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

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Feature selection for time series data

I am looking for methods for feature selection (or feature extraction) for time series data. Of course I did some research before, but it was not satisfying. I am aware of methods like PCA, ...
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Smoothing - when to use it and when not to?

There is quite an old post on William Briggs' blog which looks at the pitfalls of smoothing data and carrying that smoothed data through to analysis. The key argument is namely: If, in a moment of ...
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On forecasting, the mean squared error and realized volatity

Say one has finished estimating a correctly specified GARCH(1,1) on a daily time series and now wants to evaluate the accuracy of the one step ahead forecasts what steps or tests could one do? I ...
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How to perform a simple smoothing forecast for next 12 months (using forecast package in R) [on hold]

I currently have timeseries data (of gold prices) and I am trying to use a simple smoothing forecast to estimate gold prices for the next 12 months. I am not sure what function to use to accomplish ...
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Stationarity iff causal and invertible

Suppose $X_t$ is an ARMA(p,q) process. Is it true to say: "$X_t$ is weakly stationary iff $X_t$ is causal and invertible"? If so, why? If not, is there something similar?
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GARCH volatility forecast model in practice

I am self-studying GARCH models. I understand this is how it roughly looks: $$\sigma_t^2= \alpha_0 + \sum_{i=1}^q \alpha_i \epsilon_{t-i}^2 + \sum_{i=1}^p \beta_i \sigma_{t-i}^2$$ and I understand ...
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Transforming TS for better fit

I'm trying to find transformation for my explanatory variable (outside temperature) to better explain heating power usage. I have data from one year here. ...
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Multiple Correlation Coefficient for Time Series?

I am using Pearsons correlation coefficient to calculate the correlation between two time series. Now I would like to calculate the correlation between a set of time series A, B, C and the time series ...
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What is the use of as.numeric() in R? [migrated]

this is Ex.1 on Page 252 in Statistics and Data Analysis for Financial Engineering by Ruppert: This problem and the next use CRSP daily returns. First, get the data and plot the ACF in two ways: ...
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Subset data in R [on hold]

I have several time series and want to regress the dependent variable on the explanatory variables. My question is: Because of structural breaks in my series I do not want to include all the ...
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Detrended Fluctuation Analysis: what does a exponent > 1 mean exactly?

Detrended Fluctuation Analysis is commonly used in order to identify long-range temporal dependencies in time series data. While white noise will have a DFA-Exponent of ~0.5, scale-free, long-range ...
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Correlated time series at different aggregation levels

Correlated time series at different aggregation levels Hi, In my time series data I discovered the following behaviour. My time series are available in 500ms intervals and are about sensor data like ...
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How can I test for changes in the distribution of categorical data over time?

Each week at my organization, we receive X number of type A messages, Y number of type B messages, Z number of type C messages...etc. I want to be able to test if the distribution of these message ...
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What are the odds of having the same Lawyer make a mistake in two wills involving the same person? [on hold]

A lawyer made mistakes in my will and were caught while I was alive to have it fixed and then a loved one died and it turns out the very same lawyer made a mistake in his will that the deceased can't ...
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deseasonalizing multiple series (more than 200 variables)

I'm trying to produce deseasonalization for multiple series using x-12 ARIMA (as an alternative, if you can manage, you also could provide an idea with other methods, such as x-13 ARIMA). The thing is ...
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Identifying Reoccuring Transactions [on hold]

What methodology(ies) would be best for identifying reoccurring transactions within an account if the only data one had on the transactions were transaction amount, date, and a categorical source ...
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Definition of $X_t$ in the context of Stochastic process and Time Series

In the book An Introduction to Stochastic Modeling , Stochastic process is defined as : A stochastic process is a family of random variable(s) , $X_t$ , where $t$ is a parameter running over a ...
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Difference between recursive and rolling window estimation

I am trying to check if my Auto Regressive Distributed Lag (ARDL) model provides stable estimates over time. I am not sure if I should be using a recursive or rolling window method. I know that the ...
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Problems with time series prediction

I got a question about modeling time series in R. my data consist of the following matrix: ...
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R Time Series Forecasting: Questions regarding my output

I'm working on a forecast for the following data: ...
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Hidden Markov model question; pseudo time series?

I apologize that the title of this question isn't super specific, but I am having a very difficult time exactly and succinctly describing the problem I am facing in my implementation of a hidden ...
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Estimate statistical significance of a feature in a time series

I have a set of time series with events marked in the middle. Following the event there is a temporary dip in the series values followed by a peak so that the area under the curve is 0. ...
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Regression Model Data - Changing exponential data into linear data

I have some 20 year monthly economic data that for the first couple of years is growing at a linear rate then grows at a slight exponential rate then in the last few years takes on a linear shape ...
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How to calculate the impulse response function of a VAR(1)? (With example)

How to calculate: 1) Simple IRF 2) Orthological IRF (Y2 -> Y1) Of an unrestricted VAR(1) model: $Y_{1, t} = A_{11}Y_{1, t-1} + A_{12} Y_{2, t-1} + e_{1,t}$ , $Y_{2, t} = A_{21}Y_{1, t-1} + A_{22} ...
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Detrending or Differencing in order to make a series stationary?

