Questions tagged [arima]

Refers to the AutoRegressive Integrated Moving Average model used in time series modeling both for data description and for forecasting. This model generalizes the ARMA model by including a term for differencing, which is useful for removing trends and handling some types of non-stationarity.

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23 views

Very high MSE Arima

I'm new to regression, i'm trying to build a simple ARIMA model to forecast hourly power load, the model appears to give good forecasting, yet very high error, (MSE = 986323, MAE = 725) here is my ...
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How would you convert an ARIMA(0,0,1)(0,1,0)12 model to equation form? [duplicate]

How would you convert an ARIMA(0,1,1)(0,1,1)12 model to equation form?
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What is my 'p' and 'q' terms for below ACF and PACF

I was plotting the acf and pacf of a time series in order to find p and q values.Here is the ...
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Volatility based Markow Switching GARCH model

I am trying to model returns using ARMA-GARCH process and noticed that returns series behave differently under the periods of high volatility when compared to periods with low volatility. Therefore, I ...
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How to generate fitted values manually for a seasonal ARIMA model?

I am trying to get the fitted values for a SARIMA model, and I can only access the arima() or auto.arima() functions in 'forecast' package in R for benchmarking my results (which is probably not the ...
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Why do we fit (G)ARCH model?

The ARCH model is: $$\left\{ \begin{align*}& X_t=\sigma_t Z_t, \ \{Z_t\} \sim IIDN(0,1) \\ & \sigma_t ^2 =\alpha _0 +\alpha _1X_{t-1}^2+\ldots+\alpha _p X_{t-p}^2 \end{align*} \right. $$ ...
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25 views

Forecasting in time series (ARMA, GARCH etc.)

I've read here https://otexts.com/fpp2/arima-forecasting.html how we do forecasting in time series models like the ARMA model, but I'm wondering if we recalculate estimates of parameters of our model ...
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Accuracy of sliding window in ARIMA models

I have 245 daily stock returns with some explanatory variables. I will compare the ARIMA and ARIMAX models with some basic machine learning techniques. The training periods will be 30, 60, 90, 120 and ...
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Python: pmdarima, autoarima does not work with large data

I have a Dataframe with around 80.000 observations taken every 15 min. The seasonal parameter m is assumed with 96, because every 24h the pattern repeats. When I insert these informations in my ...
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How to fit an ARMA model along with “usual” predictors?

Is there an R package that I can use to fit a model being a blend of the ARMA model and the ordinary linear regression? I mean something like this: $$Y_t=\beta_0+\beta_1 X_1+\beta_2 X_2+\beta_3Y_{t-1}+...
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Estimation of MA parameters in ARIMA with MLE

I understand that the AR models can be estimated with both OLS and MLE, since all the values of the time series are known. However, I don't understand how the parameters for the MA parts can be ...
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Penalizing non-OLS models

Let’s consider some common linear time series models for which OLS does not usually yield unbiased coefficient estimates. These include ARIMA and ARIMAX models, regression models with ARIMA errors, ...
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test of equal predictive accuracy of forecasts for multiple nested models in R

an out-of-sample forecast experiment (time series cross validation with a fixed rolling window size) using various models are applied. Suppose I have multiple forecasts from different models (LASSO,RR,...
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handling multiple time series through common model?

I have 1.5 lac/ 150 K timeseries . These are divided by geo locations. I have total 32 geo locations.Customer is expecting to have minimum number of model for all the 1.5 lac forecasting. How should i ...
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How can I choose m in SARIMA to forecast 365 days in a daily time series data set

Pretty much what the title says I have a daily time series for the past year and I will like to predict the daily time series for the next 365 days. Adding 365 as m ...
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GARCH diagnostics: autocorrelation in standardised residuals and poor results of Goodness-of-Fit Test

I am trying to fit best ARMA - GARCH model using rugarch in Python on financial data 5 min returns series. I am using last 10k observations for this purpose. The goal is to predict next return and its ...
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Not able to capture spikes in SARIMAX model for future forecast

