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

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Questions about ARIMA

I am estimating this model: But I want to do some analysis of the variables before. In particular, I am interested in fitting some ARIMA models. First, I am doing it for the inflation rate in Mexico. ...
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calculating mean and variance of non-stationary time dependent samples

I know normal procedure for calculating mean and variance which assumes that samples are iid.. I first want to know, how to calculate these two parameters if samples are time dependent but time ...
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1answer
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ADF test showing stationary for a non stationary series

I am running an ADF test in R on the following series: This to me is clearly stationary, but when I run the ADF test: ...
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1answer
27 views

Forecasting daily time series sales revenue with many zero entries

I have been trying to forecast the sales revenue of different product groups (the displayed sales revenue is aggregated over all products for each day e.g. smartphones with different prices as one ...
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1answer
12 views

Distributional assumption for a VAR model: is normality needed?

Do all variables in a VAR (Vector Autoregressive model) need to be normally distributed? Or there is no restriction about the distributions of the variables in this model (normal or otherwise)?
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Can somebody explain how can I graph PACF and ACF for AR(1) and MA(1) in R? [on hold]

I don't know what library or code to use? I'd appreciate if somebody can give an example code.
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Which features would you extract out of these time series?

I have around 2000 time series, each of around 40 values. In the image you see a random selection of 4 of those 2000 time series with a smoothed line in orange. I would like to calculate around 3 to ...
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1answer
18 views

Comparing similarity Time Series

I have a collection of time series data. The data is structured (Country, Year, Value). ~50 countries and ~30 data points for each country Is there a way to cluster time series? Time intervals are ...
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1answer
12 views

Statistically evaluate difference between time series

I have two time series. I want to evaluate if two time series are different enough in one window or space of time. The objective is to trigger an alert when one time series divert significantly from ...
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18 views

Panel data estimation

I'm making an estimate of a panel data model and i am a beginner at this. I want to know how many observations I need to make the estimation with a panel var. I have data from 18 countries for 20 ...
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1answer
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Why is Dickey-Fuller test applied on the difference operator and not on the variable directly?

Why is not the Dickey-Fuller test applied directly on : $Y_t = \rho Y_{t-1} + u_t$ instead of : $\Delta Y_t = (\rho-1) Y_{t-1} + u_t$. Many papers apply the Dicker-Fuller on the first difference ...
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Dynamic Time Warping w/ Different Sampling Rates

I am fairly familiar with the basics of calculating the Dynamic Time Warping distance between two time series but I am not sure if it can handle the following case: Two series sampled at different ...
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What process should be used to test an ON-OFF-ON-OFF experiment?

The problem: I have N (~500) black boxes which each receive an input and output a noisy reward signal. The reward signal is non-stationary and heteroscedastic, but can be assumed stationary over short ...
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Classification of time series using rolling window, window size

I’ve been experimenting with time series classification lately and I have some wonderings regarding real-time prediction. Assume “class a”pattern we trained with [0 1 2 3 0 ] Actual data [0 0 1 ...
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Does anybody know the ARIMA(p,q,d) models for the graphs and also X_{t} and Y_{t} graphs?

I have the following graphs and I need the X_{t} and Y_{t} graphs and ARIMA(p,q,d) models to which the graphs correspond? Does anybody know the graphs or does anybody know how to do this?
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21 views

Sketch without proof the ACF and PACF for the following time series

I have the following for which I need to Sketch without proof the ACF and PACF: $ AR(1)$ with $ ϕ=0.5. $ $ AR(1)$ with $ ϕ=-0.5. $ $ MA(1)$ with $ θ=0.5. $ $ MA(1)$ with $ θ=-0.5.$ can somebody ...
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1answer
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Is the time series $Y_t = \frac{1}{2} Y_{t-1} + \frac{1}{2} Y_{t-2} - \frac{1}{3} \epsilon_{t-1} + \epsilon_t$ stationary?

