# Tagged Questions

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

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### High order Markov Chain transition probability

I'm modelling a time series using high order markov chain and estimate the transition probability of the equivalent first order markov chain. The problem is that some of transition in the equivalent ...
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### On properly setting up a Control Chart

Let me present to you the way I have being 'doing' control charts up until now. I have a series of $k$ samples of size $n$. I calculate the the sample means $\bar{x}_i$ and the grand mean ...
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### Model estimation procedure using backward elimination

I have run a multiple linear model using Minitab. The result showed that all variables are not significant. So, I use backward elimination. Lastly, I found that ...
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### Why we need for detecting and removing outliers?

Suppose we use some time series (rainfall) data and some outlier detection methods for detecting outliers. In this situation If we remove the outliers, then what are the causes affected by the ...
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### Combine several softmax output probabilities

I would like to combine the outputs of five neural networks, each with a softmax output layer of three classes each. A typical, example output is shown below:- where Figure 1 is the output of model ...
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### How to correct outliers once detected for time series data forecasting?

I'm trying to find a way of correcting outliers once I find/detect them in time series data. Some methods, like nnetar in R, give some errors for time series with big/large outliers. I already managed ...
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### Quantile regression

I have a question regarding quantile regression. Supposing that I have 10000 observations with one response variable and several predictor variables in a dataset collected each year over several ...
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### Does ARIMA require normally distributed errors or normally distributed input data?

I have two questions related to time series forecasting with ARIMA: Does ARIMA require normally distributed errors or normally distributed input data ? Are there any assumptions on input time series ...
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### Time series data analysis - determining significance between treatment and control

We have some time series data for evaluating the effect of a drug in an animal model, with two dose levels and a control. So far we've looked at ANOVA for each time point, and there's a significant ...
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### Summing variance of autocorrelated timeseries

Problem: When trying to calculate the variance of timeseries sums I get a negative variance, mostly due to autocovariances at large lag steps. Does not seem realistic. I have a timeseries which is ...
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### Boosted AR for time series forecasting?

I have time series data recorded at multiple locations, stored in a matrix $Y$. I have fit a Vector Autoregressive Model to it which forecasts the data pretty well on a test set. However, if I plot ...
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### Running a Tukey's test on a repeated measures ANOVA in R

I've come across several posts dealing with post hoc tests of Repeated Measurs ANOVA. I came up with the below code in R to attempt this, but considering some of the posts on this subject I wanted to ...
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### Statistics for multi-test replicated correlation analysis

I'm analyzing pairwise correlations of time series between two different types of microarrays done for several samples as biological replicates. So, I have M1 number of variables on type 1 array, M2 ...
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### What are disadvantages of state-space models and Kalman Filter for time-series modelling?

Given all good properties of state-space models and KF, I wonder - what are disadvantages of state-space modelling and using Kalman Filter (or EKF, UKF or particle filter) for estimation? Over let's ...
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### Best way to visualize predictions from a linear model

Let's say I'm doing some predictive analytics and am trying to predict US GDP per month using a two or three month lag. After every month, I generate new predictions and am able to compare my ...
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### Time series (stochastic process) estimating parameters using characteristic function

I have a time series of assets ${A_1, A_2, ..., A_n}$, which is described by a sophisticated distribution having the following characteristic function: $\phi(u; t;\theta)$, where $\theta$ is a vector ...
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### Which one of these looks stationary?

Step 1. To answer "Final Question" ( linked: "THE FINAL QUESTION : Order of differencing, to achieve stationary and interpretation of arima() , acf, pacf?") Expecting to find correct order of ...
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### Time series forecasts of appointments with pre-reqistration

Looking for some tips and ideas. I get a list every day of the number of appointments for each day for the next two weeks for a clinic. I have quite good history of these list, and the actual number ...
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### Order of differencing, to achieve stationary and interpretation of arima() , acf, pacf? [on hold]

** What is the "order of difference" to achieve stationary? what is the "lag" value? what does [12 ] in ...
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### why sinusoid pattern in correlogram

Why does the ACF of an AR(1) contains sometimes a sinusoid-like pattern? and what does it mean? EDIT I think the time series is fit to AR(1). As I understand it, in an AR model, the value of x ...
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### ZScore threshold and low values time-series

Example of z-score computation: 1 - E.g. Time-series: [0, 0, 0, 0, 1] Current: 1 Mean: 0.2 Std: 0.44721 Z = (1 - 0.2) / 0.44721 ~= 1.7888 2 - E.g. ...
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### Diagnostic for VAR model. non normal

I have some problem about my model. my model is based on VAR. (vector auto-.) well, I've tested ARCH test, BG test(autocorrelation p) and jarque.bera.test. Model is stable. Also I got good result for ...
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### ARIMA vs ARMA on the differenced series

In R (2.15.2) I fitted once an ARIMA(3,1,3) on a time series and once an ARMA(3,3) on the once differenced timeseries. The fitted parameters differ, which I attributed to the fitting method in ARIMA. ...
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### How to analyse my time series experiment

I have a question about how I can analyze the data from a time series experiment. I'm still a student and therefore am not really familiar with all the procedures and analyzes in SPSS, so i hope ...
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### Stationarity in multivariate time series

I am working with a multivariate time series and using VAR (Vector Autoregression) model for forecasting. My doubt is What does stationarity actually means in a multivariate framework. 1) I know ...
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### ARIMA Representation using polynomial long division

I have 2 questions from Tsay's book, dealing with ARIMA representation. I. How does the division of the polynomial work - what are the steps that lead to the solution they show? They show a "simple" ...
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### ARIMA with seasonality in Statsmodels

I'd like to have a seasonal ARIMA model implemented with Statsmodels ARIMA. Specifically, I'd like to log before the weekly seasonality and then be able to make forecasts. Perhaps an example with ...
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### How can I find out how shifts in a country's fiscal policies affect its economic health?

I have the values of certain variables for 20 years for different countries... I am unable to understand how to use the values of a particular variable for 20 years. Could anyone suggest how I should ...
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### Neural network for prediction

I am working on Neural Network for a regression problem in R using packages like nnet, caret etc. I have split my data into train, validation and test. My doubt is does the train() function in caret ...
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### What are some examples of real-world processes that are well-described by AR, MA, ARMA, or ARIMA?

Subject says it all - AR/MA/ARMA/ARIMA are often described as workhorses of time series analysis. But what are some real-world examples where these methods gave great results, and another more modern ...
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### Detrending & cross-correlation function

I am looking for some help with my time-series data. What is the best method of detrending/transformation of these two variables, so I do not violate assumptions of stationarity when applying a cross ...
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### Temporal autocorrelation in perMANOVA?

I have a data set where samples are collected once per year for 15 years at a number of sites. I am worried that these data are temporally autocorrelated and was trying to figure out if I need to ...
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### Finding a leading indicator of a time series

I am interested in finding a leading indicator of $Y_t$. Is it sufficient to find a variable $X$ for which its lagged value is correlated with $Y$? Do I have to give consideration to the spurious ...
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### Probabiltiy density function after embedding

I have a 1D noisy time series which has a probability density function (pdf) of P(X). If I embed X into $d$ dimensional higher space using Attractor reconstruction into $U$ then will the pdf and cdf ...
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### Time series as cross-sectional data

I have time series, for example, gdp and unemployment(unemp), freq= 4. What if I interpret it as cross-sectional data and do cross-sectional analysis instead of time series? My task is to test how ...
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### How to combine time-series based features with different frequencies

I have 3 features which I want to use in my classifier. They are all time-series data-based. However, they are all at different frequencies and there have different matrix dimensions. I was wondering ...
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### Using simpler models in place of more generalized and complex models

I was reading about BATS (Box-Cox transformation, ARMA errors, Trend and Seasonality) and TBATS (Trigonometric, Box-Cox transformation, ARMA errors, Trend and Seasonality) models. I was wondering ...
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### Principal component analysis with time series

When you do a Principal Component Analysis (PCA), your dataset generally looks like the following one: ...
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### When is it appropriate to select models by minimising the AIC?

It is well established, at least among statisticians of some higher calibre, that models with the values of the AIC statistic within a certain threshold of the minimum value should be considered as ...
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### One time series tends toward the (linear) function of another time series, how to find that function?

I have two time series $p_t$, the daily market price of a particular kind of good $f_t$, the daily production of such good Now assume that there is a unique relationship that tells you the optimal ...
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### Auto-Regressional & Moving Average Model Formula Properties

I seeking help in understanding specific values underlying the formula's for the MA(p) model & the AR(q) model. I am attempting to implement the models (building up to the combined ARIMA model) in ...
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### Cancellation operation in time series analysis

When studying the time series analysis, I read the following example. I do not know how to understand this cancellation process. Yes, it can be cancelled like normal algebraic formula. But this āzā ...
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### How to obtain the model behind a simulator?

I am looking for an useful statistical approach or analysis tool in order to understand the data obtained from an aeroelastic simulator of wind turbine dynamics. In this case, the simulation provides ...
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### ARIMA estimation by hand

I'm trying to understand how the parameters are estimated in ARIMA modeling/Box Jenkins (BJ). Unfortunately none of the books that I have encountered describes the estimation procedure such as ...
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### Multiple linear regression question

I am running a multiple regression of the form Y = $\beta_0$ + $\beta_1$*$X_1$ + $\beta_2$*$X^2_1$ + $\beta_3$*$X_2$ + $\beta_4$*$X_3$ on a time-series dataset. I want to plot the relationship ...
I have time series data of credit card transaction volumes for different companies. For example: week1: \$5000 week2: \$6000 week3: \$6200 week4: \$7000 week5: \\$9000 ... Is there a simple method in ...