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

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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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Resource request: parameter estimation based on PN sequence as input

In system identification or parameter estimation, various input signals are used for exciting the process models. I am interested in parameter estimation of time series model using pseudo random ...
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19 views

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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1answer
58 views

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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114 views

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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2answers
92 views

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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23 views

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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34 views

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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32 views

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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22 views

which test should I apply to find which model is significantly different? [on hold]

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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17 views

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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40 views

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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293 views

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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1answer
34 views

Season dummies in R [on hold]

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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43 views

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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29 views

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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33 views

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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28 views

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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1answer
33 views

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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Time Series Comparisons - Econometric Study [closed]

I'm trying to determine if econometrics from two industries change in a statistically significant way over time. Essentially, did one industry outperform the other after a certain date, or are there ...
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35 views

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 ...
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root mean square error in forecasting

I have to use ARIMA model to forecast real prices of aluminium and copper in eviews. I have to do in sample and out of sample forecasting. my data set is annual from 1960 till 2014. I have selected a ...
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Suggested algorithms for time series analysis of sporadic events

I have a series of sporadic, discrete time series events that appear to occur in shorter interval clusters and I am looking for a way to determine the frequencies at which the events occur. None of ...
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The sample variance is an inefficient estimator of the conditional variance in a t-GARCH model?

Harvey states in this paper (2008) at the end of the second page that: "The possible inappropriateness of letting $\sigma^2_{t|t-1}$ be a linear function of past squared observations when $v$ is ...
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Matlab : Help needed in correcting the implementation for Kalman Filter

I have implemented the Kalman Smoothing with Expectation Maximization based on the Paper Parameter Estimation for Linear dynamical system. All notations are based on this paper. The model is an IIR ...
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19 views

Differencing a series and back

I've followed this procedure: I have a non-stationary process (call it 'series_1'), which I try to render stationary by differencing. The largest value of the process (8760 observations) is about ...
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determinstic trend in VAR-models

I'm asking myself the following question. I want to build a VAR-Model with 6 time series A, B, C, D, E and F. I analysed every series univariate and I found out that A, D, E and F are stationary and B ...
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Conditional Entropy and spearman Correlation based lag in time series

I have two time series A, B. Both are seasonal and B primarily is A driven( other temporal causes may occur). B-Red, A- Green I want to calculate lag of red series with respect to green as clearly, ...
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Is the the dependence of the residual of a ARMA time series model only based on AR term?

Lets suppose we fit two time series models AR(1) and ARMA(1,1) to a data series. Should be the results of the ljung-Box test for the residuals be the same for these models? I mean does MA term affect ...
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Relation between raw and central moments

This question arose when reading Johansen's likelihood-based inference in cointegrated VAR models, the 2009 reprint, page 146. I will do my best to make my post self-contained. Let $Z_{0t}=\Delta ...
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1answer
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Estimate linear regression paramaters with chain modeling for longitudinal data?

Within a frequentist, deterministic paradigm of multiple linear regression, is there a (standard) method to accomplish "chain modeling for panel data" in a way that avoids formal identity (and/or ...