How can I tell if the series $Y_t = \frac{1}{2} Y_{t-1} + \frac{1}{2} Y_{t-2} - \frac{1}{3} \epsilon_{t-1} + \epsilon_t$ is stationary?
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1answer
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time series patterns for categorical variable

I have a large database, containing alarm data from a manufacturing cell. Each entry specifies the name of the alarm, and a matching identifying ID number. The alarm variable can only assume a number ...
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R Season in VARS function [on hold]

I am using the VARS function in R and one of my timeseries is seasonal (quarterly data). I found out that there is a seasonal argument that accounts for the seasonality. Does anyone know what it ...
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How do I to score changes to Index of Qualitative Variation overtime?

I am using an Index of Qualitative Variation to measure the mix of proportions of different dwellings in different cities, as shown on page 140 of this document: https://www.sagepub.com/sites/default/...
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VAR(p) models and its application in describing GDP growth

Im currently reading up on Vector Auto Regression models however I cant wrap my head around how you set a model to describe a variable. My goal is it use interest rate, imports and exchange rate to ...
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Mixed frequency in panel data estimation

I have a panel data of land transaction records covering around 300 cities.In which the dependent variables have quarterly time series data but most control variables are (and only meaningful) ...
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7 views

LOESS with multicollinearity test [on hold]

I wonder how should I apply multicollinearity test in R with LOESS function in gam package. Also, how should I check the result ? (for example of gam.check in mcgv package. There is no such a gam....
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1answer
28 views

How to find the p, q and d parameters for ARIMA given a model equation?

I have the equation $$ Y_t = 1/2 Y_{t-1} + 1/2 Y_{t-2} - 1/3 \varepsilon_{t-1} + \varepsilon_t $$ and I want to find the parameters p, q, and d. Can somebody explain how I can know what the ...
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How to avoid degenerate a transition matrix with a HMM? [on hold]

I'm using Matlab to fit a HMM to time series data. I discretize the data into 5 bins, then fit the transition matrix using: [estTR,estE] = hmmtrain(time_series_example,rand(2,2),rand(2,5)) ...
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22 views

Residuals Diagnostics Forecasting principales [on hold]

Help me please Are the following statements true or false? Explain your answer. Good forecast methods should have normally distributed residuals. A model with small residuals will give good ...
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1answer
32 views

Time series with two interdependent variables - is it possible?

I'm undertaking another project in R and I need to run a time series analysis. It's about topics mentioned in media articles and on Twitter. I realized that most probably (and according to past ...
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1answer
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Population autocovariance goes to zero, assuming covariance stationary

In time series context, let $\gamma_j=E[(y_t-\mu)(y_{t-j}-\mu)]$ denote population autocovariance, where $\mu$ is population mean of $y_t$, assuming covariance-stationary. Then, $\gamma_j$ goes to $0$ ...
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1answer
21 views

Imputing nested time series data with R

Does anyone know what is the superior algorithm to impute data in time series? I had strong dropouts over time because it was free to participants how many times to participate in my study (otherwise ...
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1answer
87 views
+100

Sum of autocovariances for AR(p) model

Suppose I have the following $AR(p)$ model. $$X_t = \sum_{i=1}^{p} \phi_i X_{t-i} + \epsilon_t\,, $$ where $\epsilon_t$ has mean 0 variance $\sigma^2$. I am not interested in fitting this model, but ...
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Time series data with mixed calendar and fiscal year

I am performing time series analysis with yearly frequently. However I need to regress a data compiled by calendar year against another compiled by fiscal year. Is it possible to deal with this? If ...
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How to fit an autoregressive (AR(1)) model with trend and/or seasonality to a time series?

