommended? Can I use singular spectrum analysis?
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1answer
21 views

Prewhitening with seasonal response and non-seasonal independent variable

I'm working to develop a forecasting model for a quarterly seasonal variable (quarterly estimated individual income tax payments) using several candidates for non-seasonal independent variables (...
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4 views

Interpretation of ECM coefficients

Say that we are regressing consumption $C_t$ on time $Y_t$. Furthermore, suppose that both series are $I(1)$ and are co-integrated. Given this, we set up the error correction model (ECM) as follows: $...
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6 views

autocorrelation graph in python like R (for two or more series)

In R one can call the acf function on a bivariate (or higher dimensional multivariate time series) and it will output all the self and cross correlations (for example with a bivariate series the ...
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1answer
32 views

Spurious regression - are the coefficients biased or not?

Say that we are regressing a variable $Y_t$ on another variable $X_t$, and both series are non-stationary. Specifically, let's say that both are $I(1)$ and trend upwards over time. Now, say we ...
3
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1answer
37 views

When to use AR and when to use MA model?

When to use an AR model and when to use an MA model to model time-series data. What aspects of data are modelled by the AR process which can't be done by MA and vice-versa?
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1answer
35 views

If linear combination of two time series processes is non-stationary does it mean one of the two series is non-stationary

Suppose I have 2 time-series processes. If they are jointly weakly stationary then the linear combination is weakly stationary. If the linear combination is non-stationary does it mean at least one ...
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9 views

What's the advantage of Toda-Yamamoto's Granger Causality procedure?

There are already quite a few questions here on the Toda-Yamamoto (TY) approach to Granger Causality, i.e., the blog posts by Dave Giles (2011 and 2014). What I would like to clarify is just whether I ...
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Product/SKU level time series forecasting [on hold]

Predict demand of product at each outlet for next 6 months 5 – 7 years of sales data at outlet level for each and every brand is available As it is a time series problem we need to design per outlet ...
3
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1answer
21 views

Lagged independent variable's coefficient changes when higher lags are included

I'm running a TSCS analysis with the plm library in R with which I want to explain students' performances. The data consist of approximately 1100 units and has 25 points of measurement - panel data ...
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10 views

Is it necessarily incorrect to randomize train-test split for a time series random forest model?

As part of some preliminary research, I'm experimenting with a random forest classification model for predicting whether the S&P 500 will be higher or lower at tomorrow's close versus today's ...
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23 views

How does BATS model work?

I am using BATS on a univariate time series model. I have observed strange behaviour. I have data from 2016 to till date (weekly level). If actual are considered from 2016 to 2019 May, I have used ...
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1answer
15 views

How to choose the right aggregation function? [on hold]

I have two dataframes (input and output). The Output dataframe is produced by an unknown model given the input dataframe. I am trying to build a model (to mimic the unknown model) to predict "...
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sum of a convergence serie [migrated]

I am trying to calculate: $\begin{equation} \sum_{j=0}^{\infty} (\frac{\lambda^j}{j!})(\frac{\lambda^{j+h}}{(j+h)!}) \end{equation}$ And then, I did: $\begin{equation} \sum_{j=0}^{\infty} (\frac{\...
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16 views

Analyse the influence of interior demand and trade on exports

I would like to have a primer on how the current slowdown of the German economy affects its partners, for instance France, Spain and Italy. More specifically, if it goes mainly through Germany's ...
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26 views

Simulate cointegrated prices and VAR model [on hold]

I am trying to simulate cointegrated stock prices and use a VAR Model to make forecasts. This is the code I wrote so far: ...
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9 views

Identifying anomalies multiple time series using statistical methods

I am trying to detect anomalies from a Time Series sequence, that is calculated as an aggregate count of multiple unique Time Series'. For example, in the graph below: We have aggregate counts shown ...
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1answer
40 views

Example of random process with negative variation

I study about random processes. Let us have $\{X_1, X_2, \dots X_n\}$ observations. I learned, that in stationary time series the sample autocovariance function is defined as $$ \widehat{γ}(h)= \...
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1answer
35 views

Uncertainty Quantification in Time Series Analysis

The stock market value of the data point connected by the red line is predicted by linear regression using market values as well as Twitter sentiment data and more in a certain period of time (red ...
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16 views

Using garchFit to fit an ARCH(1) process

I tried using the garchFit function FinTs library. This is what I am trying to run: garchFit(formula=~arma(0,1,2)+garch(0,1), data$`1 YR`) However I get the ...
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29 views

form of the model when using backshift operator

Be $Y_t=X_t + \epsilon_{1,t}$, in which $X_t = X_{t-1} + \epsilon_{2,t}$ and $E[\epsilon_{1,t}\epsilon_{2,s}] = 0 \forall t,s$. How could I say why this process is related with a model on the form $(1-...
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1answer
24 views

Data Mining/Statistical Methods to find trends, peaks, etc

currently I am working on a project for my final exam. The data is coming from a streaming plattform. The data I am using are some logging data (data when customers have problems with the streaming ...
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1answer
38 views

Is this time series stationary? What would be your approach to forecasting it?

