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I am trying to write a mathematical equation for a seasonal ARIMA model of ARIMA (0,0,1)(0,1,1) where the values are recorded quarterly. … I have tried to follow other examples but i cant seem to get my head around these specific examples and cant apply them to my model. Any help would be greatly appreciated …

I have a ARIMA model with three regressors as follow > fit_arima.reg Series: sales.ts Regression with ARIMA(5,1,3) errors Coefficients: ar1 ar2 ar3 ar4 ar5 ma1 … I built the equation, but the fitted values by hand (from equation) and the ones generated by R do not match. I would appreciate your help for the solution. …

I am trying to write the mathematical ARIMA equation for the following - A seasonal ARIMA(1,0,2)(1,1,1) with quarterly data using two external explanatory variables aside from the explained variable(also … I have an idea on how to write the ARIMA equation for a standard ARIMA model which does not involve seasonal differences and with just one explanatory variable. …

I have tried to generate/write equation for forecasting using ARIMA models. But I think my equations were wrong and I am stuck with it. Kindly please help me to obtain equations for 1. … s.e = 0.0987 σ^2 log likelihood= 499.4, -212.67 Is there anything I am missing for formulating the equation? …

(1) $$ My question is: how this equation has been derived? … We know that ARIMA(0,2,2) means $d=2$ (second order differencing) and $q=2$ is the MA (moving-average) order. …

I have fitted an ARIMA model to forecast GDP using the auto.arima function in R: Series: tGDPdev ARIMA(2,0,2)(1,1,0)[12] with drift Coefficients: ar1 ar2 ma1 ma2 sar1 … 1.7038 -0.7521 -1.3467 0.5857 -0.4793 s.e. 0.2523 0.2290 0.2180 0.0917 0.0842 drift 0.5334 s.e. 0.0470 I would need to know the equation thath represents this model …

What would be the corresponding model equation? … Would much appreciate any replies that can help me understand the intuition or at least the model equation. …

Could you please help to write down the exact equation? It is clear for Garch part but not clear how to add ARFIMA (1,0,1) or here just ARMA(1,1) in model equation specification. … How change the equation for same model but with Student-t distrubution ? …

. $$ Identify the specific ARIMA model. What is the mean of the series $\{y_t\}$? I think it is a ARMA (1,1) process? is that correct? And how do I calculate the mean of the ARMA model? … Appraise the patterns and judge which ARIMA model fit the series. Justify your conclusion. I identified as the AR(4). Is that correct? Since ACF has an exponential decay and PACF has a cut off? …

For the ARIMA (0,0,1) model, some books write the equation as $$Z_t = \mu - \theta Z_{t-1}$$ whereas some books write the equation as $$Z_t = \mu + \theta Z_{t-1}$$ Why is there either a negative sign … or positive sign before the moving average parameter in an ARIMA model? …

What is the mathematical equation for an ARIMA(0,1,1) model? … The R software gives the following result Series: goldtime ARIMA(0,1,1) with drift Coefficients: ma1 drift 0.2635 9.6507 s.e. 0.0654 3.8817 sigma^2 = 2260: log likelihood = -1250.51 …

Every equation of SARIMA I have found involves backshifts. I was wondering if I have an ARIMA model expressed like this: is it possible to express it in a similar way, without backshifts? … Are there any resources where I can find seasonal ARIMA equation without backshifts? …

I'm still having some difficulty understanding how an $ARIMA(p,d,q)(P,D,Q)_m$ model is translated into an equation. … Also, given some output (for example in R), how do the coefficients relate to the equation? …

I am working on a problem that I think ARIMA modeling could be useful for, and am researching the theory behind ARIMA. … I came across this website that says: ARIMA(p,d,q) forecasting equation: ARIMA models are, in theory, the most general class of models for forecasting a time series which can be made to be “stationary …

In a theoretical sense I understand ARCH and GARCH errors to be something which is estimated "on top of" the ARIMA model. … Is it that estimation feature that makes the optimal ARIMA model change, or is it due to other factors? …