I want to model an observed time series as a function plus an AR(1) process. The model has one parameter $\alpha$ and I would like to fit it. The trend/seasonality function may be non-trivial. ...
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Constant Terms in Linear Projection

In my time series textbook, it says, "Let $Y_i$ and $Y_j$ be two dependent variables in a time series process, e.g. $Y_{t+1}=\phi Y_{t}+\epsilon_{t+1}$, where $\phi$ is a constant coefficient. If a ...
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2answers
61 views

Time Series Forecast / Transfer Function

I'm trying to interpret the forecast values from an ARIMAX function, and I'm confused about what's happening in the actual forecasted values as I change the values for the predictor during the ...
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1answer
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Does optimizing the parameters in an exponential smoothing model constitute “learning”?

I'm having an argument at work with a colleague who's saying that we need to use machine learning models instead of the current exponential smoothing models (Holt, Holt-Winters) for demand forecasting,...
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AIC and BIC and number of quantization level

I want to test how many quantization levels (discretizing levels) are the best for the given data(time series) set I have. Therefore I am applying different levels of binning (like discretisize data ...
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Estimation and testing of unconditional distribution in time series models

In time series models, such as ARMA-GARCH, is it possible to estimate what the unconditional distribution is? Given that the time series is auto-correlated / persistent, how many observations would be ...
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Error in merge.zoo in R [on hold]

I try to interpolate irregular space time series into regular space, for analyzing meter value (export Wh of gas meter), by referring from this link: https://stackoverflow.com/questions/38723185/how-...
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Bacteria in hours [on hold]

How would I show a line graph of bacterial growth in 10 hours. Time on x axis and bacterial growth on Y axis. Bacterial growth reaches 262,144 in 10 hour period?
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Nominal values, constant prices and exchange rates comparability issues

I want to analyse several variables expressed in different units of measurement. X is expressed in 2017 costant prices (euro and national currency) and Y in current dollars. In what unit of ...
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Grouping similar time series (clustering, cointegration)

I have a number of time series' that I am effectively trying to understand which are similar and which can be grouped together. I have some idea of what should be grouped with each other but I am also ...
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26 views

difference between LOESS and Spline

I wonder what is the difference between LOESS and Spline. I heard that LOESS is similar with Moving Average. So, is Spline(s) from mgcv::gam is also similar with moving average ? if not, please ...
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1answer
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What model would you suggest for this?

I have been trying to understand what model i should fit to these... I find it hard to understand the shape of ACF. What ARIMA(p,d,q) model is suitable for this data? THANKS... :)
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Does it make sense to analyse an autocorrelation matrix with Random Matrix Theory?

I wonder whether you can gain valuable information about a time series by analysing its autocorrelation matrix using RMT. I know that RMT can help to extract information about the collective ...
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Metric to evaluate accuracy of time series decomposition?

I am trying to de-seasonalize a large number of business sales data. They all come from the same industry and follow idiosyncratic seasonality patterns. The number of businesses is quite large, and I ...
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Why does the Yule Walker estimator show this bias?

In R, I simulate an ARCH(1) process, i.e. $\sigma^2_t = \alpha_0 + \alpha_1 X_{t-1}^2 \rightarrow X_t = \sigma_t Z_t$. Having done so, note that $$X_t^2 - \sigma_t^2 = X_t^2 - a_0 - a_1X_{t-1}^2$$ ...
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Does sample size impact Breusch-Godfrey test results

I performed DW test (DW=4) and Godfrey test (Godfrey=4) on a small sample size (60 observations). The DW test results accept the null hypothesis (4 Pr0.05). However, for Godfrey test, only AR(1) ...
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1answer
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Temperature time series forecasting predictions converging to a certain value

I am trying to forecast the value of the ambient temperature based on given data on Python. The data frequency is 15 minutes. In order to predict future values, I am using a simple autoregressive ...
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2answers
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How to define a time series classification problem?

I have 3 sets of time series data generated from sensors, I believe they have some correlation themselves. Certain "modes" of the system can be defined from the patterns from these signals. The signal ...
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R parallel Processing code is taking time in Server [closed]

I am using Parallel Processing to build multiple models for each Product when I am running code in my laptop (i5 4th generation) is taking 100 seconds to build models for 1 Product. When I am using ...