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

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PACF for MA(1) process

I have MA(1) process: $X_t=\epsilon_t+\theta\epsilon_{t-1}$ I want to proof the equation for PACF for $n>=2$ $\alpha(n)=\phi_{nn} = \frac{\theta^k(-1)^{n+1}}{1+\theta^2+...+\theta^{2n}}$ I ...
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8 views

How to use R to get drift rate and volatility rate of stock prices changes?

I am doing a research on the historical annual stock prices changes, where I have about 30 rows of annual stock prices. How can I use R to get the drift and volatility rate?
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82 views
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Beginner level: Help in learning Kalman Smoother (Part 1)

Parameter estimation of Linear Dynamical system is a tutorial which explains Kalman Filter, Smoothing, and Expectation Maximization. I have followed the derivation for Kalman Filter. But cannot ...
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5 views

How to prove that Innovations in the Innovation Algorithm are uncorrelated?

I tried to search on the internet but could not find a proof... For the innovation algorithm, I am refering to the one used in the time series analysis to predict unknow value.
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Help in State and parameter estimation for a time series model excited by binary input

An IIR system is excited by a pseudorandom binary signal $z_n$. The output of the system is corrupted by zero mean additive white Gaussian noise and this is observed, i.e., $y_n = \mathbf{h^Ty_{n-1}} ...
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15 views

Timeseries forecasting (Cointegration)

I am trying to forecast commodity price fluctuations in a small dataset. The data I am using is here . Does my data have seasonality and Trend? Can someone explain me how to decide that? If my ...
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2answers
216 views

Timeseries analysis procedure and methods using R

I am working on a small project where we are trying to predict the prices of commodities (Oil, Aluminium, Tin, etc.) for the next 6 months. I have 12 such variables to predict and I have data from ...
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4 views

Doubt in representing Kalman filter equations

I want to represent the following 2 models as a state space representation using Kalman filter. Will be grateful is somebody please let me know if my approach is correct and rectify, if otherwise. ...
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2answers
72 views

STL + Random walk failing

We have four months of data (10 minute interval), this seems have nice pattern (at least for eye ball). We are using STL to decompose the time series and apply "random walk" to project next month ...
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7 views

What is the appropriate way to compare regressions between two time series

I have two temperature time series, both sampled at the same rate and over the same time period. What would be the correct method to compare the slopes of the linear regressions of these two datasets ...
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11 views

Can I combine stationary and non-stationary variables in a VAR model? [on hold]

Using two variables for a VAR model, I observed that one of the variables is I(0) and the other is I(1). Should I difference the non-stationary variable and combine it with the I(0) variable, and form ...
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15 views

Can the chi-squared be used to test monthly means for two time series?

Can chi-squared test be applied to compare two continuous random variables but where instead of counts we split samples into groups and into cells of the table we put means for groups? In our case we ...
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2answers
102 views

Finding occurrences of specific patterns in time series

I have to locate occurrences of Cyllinder, Bell and Funnel patterns in univariate time series $X$ of gamma-ray sensoring. This is a specific case of the general CBF synthetic problem found in a few ...
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3answers
108 views

Transforming time series to compensate for change in variance

I have a time series (shown below) that comes from a sensor whose calibration was changed in the middle of last year. As part of this change, the sensor's reading of the variance (or volatility) of ...
2
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1answer
33 views

What is the “scale” parameter in “continuous autoregressive model” in cts package?

I am trying to use the "car" command in "cts package" in R program and I see the "scale" parameter there. I wonder whether this can be assumed to be equivalent to time intervals for time series ...
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54 views
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How to use lagged dependent variables (panel data) in practice?

Working with a panel data set with a daily time series structure I was told to include a lagged dependent variable. The dependent variable is daily electricity consumption of a medium size sample ...
2
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1answer
674 views

Forecasting daily data with trend, yearly, day of the week, and moving holiday effects

I'm expanding a question I posed earlier because I think it was lacking detail. I'm attempting to forecast daily demand for a restaurant that sells take away food, primarily to office workers on ...
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1answer
227 views

How to use error term in AR (2) model for predicting future values?

We use turbidity to estimate suspended-sediment concentration (SSC)- our data was serially correlated. We ran an ARMA process and ended up with a AR (2) model. Our equation in log form is: ...
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8 views

Generating sample [on hold]

How to generate a sample of size n = 400 from the deterministic trend model yt = 1 + t + et, where et is normally distributed white noise with mean 0 and variance 2500? I don't know how to begin? any ...
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11answers
14k views

Books for self-studying time series analysis?

I started by Time Series Analysis by Hamilton, but I am lost hopelessly. This book is really too theoretical for me to learn by myself. Does anybody have a recommendation for a textbook on time ...
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1answer
124 views

Contingency table with 2 different time series

I am trying to put the two time series of my Excel spreadsheet (see link below), into a contingency table. https://www.dropbox.com/s/2f96oylxj97fuih/example.xls The first series is the number of ...
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0answers
39 views

preferential multinomial model (with memory)

I am modeling a system that is like having a container of an infinite number of colored balls. On each day $t$, I pull out a new set of $n_t$ balls and I count the number of balls that are red, green, ...
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7 views

Distribution of test statistic in ARCH LM test

To test for ARCH effects in a time series, there is the ARCH LM test. Its test statistic is $\chi^2(n)$-distributed, where $n$ is the number of lags in the test regression. But if you have run ...
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1answer
170 views

Data analysis: Time series for Bacterial population data

Could anyone please help with data analysis. Briefly, I am studying how the population of a bacteria changes at different points (port 1 to port 10) within a biofilter over the course of 30 days(like ...
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5 views

How to obtain cross-correlation function from cross-spectrum?

