# Tagged Questions

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### Is there any tool that can do Vector ARIMA modeling in time series

Vector ARIMA model is used in multiple time series analysis. I am just wondering if there is any software or tool can be used to build the model. Some tools,like R, can only be used to predict the ...
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### Representation of ARMA processes

Question Consider the following process: $$2y_t-3y_{t-1}+y_{t-2}=\epsilon_t-\theta\epsilon_{t-1}$$ What is the model for the process $w_t=\Delta y_t = y_t-y_{t-1}$? Attempt I have solved the ...
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### What is the difference between forecasting based on ARIMA and logistic curve? R

I'm making a project connected with identifying the dynamics of sales. My database concerns 26 weeks (so equally in 26 time-series observations) after launching the product. This is what my database ...
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### Is ARIMA model appropriate for this dental research?

Please, I have a doubt in my study for doctoral thesis… Title: “Development of a thermal cycling protocol for dental materials”. Objective: to create a protocol for thermal aging, from measurements ...
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### High Ljung-Box p-values at large lags

I am trying fit an ARIMA model to stock returns. I have reached a decent model using the AIC criterion. However, the ljung-box p value under a diagnostic plots are pretty weird. The null ...
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### ARIMA SARIMA model mathematical formula

I need help writing a SARIMA model I have obtained mathematically. My model is ARIMA(1,0,4)(2,0,2) period 12. I understand what the different parts actually mean but get very lost trying to write ...
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### Time series and stationnarity tests

I perform some time series fitting with the help of the forecast and urca packages. I have a question regarding the correspondance between results coming from statistical test such as KPSS, ADF or ...
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### Estimation of residual in ARIMA model

How do I estimate the residual $\varepsilon_{t}$ of a Seasonal ARIMA model $\hat{Y}_t=\hat{\phi}{Y}_{t-1}+\hat{\Phi}{Y}_{t-12}+\varepsilon_{t}$? If the MSE is 0.114, what does it mean?
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### Separating Base and Promotional Volume

I am working on a project where I have to separate base and promotional volume from the sales data. I have sales data for the last 4 years at week level. How can I separate base and promotional volume ...
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### Arima modelling estimate in SAS and find out if model is adequate or not

I have been attempting to do an ARIMA modelling in SAS. The series is not stationary but when I estimate the ACF and PACF p-values I don't get appropriate answers to find out if my model is adequate ...
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### ARIMAX for modelling daily sales

I am trying to model daily sales for a take out restaurant. They are only open on business days - no holidays or weekends - as their primary clients are office workers on their lunch breaks. Below is ...
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### 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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### Warning message in auto.arima

I am using auto.arima() for prediction, and getting the following warning message. I want to know if I can ignore this warning message or if I should be worried. ...
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### Calculating phi11 (or phi22) from an MA(1) process

I've come across a question where I have an MA(1) process like so: $X_t = b_t - 0.4 b_{t-1}$ (where $b_t$ is a white noise process and $t$ is the time index) The question asks me to find $\phi_{11}$ ...
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### Regression with TBATS error?

I'm working on a time series model which includes multiple seasonal components (daily and weekly). I believe the best way to approach this would be BATS/TBATS model, however I have a concern if I can ...
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### How do I interpret regression coefficients with autocorrelated residuals?

I am building a regression model of time series data in R, where my primary interest is the coefficients of the independent variables. The data exhibit strong seasonality with a trend. The model ...
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### Combining ARIMA models

I have $n$ ARIMA(1,1,1) models. $Y(t)= \mu + Y(t-1) + \phi(Y(t-1)-Y(t-2))-\theta\epsilon(t-1)$ They are all trained on different blocks of data for the same univariate time series. Now I get a list ...
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### help on how to include term $\exp(β_t)/(1+\exp(β_t))$ in AR(2) model

I am trying to include a term in an AR(2) model: $$Y_t=\left( a_0+a_1 \frac{\exp(\beta_t)}{1+\exp(\beta_t)}\right)Y_{t-1}+bY_{t-2}+\delta\epsilon_t$$ Can anyone please help me with this? I don't seem ...
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### SARIMA (1,1,0)x(1,0,0) [duplicate]

Can anyone please write out the model of the ARIMA(1,1,0)x(1,0,0) with AR(1) coef 0.0902 SAR(12) coef 0.107 constant 0.15. Am really confused with how the model should look like
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### Performing a time series ARIMA model on natural gas power demand using the forecast package from R

I've been attempting to forecast natural gas power demand and how it is affected by temperature and price. I'm not sure if I have done everything correctly (relatively new to R), but I do seem to get ...
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### Fitting a reduced-form MA(3) time series model in R

I am trying to fit an ARIMA model for a certain financial time series. I've used EViews for modeling, and have decided to fit a so-called reduced-form MA(3) model, where only the third lag is ...
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### What are the stationarity requirements of using regression with ARIMA errors for inference?