I got several time series for which I want to find out if they are stationary or not. So I computed for each series the kpss.test(). But before making further ...
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Is a random walk + white noise modal an ARIMA(0,1,1)? [on hold]

Let $Y_t=Y_{t-1}+\epsilon_t$ be a random walk and $Y_0=0$ Why is it true that the process $X_t=Y_t+\eta_t$, where $\eta_t$ is a white noise, so that $cov(\epsilon_t,\eta_s)=0$ for all $t,s$?
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Missing values in Time Series

Missing values are very common in large time series data. How should the missing values of a time series be estimated? Is interpolation useful or I need to forecast them from the past values?
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How do I check for seasonality at different time scales with Excel?

I have a table of e-commerce transactions. Sample data follows: ...
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which test should I apply to find which model is significantly different? [closed]

I have two questions 1- regression I have performed many regression models (10 models) and therefore, I have 10 prediction columns and one column or more for my real data (independent variables) ...
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backward shift operator as a sum (heuristic solusion)

I am interested in converting $(1-L)^n$ to a sum, where $L$ is backward shift operator. Let give you an example, \begin{align} \triangle^1 &=X_{i+1}-X_{i}\\ \triangle^2 & ...
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How can I see sample autocorrelation from time series plot?

Lets say I am given time series plot. How can I estimate $r_1$ and $r_2$ which are sample correlation? I don't understand how to see correlation from data plot. I know how to get and use ACF and ...
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Multiple time points, relation between quantified change in environment and sample population

For a current research, I'm trying to view a relation between a country-level variable index and the financial structure of companies in that country over time. I have annual data for four years, ...
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What does a random walk do exactly?

To be honest, I have read many websites and answers regarding to this question, and none explained it in simple words which are understandable. What I want to do is to understand what a random walk ...
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Season dummies in R [closed]

I have heating power data from one year (8670 observations). I also have regressors for day length and temperature (8670 observations also). I would like to add seasonality with 24h (1 day) 168h (1 ...
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Spectral density of product

Let $X_t$ and $Y_t$ stationary, zero mean, independent processes with $\phi_x(\lambda)$ and $\phi_y(\lambda)$ spectral densities. How can I prove that the process $Z_t=X_tY_t$ has a spectral ...
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how to specify range of lag in prewhiten CCF using package TSA in R

I am doing time series regression using package TSA in R. I have 2 time series, say x and y, so I started by doing prewhitened CCF. So, 2 issues I have encountered and would really appreciate if any ...
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Does it make sense to calculate the variance of a percentile measurement of a timeseries?

Developers often look at a percentile measurement of how long a task takes to complete as a measure of performance (e.g. 95th, 99th percentiles of page render time). However, in order to measure the ...
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OLS estimates consistent estimators of a pth order autoregression

I have a question from Hamilton's Time Series text. It is number 8.4: Consider a covariance stationary process of the form: \begin{equation} y_t = \mu + \sum_{j=0}^\infty \psi_j \epsilon_{t-j} ...
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bonferroni and scheffé' simultaneous confidence interval graph in minitab

I need to calculate bonferroni and scheffé' simultaneous confidence interval by hand as a homework. However, I also want to add minitab outputs and graphs to my homework task. How can I plot these ...
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How to Calcuate Segment & Symbol Periodicity

I want to calculate segment and symbol periodicity using R. Has any one done it before as i am relatively new to R? i have a lot of timeseries with irregular sporadic data and i want to find out if ...
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The constant term after 1st differencing

My instructor stated that when the dependent variable is 1st differenced, the constant term represents the deterministic change or trend in the dependent variable. When I search for information ...
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Providing 1 year monthly data (12 points), how to forecast next month

I got an interview question: Providing 1 year monthly data (12 points), can be traffic, product consumption, etc. How to forecast next month? I am confused. This question doesn't looks like a time ...
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Large-sample distribution of the Autocovariance function

I'm trying to understand property 1.1 below ($x_t$ is white noise), from Theorem A.7(also below). From the formula for the $W$ matrix, using the more convenient one, I get $W_{pq}=0$ when $p\neq q$ ...
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Understanding Chib (1998) Bayesian multiple changepoint model

Ungated link to the paper Chib, S. (1998). Estimation and comparison of multiple change-point models. Journal of Econometrics, 86(2), 221–241. doi:10.1016/S0304-4076(97)00115-2 The context of the ...
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How would you find the variance of an autocorrelated error?

Given the equation $e_t = pe_{t-1} + v_t$, and given the values of p and $Var(v_t)$, how would you calculate $Var(e_t)$?
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Holt-Winters optimal parameters with gradient descent

Can we use gradient descent in order to find optimal alpha, beta and gamma for Holt-Winters model? And more generally, are there any academic works that suggest methods for finding optimal values for ...
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DCC GARCH - specifying ARCH and GARCH parameter matrices in Stata

The command in Stata to estimate the DCC model of two variables is: mgarch dcc ( x1 x2=, noconstant) , arch(1) garch(1) distribution(t) $$ \begin{bmatrix} ...
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How to specify a state space model with cycle in this case?

I am trying to specify a state space model for the dependent variable from this graph. As you can see, there clearly seems to be cyclical behaviour. Therefore, I tried to specify the following state ...
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How many lags should I include in the VAR-model

When building a VAR-model with six variables I had the following situation: after building a VAR(1) the overall portmanteau test says that the residuals are ok (p=0.85, p_adjusted=0.22). But when I ...
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Definition of Time Series

Time series model is defined as : A time series model specifies the joint distribution of the sequence ${\{X_t}\}$ of random variables. For example:$$P[X_1\le x_1,\ldots,X_t\le x_t]$$ for all $t$ and ...