I have implemented a piece of code based on the Lomb-Scargle approach for determining the cross-spectrum of two time series. My cross spectrum contains complex numbers and I have used the basic fft ...
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2answers
135 views

Measuring length of intervention effect

I ran a study in which participants were randomized to either a control or an intervention, with outcomes in the form of time-to-event data. While overall time-to-event is shorter in the intervention ...
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23 views

Augmented Dickey-Fuller Trend and Intercept

I am trying to determine if I should include an "intercept" or a "trend and intercept" when using the Augmented Dickey-Fuller (ADF) test. I ran a regression with my dependent variable and a time ...
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9 views

Add columns and Arithmetic with Time in R [migrated]

I`m new in R. I have a table in .csv format with 12K rows like below: ...
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1answer
44 views

Measures to compute the similarity between two time series whose amplitude is periodic ignoring any phase differences

Question: Given two time series whose amplitudes are periodic, what measures could i use to quantify the similarity between them ignoring any phase difference? Specifically, i am looking for measures ...
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24 views

Arima modeling with limited data

Our 250 weekly datapoints are shown in the figure, along with correlograms of 1st differences. Are we correct to conclude, from overdifferenced correlogram, that for this process we should have much ...
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1answer
33 views

Time series periodicity bootstrapping

I'm interested in analysing the periodicity of a parameter X, measured over time on cells. The method I am using is destructive, so I cannot follow the same cell over time, but I am rather measuring ...
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14 views

Questionable Output from Time Series Forecast Using MSTS and TBATS from R forecast package

Using historical daily order totals, I'm wanting to forecast the totals of the next 7 days. It's known in my field that these totals fall subject to weekly and yearly seasonal trends. Called ...
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1answer
42 views

Normalized RMSE

I have several time-series in a VAR(1) and, due to some of them haven't the same unit of measure, I'd like to estimate the RMSE in percentage. I know that it could be done in several ways (see below) ...
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9 views

Correlation/similarity binary time series

Which are the best or most used methods to find similarities between binary time series? ...
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2answers
224 views

What is the implication of unit root of MA?

A ARMA(p,q) process is weakly stationary, iff the root of its AR part is not on the unit circle. So its weak stationarity doesn't depend on its MA part. But what can the positions of the roots of its ...
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How to obtain cross-spectrum using the Lomb-Scargle approach?

I would be interested if you could direct me to an implementation in R for finding the cross-spectrum because all the implementations I have seen deal just with the power spectrum.
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1answer
24 views

Identities in a VAR model

I am working on a VAR model where one of the equations is an identity. For example: $$ \begin{cases} A_t = \alpha_{11} + \alpha_{12} A_{t-1} + \alpha_{13} B_{t-1} + \alpha_{14} C_t + ...
2
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1answer
107 views

Does dummy interention variable (pulse or step) must be differenced when it is added to ARIMA model?

I have read some opinions from this forum and from other sources that when the dependent variable in any from of ARIMA model (whether ARIMA errors, ARIMAX or transfer function)is differenced, you ...
2
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1answer
65 views

Kalman filter with control inputs in python?

i am trying to fit a simple kalman filter with input controls (in this case step input) in python. i am using filterpy (http://filterpy.readthedocs.org/). my code is: ...
2
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1answer
276 views

Analysis of discrete (count) time-series data

I have a 2X2 factorial experiment where I am interested in seeing the effect of two different nutrient solutions (N and W) on the appearance of root tips of two different plant species (A and B). I ...
2
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1answer
21 views

Suggested method for estimating door counter stats when data is lost

I'm wondering if you have any advice about a methodology to use to estimate "door counter" stats (i.e., an automated count of visitors to our organisation, based on "break beam" door counters ...
2
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1answer
235 views

Time Series Data Mining Library?

Can anyone recommend a library for time series data mining tasks other than predictive modeling and statistical analysis? There seem to be a number for these purposes (e.g., Gretl), but nothing for ...
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21 views

the decision of being White noise on e-view

And for example, let's take SMA(2) model in this table does there exist white noise ? Which value I observe to decide the existance of white noise? Please explain it. Thank you
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35 views

White noise ACF - PACF

I found PACF and ACF like the following table . But, how can I decide whether there exists white noise? And what is white noise? If there is no white noise, can I say being stationary?
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1answer
99 views

Chow's test and serially correlated model errors

how can one handle a time series with the Chow's test (in order to find a structural break) so that the assumption of independent model errors holds? I'm using the R function chow.test {gap}
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7 views

Extract ETS method used for automatic forecasts of hierarchical time series with hts package [migrated]

I'm trying to extract the ETS method that is automatically chosen when we apply the forecast function to an hierarchical time series using the hts R package. When I look in the structure of the ...
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34 views

Incorporating intraday data into end-of-day forecast

my target variable is observable intraday but I am interested only in EOD forecasts. I will denote the variable $\ y_{D,24}$ as the reading of interest for day D is ...
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r package for non-decimated /stationary wavelet [on hold]

Which r package is should be used for forecasting and plotting stationary wavelet transformation?