ARIMA Model for Stock Forecasting

ARIMA (autoregressive integrated moving average) is one of the most common statistical technique which used to fit time series data and forecasting. ARIMA is a generalized version of ARMA (autoregressive moving average) process, where ARMA process is applied to differenced version of the data instead the original data. The ARIMA model use p, d and q to specify order, where p represents order of AR, d represents the order of difference and MA part represents the MA part.

Auto Regression (AR) and Moving Average (MA) process

Auto Regression (AR)

AR is a class of liner model where the variable of interest is regressed on its own lagged values. So, AR can be written as follows:

$y_{t}=\delta +\phi _{1}y_{t-1}+\phi _{2}y_{t-2}+--------+\phi _{p}y_{t-p}+\epsilon _{t}$

Moving Average (MA)

MA is another class of linear model. In MA, the output or the variable of interest is modeled via its own imperfectly predicted values of current and previous times. It can be written in terms of error terms:

$y_{t}=\mu +\theta _{1}\epsilon_{t-1}+\theta _{2}\epsilon_{t-2}+-----+\theta _{q}\epsilon_{t-p}+\epsilon _{t}$

ARIMA model for time series

The ARIMA model can be represented as follows by combining both AR and MA model.

$y_{t}=\delta +\phi _{1}y_{t-1}+\phi _{2}y_{t-2}+------+\phi _{p}y_{t-p}+\theta _{1}\epsilon _{t-1}+\theta _{2}\epsilon _{t-2}+------++\theta _{q}\epsilon _{t-q}+\epsilon _{t}$

ARIMA Model for Stock Forecasting

ARIMA (Autoregressive Integrated Moving Average) for Stock forecasting with R

May 22, 2020 • Ashiq Zaman

Auto Regression (AR) and Moving Average (MA) process