Data has the spike in 2013 and 2017. To capture this effect in 2021, dummy column is introduced with 1 as spike in a month otherwise 0. Below is the output and the model used, Why the model is not ...
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45 views

Covariance of a non-stationary AR(2) process

I have the following AR(2) process: $(1+B^{2})X_t=Z_t$ where $X_0=X_1=0$ and $t=1,2,3...$ This is clearly not stationary since the roots are i,-i and therefore have modulus of 1 (i.e on the boundary ...
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time series: What is the performance difference between ARIMA models and Bayesian Structural Time Series models

I have been looking at ARIMA/SARIMA models and some of the Bayesian Structural Time-Series models lately. The formulation of the two models does not seem that different but the fitting method of ...
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ARIMA + GARCH modelling in Python

I am trying to implement ARIMA(4,0,4) - GARCH (P,Q) model in Python (the ARIMA orders were selected based on best AIC/BIC). Multiple sources suggest fitting ARIMA and GARCH simultaneously rather than ...
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How to introduce Product Relaunch effect in ARIMA model

I am using SARIMAX to forecast 15 Months ahead, based on data since Jan-2014. Couple of times same product was re-introduced in market and it can be seen with huge sales spike in the month of product ...
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ARMAX with lagged exogenous variables

I have difficulties finding the implementation of ARIMAX, ARMAX model where the exogenous variable would be also included with the time lags: $X_{t}=\varepsilon_{t}+\sum_{i=1}^{p} \varphi_{i} X_{t-i}+\...
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Pacf plots show unusual spike at high lag

The time series data has 108 points altogether with a few outliers. So after removing the outliers, I plotted pacf and acf of the original as well as differenced series. Acfs: Pacfs: ...
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56 views

Unable to model an AR(1) process

This is my AR(1) series where X(t) = 0.9 * X(t-1): ...
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34 views

Can autocorrelation confound causal inference?

I'm working with a weekly aggregated time series that has autocorrelation and I'm trying to find out why the trend has been decreasing by regressing other features onto - I noticed that when I use an ...
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No ARIMA model fits my data

I tried to fit an ARIMA model to a data, but no success!! I shared my data and the R-codes below to check any mistake! dt=c(15,18,13,16,11,14,19,20,16,17,13,11,13,15,8,12,15,14,15,15,18,11,13,15,11,11,...
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ARIMA(0,0,0) model with multivariate covariates?

Lets start with my dataset in which the first column, Y, is a time series observation along with 10 covariates, X1, X2, ..., X10. In fact, I have multivariate regressors and wanted to fit a times ...
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Is there a point on performing time series analysis on data that are not gathered with a consistent frequency?

To be more specific, what I have in mind is data gathered from android games. These data wouldn't have any time consistency because a user is free to play as many games as he wants whenever he wants, ...
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Mathematical equation of ARIMA(2,3,2) [duplicate]

Suppose we have ARIMA(2,3,2) in a study. How to write the final formula for this model? The parameters are: AR1 and AR2 for auto-regressive part, MA1 and MA2 for the moving average part. Most of ...
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ARIMA Transfer Function Model in equation form

Can someone help me understand the different terms in a transfer function model with ARIMA errors. I am using SPSS, and the tool produces the parameter estimates and forecasted values. However, I need ...
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Statsspace SARIMA seasonal_order

I have daily data, with non-nan values. I am using statsspace api. Question: Why can't you have a seasonal period of 7 when you have lags of 7? Here is sarima = sm.tsa.statespace.SARIMAX(tra,order=(7,...
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Working with Time Series: What drives a trend change?