What are the stationarity requirements of using regression with ARIMA errors (dynamic regression) for inference? Specifically, I have a non-stationary continuous outcome variable $y$, a ...
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### Distribution fitting (maximum likelihood) for autocorrelated data

I have some time series data that shows autocorrelation and seasonality. I want to fit a distribution to it. To use maximum likelihood it needs to be uncorrelated. I first fit a GARCH and an ARIMA ...
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### Time series analysis for 2 series where one is dependent on another

If I have two time series $A$ and $B$. $A$ is dependent on $B$. I want to forecast future values of $B$. What statistical techniques should I learn and try? As an example consider a time series of ...
192 views

### Good references for time series?

I am wondering if anyone has book references for time series. I would like something comparable (in popularity) to the 'ESL' or to 'Machine learning' from Murphy in the machine learning field. Does ...
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### ARIMAX model's exogenous components?

Does anyone know, considering an ARIMAX model that fitting a stationary process Y, then does the exogenous components for the model need to (weakly) stationary? I think exogenous components can be ...
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### Forecast model developed now, but only used later, is it still valid?

I am not sure what the appropriate title for my question is, so I am open to suggestion/correction. Now, the question: I observed a daily series $X_t, t=1,...,T$ also series $Y_t, t=1,...,T$. ...
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### Solving for arima and exponential smoothing coefficients

I am looking to How do you solve for the optimum values with the lowest MSE for the coefficients and dampening constant in exponential smoothing and ARIMA models? What are the equation used?
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### R - ARIMA model with long seasonal periods - Error: “length of x and xreg does not match”

i want to use an ARIMA model in R for predicting an electrical load on a minutely basis. By examining the ACF I figured out which model could suit. The ACF has shown that the value one day ahead has a ...
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### Removal of abnormalities in a month-data

I am studying the article Barcelona baby boom: does sporting success affect birth rate?. They are using month-data for their analysis of birth. They have normalised one month to be 30 days. So they ...
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### Examples of time series models on other than economic data

All our text book examples are based on macro economic problems, but there must be many applications of time series models on other data, such as for example windspeed, average heartbeat, gas turbine ...
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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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### 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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### 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 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 can I form ARIMA equation given MA and AR terms

Above is output from SAS. What would be the corresponding ARIMAX equation? I would appreciate if someone could help me write the mathematical equation, preferably in the following form:  Y(t)= ...
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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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### 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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### Why does differencing time-series introduce negative autocorrelation

For example, this mentioned here: link. I also saw this in my data. I wonder - does anyone know a good reference where this is explained and justified more rigorously with some math and for some ...
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### What are the assumptions of ARIMA modeling for forecasting time series?

What are the assumptions of ARIMA / Box-Jenkins modeling for forecasting time series?
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### Estimate single ARIMA for multiple timeseries

I have two groups of time-series, each group represents one type of data. However within each group, each time series may be fitted with a different ARIMA(p,d,q) from the other time series in the same ...
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### Extract BIC and AICc from arima() object

Problem: I would like to extract the BIC and AICc from an arima() object in R. Background: The arima() function produces an output of results, which includes the estimated coefficients, standard ...
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### Pandas Statsmodels Time series seasonal forecasting

Using Stats models and Pandas (and requests for the data) I'm working on a forecast model.. my 1st step is just getting the Arma function working and understood. My data is available publically and is ...
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### What is the minimum historical data/sample data required for a time series forecasting analysis?

Are there any statistical power analysis/sample size deteminations methods for time series data analysis/forecasting? For example if I have time series of 30 data points, how can I with confidence ...
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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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### Transfer functions in R (TSA package)

In Time Series models’ transfer functions there is a decay parameter in the formula (let’s call it b). In TSA package that decay parameter is not mentioned. When I used other software before (such as ...
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### Time Series Modeling with Lagged Variables

I have a dataset with columns that represent lagged values of predictors. To illustrate with a simple example, suppose we had car sales data for 3 years and the only predictors available were income ...
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### Which AIC value to use from R's sarima() function for model comparison

I'm using R's 'astsa' package and I get the following output from sarima. Which AIC value would I use to compare this model (let's call it A) against others? When trying another model (B), model A's ...