I've been working on the time series prediction of a signal and came across a small misunderstanding. The signal is depicted below: Apparently it looks like there are several stationary local areas ...
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1answer
23 views

why isn't the tscv function allowing for step-size other than 1?

the tsCV function from the forecast package allows for forecasting using a rolling forecast window. Why is it that the step-size is always 1 sample ahead, and the ...
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4 views

How can I accomodate the forecast series to separately fit and predict workdays and weekends?

I'm using the forecast R package. I have the same dilemma as How to forecast daily time series with weekends and holidays?. I understand that the answers consensus ...
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9 views

extracting seasonality - using fourier transform vs. learning the coefficients of fourier terms

I'm following hyndman's advice for using fourier terms when fitting a linear regression model to the taylor time-series (with the very long seasonality of 336). My ...
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16 views

ARIMA forecast for upcoming 2 days

I am trying to forecast the battery charge for the next 2 days. I have data for 3 days with 5 mins interval. I have tried the below code: import statsmodels.api as sm arima_mod = sm.tsa.ARIMA(...
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1answer
30 views

ARIMA forecast confidence intervals

Can someone explain how confidence intervals for ARIMA forecasts are derived? I can't seem to find any good explanation of it. From what I've read it seems like because an ARIMA process can be ...
3
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1answer
37 views

LMER model with uneven time points

Does it matter that my time series are taken at random points? All the examples I've seen have nice time series, like every day or whatever. I have what is otherwise a pretty simple model: one fixed ...
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17 views

Show that the autocovariance function of stationary process {${X_t}$} is positive definite

Show that the autocovariance function of stationary process {${X_t}$} with mean $\mu_X$ and variance $\gamma_X (0) > 0$ is positive definite, i.e., $\begin{equation} \sum^n_{t=1} \sum^n_{t'=1} ...
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1answer
40 views

find the autocovariance function of the process $Y_t$

Consider the processes $X_t = \phi X_{t-1} + v_t$ and $Y_t = \phi Y_{t-1} + X_t + e_t$, in which $|\phi| < 1$ and $v_1$ and $e_t$ are non-correlated random errors with zero mean and variances equal ...
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5 views

How do I introduce the time series data if I have just a column with the data? [closed]

I have tried to use the programa with a time series in columns and I got the error trying to get slot "y" from an object of a basic class ("numeric") with no slots How can I input this data into the ...
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16 views

Forecasting based on previous realizations

A given process has multiple variables moving to a target point. I can collect data of several realizations of this process. What forecasts methods exist for this? I'm familiar with exponential ...
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0answers
5 views

Converting numericals into regression coefficients from Coxph [closed]

how can i manually convert a set of numerical values into regression coefficicents so that it can be applied into another dataset for prediction purpose using Coxph? Example: height 0.004 ...
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22 views

Time series plots, polynomial coefficients and PCA

I have several time series plots that I have their polynomial coefficients (curve fitting using Matlab polyfit). Is it possible and valid to use Principal Component Analysis (PCA) to try to classify ...
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0answers
14 views

Deciding upon the important regressors for a SARIMA model

I have 14 months(01/07/2018 to 30/08/2019) of one minute data, which I have aggregated to 10 mins block. So I have a data of dimension "61056 * 350". From this I am using 12 months of data to train ...
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1answer
31 views

One year of historical data with yearly and daily seasonality

I have 14 months(01/07/2018 to 30/08/2019) of one minute data, which I have aggregated to 10 mins block. So I have a data of dimension "61056 * 350". From this I am using 12 months of data to train ...
1
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0answers
11 views

“nested” time-series comparison

Hope you can help me with a methodological issue. I want to compare two sets of observations made in two independent groups (15 subjects per group) over time. The two groups are cell cultures derived ...
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0answers
29 views

ARIMA model on sales data

I have a 'theory' question based on the ARIMA model. I have daily sales data for about 3 years, so I could apply ARIMA to the data. However, the data contains categorical variables. My data structure ...
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7 views

“Nested” time-series comparison?

I'm Stick with a methodological problem and I'm not sure how to manage a possible solution. I want to compare two sets of observations made in two independent groups (15 subjects per group) over time. ...
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16 views

Are two duration sequences related?

I am so sorry I'm bad at statistics but I need this for my seminar. And, so sorry, I need a really simple answer :( My head already feels like exploding from this seminar :( I've segmented a video ...
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10 views

How to tell if it is the trend that's changing or the seasonality in a time series

I am looking at the plastics data from the fma R package. The data describes monthly sales of a product over a five year period. I am trying to figure out whether it is the trend that is changing, or ...
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1answer
18 views

Linear regression results interpretation check

I have below results of my linear regression and my interpretation. Is it correct? Regression Statistics ...
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0answers
13 views

Daily Time Series with multiple observations for each date [closed]

I am trying to convert my data frame into a daily time series starting from "2006-01-03" to "2017-12-29". I tried frequency=12 and it gives me a monthly trend from 2006-2017. Using frequency=365 ...
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16 views

What is the best way to model a spatialtemporal (3d) problem?

A very common problem in machine learning is that we have time variables. For this we use more statistical approaches like ARIMA or more ML approaches like LSTM. A sophistication of a time series is ...