I'm working with a time series that had a clear trend changepoint where it went from having an upward trend to a downward trend (After accounting for seasonality). The problem that I'm running into is ...
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Any transformation to make a process covariance stationary

In a typical AR model, for simplicity take AR(1), we know that if it is of the form $x_{t}=\alpha_{0}+\alpha_{1}x_{t-1}+\epsilon_{t}$, it may not be mean stationary as $\alpha_{0}$ is 'reinforced' by ...
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Sampling with python statsmodels ARIMA package [closed]

Assume I have a model following ARIMA(p,q,d) with statsmodels package of python. Given a time series given by a numpy array "serie", the code looks like: ...
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ARIMA model with multiple covariates, XREG

I have shared the main data d2015.txt, includes 5 columns. The first column is the $y_t$ the time series observation. The 2nd to the 4th column is the covariates/regressors and the fifth column is ...
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Contradictory KPSS and ADF Test Results: Look for Seasonality Using R

I'm working with a time-series from January 2016 to March 2020. My goal is to identify seasonality in the data and perform a Seasonal Dummy model regression to capture monthly seasonality. My first ...
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Detrended data and ARIMA modeling

What data should I use in ARIMA modeling when I do detrending, is it the original data or the detrended one? Then, what is the d component of the ARIMA model, is it d=0 or d=1?
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Calculating ARMA(p,q) variance [duplicate]

i have ARMA model Ay=Cv, where v is white noise with zero mean and variance of 1. A is polynomial of q^-1 with coefficients [1 -1.6 0.78 -0.18] and C is [1 0.3] respectively. How to calculate variance ...
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Is it possible to create a general forecast model working on several data sets?

I am working on a project, where the task is to create forecast models that can be used on a wide variaty of data sets. Some of which are stationary and some which aren't. Both ARIMA and Exponential ...
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Ljung-box test on weekly percentage of total quarter bookings

I have a data on the weekly percentage of the total quarter bookings. The data looks as follows (note: weekly percentages add up to 100 for each quarter) : (not real data) I used the Ljung-box test ...
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does arimax handle both transfer functions and reg with arima errors?

In The ARIMAX model muddle (I think written by hyndman), the author writes that tsa::arimax fits a transfer function model: $$ y_t = \frac{\beta(B)}{v(B)}x_t + \frac{\theta(B)}{\phi(B)}z_t $$ where $B$...
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33 views

Best practices for regression when using seasonal data? [closed]

I have a variable $y$ that I would like to model using a set of independent variables $X$. Both $y$ and $X$ are monthly measurements (~10 years in total) and appear to be subject to seasonal ...
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Inference in Time Series: Prophet vs. ARIMA

I read through Prophet's white paper and they mention that their algorithm, "gives up some important inferential advantages of a generative model such as an ARIMA." (page 7) So now I'm ...
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Which ARMA(p,q) to choose from tables of Squared Canonical Correlation Estimates and SCAN Chi-Square Probability Values?

I have the following output (from SAS) Squared Canonical Correlation Estimates \begin{array}{|r|r|r|r|r|r|r|r|r|} \hline \text { Lags } & \text { MA 0 } & \text { MA 1 } & \text { MA 2 } ...
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ARIMA interpreting results and how to out-of-sample forecast

I am trying to learn ARIMA using Python and the data in https://www.kaggle.com/c/demand-forecasting-kernels-only. I'm using the sales for Store == 1. Here is how the data looks like: Here is my ARIMA ...
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What is the meaning of crossed Lag_plot?

Good Morning. I have a theoric-practical question. Let say I’ve got a seasonal serie without trend. I’ve tried to remove any covariances and fit an arima model. I’ve just tried several options and ...
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How do you determine that your timeseries forecasting model is good enough?

Pardon me, I am new to timeseries forecasting. Given that there is not always a clear cut way to know whether your forecasting model is good enough and there's a significant degree of subjectivity in ...
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How to use auto.arima when attaining different results with a manual model selection?

I have daily sales data for over 2 years. I am having several questions of how to manually define model order and how to do it using auto_arima. Manual The first step I do it to see if my data is ...
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Advantages of using PACF

Box-Jenkins approach to time series analyses uses a series of diagnostics, one of which calculating Partial autocorrelation function (PACF). The goal is to determine the order ...
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Autocorrelation in residuals of a regression model with ARIMA errors (example in Rob Hyndman's book) - Part 2

Part 1 is here What does the forecaster do when there's correlation in the residuals of an ARIMA model that's used to model the errors from a regression model? Does this mean the forecasting approach -...

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