ARIMA Modelling in R

Hello friends,

I have tried to keep it very simple. ARIMA stand for Auto-Regressive Integrated Moving Average. It is a very simple technique of time-series forecasting. Here the terms are:

Auto-Regressive: Lags of the variable itself

Integrated: Differencing steps required to make stationary

Moving Average: Lags of previous information shocks

ARIMA(p,d,q)

Different Names of ARIMA

AR Model: If only AR terms are there, i.e. ARIMA(1,0,0) = AR (1)

MA Model: If only error terms are there, i.e. ARIMA(0,0,1) = MA (1)

ARMA: If both are there, i.e. ARIMA(1,0,1) = ARMA(1,1)

ARIMA: If differencing term is also included, i.e. ARIMA(1,1,1) = ARMA(1,1) with first differencing

ARIMAX: If some exogenous variables are also included.

Prerequisite

The data should be stationary

Pros

1.  Better understand the time-series patterns
2.   Forecasting based on the ARIMA

Cons

Captures only linear relationship, hence, Neural network models could be used if a non-linear  association is found in the variables. 

The procedure is as follows to fit ARIMA (Box-Jenkins Approach):

1. Make correlograms (ACF and PACF): PACF will indicate AR terms and ACF will show MA terms.
2. Fit the model
3. Find the residuals and do diagnostic tests. If the residuals are IID, then the fitted model is good. Otherwise, repeat the same process.
4. Use the fitted model for the forecasting purpose.

Please watch the video to learn how to do ARIMA modelling in R: