# Tag Info

### Time series model without ARMA component and with exogenous variables

what you have is fine ( no ARIMA terms necessary ) but three things to consider: should the X's be lagged by one time unit ? or do they really occur so that the current X's influence the current 𝑌 ? ...
• 2,307

### Manually compute ARIMAX forecast

Your manual computation computes an ARIMAX forecast. Unfortunately, that is not what arima() models. Rather, arima() models and ...
• 117k

### Multiple predictions using ARIMA

Overall, your approach makes sense. One point I would definitely change: move step 2 (which I presume refers to SARIMA order selection) either between step 6 and step 7, or into step 7. Why? Selecting ...
• 117k
1 vote

### Why should we remove trend and seasonality before forecasting?

I can think of two reasons: It is often useful to decompose a hard problem into several minor issues which are easier solve. Since we can often think of a time series being composed by several ...
• 191
Accepted

### ARIMA - Identifying an outlier in residuals

The plot does not show residuals. It shows the autocorrelation function (ACF) of the residuals, i.e. the values of autocorrelation $\text{Corr}(u_t,u_{t-h})=1$ for a numer of different lags $h$. ...
• 64.7k
Accepted

### SARIMAX.predict() and SARIMAX.forecast() exog? Does exog need to be preknown for predict()?

It depends on how you set up your model. To take a very special case of zero-mean ARX(1), it can be $$y_t=\varphi_1 y_{t-1}+\beta x_t+u_t$$ or $$y_t=\varphi_1 y_{t-1}+\beta x_{t-1}+v_t.$$ In the ...
• 64.7k
1 vote

### Let $X_t$ be an ARIMA(1,1,1) process and $Y_t = Y_{t-1} + X_t$. What kind of process is $Y_t$?

The process $Y_t$ is the integration of $X_t$ $$Y_t = \sum_{-\infty}^t X_t$$ So you have one more integration step and that means that it is an ARIMA(1,2,1) process. Indeed, the recursive formula can ...
• 71.8k
Accepted

### Role of trend argument compared to integral order in ARIMA model

ARIMA Elements: AR (AutoRegressive): Uses lag to measure the correlation between observations; in other words, it uses past values in the series to predict future values. I (Integrated): that data has ...
• 56.7k
1 vote

### How is forecasting values for stationary time series even possible?

I very much recommend section 1.4 in Shumway & Stoffer, Time Series Analysis and Its Applications (4th ed.). They introduce strict stationarity and weak stationarity, and immediately say that by &...
• 117k
ARMA is a pure time series model, i.e. it doesn't have exogenous variables $X_t$ unlike a typical regression $y_t=X_t\beta+\varepsilon_t$. In a generic formulation of ARMA such as \$\phi(B)y_t=\theta(B)...